Analysis and Modeling of Residential Energy Consumption Profiles Using Device-Level Data: A Case Study of Homes Located in Santiago de Chile

Abstract

The advancement of technology has significantly improved energy measurement systems. Recent investment in smart meters has enabled companies and researchers to access data with the highest possible temporal disaggregation, on a minute-by-minute basis. This research aimed to obtain data with the highest possible temporal and spatial disaggregation. This was achieved through a process of energy consumption measurements for six devices within seven houses, located in different communes (counties) of the Metropolitan Region of Chile. From this process, a data panel of energy consumption of six devices was constructed for each household, observed in two temporal windows: one quarterly (750,000+ observations) and another semi-annual (1,500,000+ observations). By applying a panel data econometric model with fixed effects, calendar-temporal patterns that help explain energy consumption in each of these two windows have been studied, obtaining explanations of over 80% in some cases, and very low in others. Sensitivity analyses show that the results are robust in a short-term temporal horizon and provide a practical methodology for analyzing energy consumption determinants and load profiles with panel data. Moreover, to the authors’ knowledge, these are the first results obtained with data from Chile. Therefore, the findings provide key information for the planning of production, design of energy market mechanisms, tariff regulation, and other relevant energy policies, both at local and global levels.

1. Introduction

Studying energy consumption behavior has become extremely relevant in today’s world, not only due to its impact on the environment, but also for obtaining quality information for energy production planning, maintenance, expansion, and improvement of the electrical grid. At the same time, obtaining specific consumption patterns of residential households can help design better policy mechanisms and instruments such as tariffs, rationing quotas, and incentives for new technologies. From this empirical point of view, energetic load profiles have become a crucial tool for analyzing and characterizing specific consumption patterns. In particular, McLoughlin et al., 2012, [1] and Yohanis et al., 2008, [2] showed that consumption levels and hourly consumption profiles have considerable differences among different types of residential consumers.

The body of research studying load profiles is quite extensive and, in turn, has different groups of analyses that model profiles for various purposes. A vast amount of literature uses the study of load profiles as part of a bottom-up demand construction technique [3,4], a key input for projections. There is also literature that uses load profiles to characterize demand, attempting to identify its determinants and, therefore, the behavior of electrical consumers [5,6,7]. There is literature on studies that use load profiles as part of customer segmentation methodologies, adding demographic and climatological variables [8], among others. Similarly, and closely related to this research, there is extensive literature measuring models with panel data and fixed effects [9,10,11], most of which focuses its explanations on aggregated data at the household level, with larger aggregation units.

However, despite the creation and installation of smart meters allowing for better data availability at a high temporal resolution, frequently by minutes, no research has been found that seeks to explain consumption by disaggregating it at the device level and econometrically modeling such consumption. This is of the utmost importance, as for all tasks in which load profiles can be used, having modeled calendar-temporal patterns that help explain this consumption are a vital input for production planning and modeling proposals for flexible tariff systems, among other applications.

Although the literature on load profiles is extensive, and this research has reviewed much of it, to the authors’ knowledge, there are no other studies that model consumption using regression models with fixed effects, nor models that use data from Chile in their application. Therefore, this research addresses this gap in empirical evidence. In this inquiry, a process of measurement, collection, and systematization of information was carried out to construct seven data panels for seven households located in different communes (equivalent to counties in the USA) of the Metropolitan Region. Therefore, a case study was conducted, whose statistical inferences only had internal validity. However, the practical exercise of estimating such impacts of calendar-temporal patterns in consumption serves as a methodological guideline to be implemented in future research related to planning, regulation, or energy tariff policy.

In line with the above, the main objective of this research is to carry out a general characterization of consumption profiles based on empirical data. Obtaining these consumption patterns for different households with real data allows for a much clearer understanding of the behavior of residential consumers. At the same time, measuring this phenomenon with disaggregated data at the device level is key to understanding intra-household patterns and how they are affected by different technologies. Additionally, this presents opportunities for improvements in energy consumption efficiency.

The results confirm differences in hourly, daily, and monthly patterns. In turn, each day of the week exhibited its own behavior, and each device had its own consumption pattern. Additionally, these were subjected to a temporal sensitivity analysis, checking the model’s fit for a 3-month window versus a 6-month temporal window. The set of variables that held statistical significance were fewer in the semi-annual model. The results show that temporal patterns help to explain consumption, with goodness of fit ranging from 1.6% to 82% for the 7 households when analyzing the quarterly model, versus 0.1% to 65.7% when analyzing the semi-annual model. This serves to confirm that the proposed model helps to better explain the observed differences in consumption in the short-term temporal horizon.

The article is organized as follows: Section 2 presents the empirical and applied literature within which this research is framed. Section 3 describes the source of the database used, the algorithms followed for its construction, and the methodology used to characterize the temporal patterns of consumption profiles, specifying an econometric model for this purpose. Section 4 shows and interprets the results obtained in the empirical estimation. Section 5 summarizes the main findings arising from this research and discuss their main implications. Finally, Section 6 concludes the article.

2. Literature Review

2.1. Empirical Literature on Load Profiles or Consumption Patterns

The study and characterization of energy consumption profiles are highly relevant as they aid in the estimation and construction of demand curves, allowing for better information in the management and planning of future energy supply. In the study by Köhler, S. et al., 2022 [12], it is stated that “Electric consumption profiles are particularly crucial for reliable results in the design, operation, simulation, and optimization of energy systems, sustainable districts, and electrical networks”. The literature shows a broad interest in this topic, as demonstrated in studies such as Stegner et al., 2019 [3], who proposed a validated method for estimating consumption profiles using smart meter data at 15-s intervals.

The increasing investment in smart metering equipment provides real-time access to energy consumption data, which has facilitated a vast literature seeking to measure and simulate energy consumption profiles using various techniques across different geographic sectors, utilizing real-time high-frequency data. Studies on energy consumption profiles using smart meters are available for countries such as Qatar [13], where a method is proposed to estimate demand based on high-resolution load profile data. In Ecuador [14], the authors proposed classification models to identify temporal grouping patterns and neural network models to predict energy demand. Evidence for Korea [5] shows that in addition to classification algorithms, socio-demographic information is also included in consumption predictions at the neighborhood level.

Evidence is also available for Austria, Germany, and England [15], where the authors used smart meter data to decompose observed consumption profiles into the average under normal conditions and a cyclical component using a stochastic model. The literature seeking to identify determinants of consumption also has a rich tradition, particularly those studies that used socioeconomic factors to explain energy consumption. For example, a method for customer segmentation based on sociodemographic variables was proposed in [6], and a study based on Danish data [7] investigated how socioeconomic characteristics associated with households (obtained from the Census) were related to specific consumption patterns observed over time from an econometric perspective. A more in-depth approach to the use of exclusively social or cultural factors was found in the investigation of [16], who studied the possible influence that factors such as ethnic origin and religion can have on energy consumption.

There are also various studies analyzing the relationship between climatological variables and energy consumption. This line of analysis includes research based on data from Ireland [8], as well as [17,18,19], among others.

2.2. Fixed Effects Methodology and Consumption within the Household

The use of high-granularity consumption data from smart meters has been increasing over time, and the methodologies applied for their analysis have been quite varied. In this section, two additional lines of analysis will be reviewed: firstly, research that utilizes the technique of estimating econometric models with panel data with fixed effects, using data from smart meters. Secondly, works that measure electrical consumption by differentiating the various devices through which it is generated will be explored.

The use of high-granularity panel data has expanded in the literature related to the measurement of energy outputs. In the work of [9], the benefits of its use are highlighted, discussing the factors that affect the gains that high granularity can provide. There are several studies that use an identification strategy based on fixed effects models in energy literature. In the work of [20], data from 2008 to 2010 from the EnergyWise Smart Meter Pilot of Connexus Energy are used, where it is determined that displays showing energy expenditure and the use of smart thermostats reduced consumption by 15% during peak hours. In the research of [10], data from residential buildings were used, and their models were estimated separately (very similar to the treatment that this research will provide to the households in the sample), also specifying fixed effects by hour of the day and adding temperature variables. The research of [21] also used data from buildings, in this case, commercial, and related consumption to construction attributes, using a linear mixed-effects model, allowing for fixed and random effects of each building, applying it to data from smart meters.

In the same literature analysis, there were recent studies that investigated how the socio-political environment characteristics could affect consumption; for example, in [11], using fixed effects, the impact of federal policies on smart meter use in the United States was considered, and an energy efficiency campaign in Switzerland [22] was estimated. There were also studies like [23] that, considering the demographic and age variables, predicted that the energy demand was likely to increase in the coming years, despite the population decrease.

While these studies conducted extensive analysis on electric energy demands, they did not delve into details about what happens within the household or analysis unit (office, shopping center, among others). However, there were examples in the literature that tried to analyze how data on devices could help understand their impact on household energy demand. In [4], a stochastic model was used to explore the impact of occupants’ behavior, appliance stock, and efficiency on the electric load profile of individual households. Using data from German households, profiles of appliance usage and existence in households were constructed. Additionally, in the research of [24], a review of the types of data available for estimating electricity consumption at the appliance level in US households is provided.

This research joins the empirical literature using the fixed effects methodology to measure impacts and determinants in energy consumption. However, its novelty lies in seeking to understand what happens with energy demand at the most disaggregated level possible, incorporating controls for different devices, in order to measure their influence on energy consumption. Moreover, another novel characteristic is related to the fact that it is important to note that as Chile applies Daylight Saving Time (DST), which mandates a change in time usage between winter and spring (i.e., “summer time”), a variable will be coded to control for estimates of the possible impact of this phenomenon. This will allow for the quantification and explanation of energy consumption behavior considering a broader set of factors. For this reason, the following section will describe the literature that studied this impact to provide a reference framework for addressing it in our study.

2.3. Empirical Literature on Daylight Saving Time

The literature measuring the effects of DST policies on energy consumption spans at least 50 years, with inaugural studies such as [25,26]. These studies focused on examining the savings or increased costs generated by these policies through various methodological approaches. Studies like [27,28,29,30,31] showed null impacts of DST policies on energy savings. On the other hand, more recent studies, such as in [32], found an impact of around 0.5%, using a technique known as “equivalent normalization day” [30], in conjunction with the difference in differences (DiD) approach. Additionally, in [33], a quasi-experimental approach was used, where they found a 15% decrease effect in Canada. Along these lines, natural experiments were also used, as in [34], where small impacts on energy demand and generation costs were found, but with a significant effect in redistributing consumption.

In Latin America, studies like [35,36] were found, both of which used a natural experiment approach to estimate, using the DiD method, average savings of [0.4–0.6]% in Argentina and 0.5% in Mexico. In the same geographical region this study is found [37], which analyzes the impacts of ceasing to apply this policy DST in Brazil, contrasting these impacts with the energy trading scheme and empirically demonstrating that the latter’s effects were positive, with benefits three to five times greater than DST, depending on the metric with which the problem was analyzed.

The most recent literature expands the analysis of the impact of DST beyond natural experiments and quasi-experiments based on DiD. In the following work [38], a meta-analysis was conducted as a robustness test. In the research of [39], natural and social factors were incorporated, finding that DST increased energy demand, especially in regions with later sunrises. Similarly, [40], using data from Spain and a similar specification technique, focused on the impact of daylight on energy consumption, modeling the potential effects of three time change regimes. Finally, in the study of [41], the effects of DST were analyzed considering interactions with high temperatures and air conditioning use, empirically demonstrating the relationship of these variables with the policy’s impact. Additionally, the study in Turkey [42], using a multimethodological approach, concluded that DST did not generate significant energy savings, as the country stopped applying it in 2016.

To achieve the goal of analyzing the internal behavior of household energy consumption in a disaggregated manner using different devices, this research collected microdata on energy consumption in seven homes located in the Metropolitan Region of Santiago. In each of these houses, an energy measurement device was used for six electrical devices to increase the level of information disaggregation processed. This information received data processing to achieve a complete data panel for each house, in which the unit of analysis was the device. Then, a panel data econometric model was specified that attempted to explain the energy consumption of each device, based on different dichotomous variables that controlled the effects by hour, day of the week, day of the month, month of the year, holidays, as well as for the period of the year where the daylight saving time policy was applied. Finally, the proposed model was analyzed in two time windows, one of 3 months and the other of 6, with the aim of finding out if the proposed model had a better explanation in a short period of time or in a more extended window.

This research contributes to the literature on energy consumption measurement, specifically addressing gaps in empirical evidence. It provides results based on a dataset, enabling a “micro” level analysis of disaggregated household appliance behavior. This work is a contribution that bridges empirical gaps, as there is still insufficient evidence regarding in-home behavior. By utilizing econometric identification techniques such as fixed effects, commonly employed in econometrics, this study offers empirical evidence, although it possesses only internal validity. It paves the way for future research and imparts valuable lessons in data collection.

3. Materials and Methods

This study is based on the construction of 7 energy consumption panels per household or home, where the units of analysis that were followed periodically over time were the household electrical devices, that is, the smallest possible disaggregation. The panels were composed of periods measured in minutes $t=1,2,\cdots ,T$, for the 6 m $i=1,2,3,4,5,6$. A database was collected, cleaned, and assembled with high−frequency observations, every minute, of energy consumption. In some cases, there was more than one observation in the same minute, which was solved by maintaining the observed average in that minute (for an image of the raw temporal data, see Figure A1, Figure A2, Figure A3, Figure A4, Figure A5, Figure A6 and Figure A7 in Appendix B). Therefore, this case study was based on 7 data panels, 1 for each household, composed of 6 devices or units of analysis, to which energy consumption was measured at a minute frequency, during 3 and 6 months. Additionally, to explain this energy consumption, variables were specified that measured the hour at which this consumption occurred, the day of the week, the day of the month, as well as differentiating holidays from other normal days, the month of the year, among others.

In this section, we outline the data sources and methods utilized in this article. This section is divided into three parts: The first segment offers a comprehensive account of the data engineering process applied to the information collected from household measurements, specifically focusing on device consumption. The second part presents a descriptive statistical analysis of the variable under scrutiny: electric consumption measured in kilowatt-hour per minute (kWh/mint). This analysis encompasses temporal visualizations by month as well as for each of the households considered. Finally, it provides an explanation of the empirical strategy employed in this case. This structure allows readers to gain a broad understanding of the observed consumption patterns being modeled and elucidated in this research.

3.1. Data Manipulation and Cleaning

The data collection process began with the manufacture of an electrical measurement device. This device consisted of a 220VAC 10A male plug, which was connected to the low voltage network where the electronic or electrical equipment to be measured was connected, along with its respective current protection and communication module. This electrical measurement device sent the data to a computer located in the house where statistical samples were taken, and then forwarded the information to a remote internet server where the information was stored in a database.

With the set of information obtained from electrical measurements already transformed into a database, there was a file containing data on total energy demand for 6 different devices, which were measured in 7 houses in the Metropolitan Region, located in the communes of Cerro Navia, Estación Central, La Reina, Macul (2 houses), and Providencia.

It’s important to note some limitations of the obtained database: the same devices were not taken in each home, so comparisons between the 7 homes could not be made. Furthermore, the conclusions drawn from the use of this database did not have external validation. This means that the behavior analyzed for these 7 homes in Santiago could not be extrapolated to all homes in the region. Therefore, this study only had internal validity of its results.

For each of the six devices, two time series were analyzed: a wide one from July 2021 to December 2021, and a narrow one from October 2021 to December 2021. These individual time series by device were grouped according to the house to which they belonged. In this way, all the analyses in this research were carried out for each of the 7 houses, considering each house as a panel data, where the unit of analysis was the devices. In addition to the information contained in the databases about date–time and energy, information from other sources was also extracted for the coding of the variable that measures the application of DST, particularly the Official Gazette of the Republic where the respective dates were reported.

There were then 42 .csv files, where each file represented the daily measurement, with minute frequency, of the electrical energy consumption for each device within a house. The data were grouped into 7 different houses, in which the behavior of the consumption of each device, and of each house, at each moment in the considered time was collected. To obtain the final database, a data processing was carried out that included different stages (see Figure 1), starting with the respective arrangement of the data, to subsequently adding and encoding the necessary variables for the econometric modeling of consumption, which were of our own elaboration, such as the application of DST.

In the data collection stage, the first step was to generate an input for data sorting, which was achieved with the variables total energy, as well as date and time of measurement, all of which were present in the information provided. In this step, the variable for consumption per minute had to be created as the difference in energy demand between one minute and its predecessor.

After grouping each individual time series by house, the missing observations in the time series were filled in through a process of balancing the panels of each house. This was necessary because some devices registered consumption at irregular intervals, leading to gaps in the data. For example, a device may have registered consumption at 13:31:00 and then again at 13:38:00, resulting in a gap of 6 rows without information. This occurred in several intervals in the time series, and the gaps were often more than just 6 rows.

To address these issues, the data collection was conducted in two stages. Firstly, a complete series of data was created for each device in the analyzed period, with the consumption variable left empty (we called this the “ideal series”). Then, a join was performed between the ideal series and the observed series with gaps. This produced a time series without gaps in the dates and minutes, but with some empty consumption data.

An interpolation algorithm was then applied to fill in the missing consumption data. This algorithm analyzed the last observation that recorded consumption and filled in the missing consumption data with that value for all of the subsequent empty rows in the database. This interpolation rule is known in the literature as the last observation carried forward ($LOCF$).

Finally, with the imputed data, two samples were created for analysis. The first sample was based on a 3-month window (October, November, and December) containing approximately 773,000 observations for devices grouped by house, while the second sample was based on a 6-month window (July–December) containing approximately 1,827,000 observations for devices grouped by house. The purpose of having these two time windows was to compare the specified models over different time horizons: quarterly vs. semi-annual. Now that the data collection and processing have been described, we will move on to the main descriptive statistics associated with the collected data.

3.2. Descriptive Statistics Analysis

Next, we present some of the most important descriptive statistics to understand the phenomenon addressed in this research. In particular, average consumption statistics will be shown for each of the months considered in the aforementioned data panel. This will only be performed for two representative houses from the group under study. Figure 2 shows a bar graph of the average consumption recorded in House 05, during the time window from July to December. As the reader can observe, the months of October and November were where a greater increase in energy consumption was generated.

Clearly, there was an observable upward trend in the average consumption of the end-of-year months (except for September, where there may be a seasonal effect due to the number of holidays). This is in line with many aggregate behaviors that remain over time, including the upward trend in energy demand. However, it is also notable that the increase in average consumption was greater in October than in November. That is, energy consumption did not increase as summer approached. This type of behavior could also be related to the implementation of the daylight saving time policy. The purpose of measuring the application of this policy was to better identify and understand the differences observed in this case analysis. Below, we replicated this graph of monthly consumption behavior, now for house 07 of the group (Figure 3) (“Since the interpolation algorithm was applied to the data from house 07, the original database contains only a few observations for that month, with ‘0’ consumption. Therefore the LOCF interpolation method replaced that zero for the whole month. This represents then an average consumption of “0” which is not reflected in the graph”).

In this case, a different behavior from house 05 was observed. In house 07, the highest average consumption was recorded in September (month 09). Following that, October (month 10) had a lower consumption than September, and this trend continued until the end of the year in December (month 12).

3.3. Empirical Methodology

The main objective of this research was to understand the energy consumption profiles within households, differentiating significant hourly patterns, as well as other relevant temporal patterns. Additionally, the hypothesis that the days on which measures of application of a different time zone were recorded may have some different behavior in terms of energy consumption, and this effect differed by devices within a dwelling, will be tested.

To achieve this goal, an econometric model was specified. This model was based on a specified regression function, which was assumed to govern the behavior of the dependent variable and its statistical relationship with other variables in the study population. In econometric literature, this function is known as the population regression function (PRF), and there is interest in estimating this model at the sample level in order to infer the population values of the relevant parameters of the polynomial called PRF.

Additionally, two models were specified, which allowed for analyzing the sensitivity of the results to the set of observations over time, and the use of different control variables. The specification used for each of the two proposed models is described below. The two models sought to analyze the impact that a broad set of variables had on the energy consumption of an electrical device “i” at a given time “t”. As for the set of explanatory variables, the convention of grouping binary variables that refer to the same category (hours, months, days, and devices) into a sum of factors was used. For this reason, we referred to vectors of variables.

The first model for the smaller time window from October 2021 to December 2021 was as follows.

$$\begin{array}{cc}\hfill Consumptio{n}_{it}=& \alpha +\sum _{h=1}^{23}{\beta }_h{\left(hour\right)}_{it}+\sum _{m=11}^{12}{\gamma }_m{\left(month\right)}_{it}+\hfill \\ \hfill & +\sum _{e=2}^6{\delta }_e{\left(device\right)}_i+\sum _{j=2}^{31}{\lambda }_j{(day-month)}_{it}+\hfill \\ \hfill & \sum _{d=2}^7{\theta }_d{\left(weekdays\right)}_{it}+\mathrm{\Gamma }{\left(holiday\right)}_{it}+{\mu }_{it}\hfill \end{array}$$

(1)

As the reader can see in Equation (1), the variable of interest in this case was the observed energy consumption of the i-th device, at time t, denoted by (consumption), which was recorded per minute, using a smart meter. On the right-hand side of the equation, a wide range of explanatory variables, according to device and temporal controls of hourly, daily, and monthly nature, were specified. The aim of adding all these types of controls was to measure significant differences in consumption when a statistical observation was made at a time that satisfied one of these temporal factors.

Firstly, the variables contained in the $hour$ vector refereed to the set of variables that measured the fixed effect of each hour of the day ($h=0$, 00:00 h is the reference category). The variables contained within this vector served to capture possible differences in energy consumption associated with the time of day when consumption occurred. With this vector of variables, the hypothesis of heterogeneous consumption behavior throughout the day could be tested. The variables contained in the $month$ vector referred to the set of binary variables that measured the fixed effect of each month of the year from November to December ($m=10$, October was the reference category), this could help us to test the hypothesis of differences in energy consumption related to the month in which the consumption occurred. The variables of the $devic{e}_i$ vector collected the fixed effect that each device had on household energy consumption, which was assumed to be constant over time. As the control device or reference category changed between houses, the device used as the reference in each house was noted in

Table 1. Equipment considered in each house, ordered by consumption.

N° House	Commune	Device 1	Device 2	Device 3	Device 4	Device 5	Device 6
House 1	Nunoa	Electric kettle	Television 40″	Television 42″	Notebook	Lamp	Refrigerator
House 2	Cerro Navia	Computer	Television 55″	Refrigerator	Television 43″	Electric heater	Microwave
House 3	Estación Central	Refrigerator	Wahing machine	Oven	Computer	Television 55″	Electric heater
House 4	La Reina	Television	Refrigerator	Electric water heater	Computer	Kettle	Television 32″
House 5	Macul	Television 41″	Vertical freezer	Television 50″	Washing machine	Refrigerator	Cooler
House 6	Providencia	Oven	Electric kettle	Power strip	Television 55″	Refrigerator	Router
House 7	Macul	Refrigerator	Oven	Notebook	Microwave	PC Tower	Television 55″

Source: own elaboration based on data provided.

. The criterion for choosing the reference device was to use the one with the highest average consumption in that household. Control vectors were also added for day of the month ($j=1$, first day of the month was the reference day), day of the week ($d=1$, Sunday was the reference day), and holidays, with a binary variable used as the reference category (non-holiday days was the reference category).

The above-mentioned model of 1 was used as a comparison against an extended model, where, by using a longer time window (August 2021 to December 2021), it was possible to specify a greater number of monthly controls; in particular, dummy variables were added for September and October (August was the reference category in this model). At the same time, this extended model allowed for innovating and constructing a variable that controlled for the application (or not) of daylight saving time (−03:00 GMT) in the national territory, whose variation could eventually change the effect that other controls had on consumption, for example, the variables in the $month$ vector. Based on the changes mentioned above, the population regression function specified for the model estimated with a longer time window of data was as follows:

$$\begin{array}{cc}\hfill Consumptio{n}_{it}=& \alpha +\sum _{h=1}^{23}{\beta }_h{\left(hour\right)}_{it}+\sum _{m=7}^{12}{\gamma }_m{\left(month\right)}_{it}+\hfill \\ \hfill & +\sum _{e=2}^6{\delta }_e{\left(device\right)}_i+\sum _{j=2}^{31}{\lambda }_j{(day-month)}_{it}+\hfill \\ \hfill & \sum _{d=2}^7{\theta }_d{\left(weekdays\right)}_{it}+\mathrm{\Gamma }{\left(holiday\right)}_{it}+\Delta \ast DS{T}_{it}+{\mu }_{it}\hfill \end{array}$$

(2)

As the reader can see, expanded model 2, by considering a longer temporal window of 6 months, allowed for the addition of five variables that controlled for fixed effects of each month instead of 2, and allowed for the specification of a binary variable that takes a value of 1 for those observations made on a device during the application of daylight saving time in Chile (as mentioned earlier, this variable is based on proprietary coding that uses the information contained in the Official Gazette of the Nation). All other variables have the same interpretation as in Model 1, so they will not be explained again.

Table 2. Vectors of Variables used as regressors in the models.

Name of Variable (s)	Description
$hour$	Dummys for each hour of the day
$month$	Dummys for each month of the year (Aug–Dec)
$device$	Dummys for each device analyzed inside the house
$day$–$month$	Dummys for each day of the month (2–31)
$weekdays$	Dummy for each day of the week (Mon–Sat)
$holiday$	Dummy for holiday = 1
$DST$	Dummy for Daylight Saving Time = 1

Source: own elaboration.

shows a summary of the explanatory variables used in the two specified models.

All seven houses considered in this study belonged to different communes in the Metropolitan Region (region where the city of Santiago, capital of Chile, is located). It is important to mention that the devices measured in each house were not the same. For this reason, the specified models were measured for each house separately, as an individual database. That is, the analysis of the estimation performed could be understood as part of a bottom-up process of creating consumption profiles. Therefore, given that seven houses were analyzed, it is important to consider when reading the results and interpretations which devices we were being referred to, using Table 1 as a guide. The main results were estimations of the previously proposed model using the data described in this section for the seven households considered, within the two proposed time windows.

4. Results and Discussion of the Estimation

The model was estimated using the ordinary least squares (OLS) method, which provided the estimated parameters that minimized the mean squared error in the sample [43]. The results of the estimation can be seen in

Table 3. Results of the Model 1 consumption by house: October 2021 to December 2021.

	House 1	House 2	House 3	House 4	House 5	House 6	House 7
month11	0.00004	−0.00002 ***	0.001 ***	−12.686 ***	−3.114 ***	0.252 ***	−0.005 ***
	(0.00004)	(0.00001)	(0.0002)	(0.281)	(0.235)	(0.023)	(0.0004)
month12	0.002 ***	−0.001 ***	−0.0004 *	−13.316 ***	9.255 ***	5.590 ***	−0.006 ***
	(0.0001)	(0.00004)	(0.0002)	(0.363)	(0.412)	(0.070)	(0.001)
device1	0.001 ***	0.0004 ***	−0.0005 *	2.170 ***	−50.571 ***	−0.589 ***	−0.012 ***
	(0.0002)	(0.00001)	(0.0003)	(0.371)	(0.779)	(0.035)	(0.001)
device2	−0.0001 **	0.001 ***	Ref	−13.357 ***	−45.231 ***	0.219 ***	−0.013 ***
	(0.0001)	(0.00001)		(0.321)	(0.687)	(0.038)	(0.001)
device3	−0.001 ***	0.0004 ***	−0.002 ***	Ref	−51.426 ***	Ref	−0.013 ***
	(0.0001)	(0.00001)	(0.0002)		(0.718)		(0.001)
device4	−0.001 ***	0.00003 **	−0.001 **	−24.461 ***	−61.613 ***	0.457 ***	−0.012 ***
	(0.0001)	(0.00001)	(0.0003)	(0.352)	(0.818)	(0.030)	(0.001)
device5	0.001 ***	Ref	−0.002 ***	−8.043 ***	−51.333 ***	−0.271 ***	−0.007 ***
	(0.0001)		(0.0002)	(0.283)	(0.762)	(0.027)	(0.001)
device6	Ref	N/A	−0.002 ***	−16.435 ***	Ref	N/A	Ref
			(0.0002)	(0.284)
mon	0.00001	0.00004 ***	0.0002	−1.378 ***	−1.672 ***	1.330 ***	−0.004 ***
	(0.0001)	(0.00002)	(0.0001)	(0.474)	(0.551)	(0.038)	(0.001)
tue	0.002 ***	0.00003 *	−0.0002	−10.300 ***	−5.521 ***	1.118 ***	0.0004
	(0.0003)	(0.00002)	(0.0002)	(0.491)	(0.527)	(0.039)	(0.0003)
wed	0.001 ***	0.00002 *	0.0004	−1.817 ***	0.125	0.634 ***	−0.005 ***
	(0.0001)	(0.00001)	(0.0002)	(0.408)	(0.486)	(0.034)	(0.001)
thu	−0.0004 ***	−0.0001 ***	0.0004 ***	−2.724 ***	−1.905 ***	−0.806 ***	0.005 ***
	(0.0001)	(0.00001)	(0.0001)	(0.389)	(0.475)	(0.050)	(0.001)
fri	−0.0003 ***	−0.00003	0.001 ***	−12.024 ***	−7.060 ***	0.748 ***	0.001 ***
	(0.0001)	(0.00002)	(0.0002)	(0.512)	(0.574)	(0.036)	(0.0005)
sat	0.003 ***	−0.00001	0.001 **	−0.431	−0.617	0.929 ***	−0.001 *
	(0.0002)	(0.00001)	(0.0002)	(0.451)	(0.565)	(0.033)	(0.0004)
holidays	−0.004 ***	−0.0004 ***	−0.0003 **	3.087 ***	−1.499 **	−5.844 ***	−0.003 ***
	(0.0003)	(0.00002)	(0.0001)	(0.404)	(0.586)	(0.107)	(0.001)
Constant	0.002 ***	0.001 ***	0.001 ***	21.487 ***	48.485 ***	−0.880 ***	0.043 ***
	(0.0003)	(0.00005)	(0.0004)	(0.731)	(1.048)	(0.092)	(0.005)
Observations	746,259	603,075	728,203	718,326	679,465	538,216	735,553
$R^2$	0.033	0.032	0.002	0.797	0.510	0.826	0.016
Adjusted $R^2$	0.033	0.032	0.002	0.797	0.510	0.826	0.016
Residual Std. Error	0.017 (df = 746,191)	0.002 (df = 603,008)	0.034 (df = 728,135)	31.749 (df = 718,258)	34.593 (df = 679,397)	2.764 (df = 538,149)	0.081 (df = 735,485)
F Statistic	378.505 *** (df = 67; 746,191)	299.483 *** (df = 66; 603,008)	20.106 *** (df = 67; 728,135)	42,075.420 *** (df = 67; 718,258)	10,554.980 *** (df = 67; 679,397)	38,638.270 *** (df = 66; 538,149)	182.887 *** (df = 67; 735,485)

Note: *** p < 0.01, ** p < 0.05, * p < 0.1.

and

Table 4. Results of the Model 2 consumption by house: August 2021 to December 2021.

	House 1	House 2	House 3	House 4	House 5	House 6	House 7
month8	N/A	−0.001 ***	−0.001 ***	−0.063 ***	−0.0003	0.263 ***	0.027 ***
		(0.0001)	(0.0001)	(0.003)	(0.001)	(0.022)	(0.002)
month9	−0.001 ***	−0.001 ***	−0.001 ***	−0.141 ***	−0.007 ***	2.462 ***	0.022 ***
	(0.0001)	(0.0001)	(0.0002)	(0.011)	(0.002)	(0.047)	(0.001)
month10	−0.002 ***	−0.00003	−0.001 ***	0.213 ***	−0.00002	2.626 ***	0.010 ***
	(0.0001)	(0.0001)	(0.0002)	(0.028)	(0.004)	(0.052)	(0.001)
month11	−0.002 ***	−0.0001	−0.00001	−0.121 ***	−0.006 ***	2.692 ***	0.005 ***
	(0.0001)	(0.0001)	(0.0002)	(0.008)	(0.002)	(0.051)	(0.0004)
month12	N/A	0.001 ***	−0.002 ***	−0.080 ***	−0.012 ***	9.285 ***	N/A
		(0.0001)	(0.0002)	(0.007)	(0.003)	(0.093)
device1	0.006 ***	−0.005 ***	−0.0003	−0.248 ***	−0.017 ***	−0.719 ***	−0.017 ***
	(0.0001)	(0.0002)	(0.0002)	(0.017)	(0.002)	(0.016)	(0.001)
device2	0.001 ***	−0.005 ***	Ref	−0.301 ***	−0.023 ***	−0.274 ***	−0.022 ***
	(0.00004)	(0.0002)		(0.021)	(0.002)	(0.023)	(0.001)
device3	−0.001 ***	−0.005 ***	−0.001 ***	Ref	−0.026 ***	−0.393 ***	−0.019 ***
	(0.00003)	(0.0002)	(0.0001)		(0.002)	(0.069)	(0.001)
device4	−0.001 ***	−0.005 ***	−0.001 ***	−0.275 ***	−0.026 ***	0.189 ***	−0.021 ***
	(0.00003)	(0.0002)	(0.0002)	(0.018)	(0.002)	(0.019)	(0.001)
device5	0.001 ***	Ref	−0.001 ***	−0.269 ***	−0.013 ***	−0.301 ***	−0.014 ***
	(0.0001)		(0.0002)	(0.017)	(0.002)	(0.015)	(0.001)
device6	Ref	−0.005 ***	−0.001 ***	−0.259 ***	Ref	Ref	Ref
		(0.0002)	(0.0002)	(0.018)
mon	−0.00001	0.0002 **	−0.0001	0.052 ***	−0.002 ***	0.255 ***	0.017 ***
	(0.00005)	(0.0001)	(0.0002)	(0.007)	(0.0005)	(0.020)	(0.001)
tue	0.001 ***	0.0001	−0.0003 ***	0.012 **	0.002	−0.258 ***	0.004 ***
	(0.0001)	(0.0001)	(0.0001)	(0.005)	(0.002)	(0.022)	(0.0005)
wed	0.0004 ***	−0.0001	−0.0001	−0.005	0.003 **	−0.135 ***	0.006 ***
	(0.0001)	(0.0001)	(0.0001)	(0.003)	(0.001)	(0.022)	(0.001)
thu	−0.0003 ***	−0.0003 ***	−0.0003 ***	0.021 ***	0.003 ***	−0.274 ***	0.008 ***
	(0.00003)	(0.0001)	(0.0001)	(0.008)	(0.001)	(0.021)	(0.001)
fri	−0.0001	−0.0002 ***	−0.0001	0.259 ***	−0.0002	−0.012	0.003 ***
	(0.00004)	(0.0001)	(0.0001)	(0.027)	(0.001)	(0.019)	(0.001)
sat	0.001 ***	0.0001	−0.0005 ***	0.006 *	0.002 **	−0.245 ***	0.009 ***
	(0.0001)	(0.0001)	(0.0001)	(0.004)	(0.001)	(0.022)	(0.001)
holidays	−0.004	0.0003 **	−0.0003 ***	0.020 ***	0.003 *	−3.080 ***	0.031 ***
	(0.0003)	(0.0001)	(0.0001)	(0.006)	(0.002)	(0.047)	(0.002)
Constant	0.003 ***	0.006 ***	0.002 ***	0.191 ***	0.024 ***	−1.481 ***	−0.013 ***
	(0.0004)	(0.0002)	(0.0002)	(0.010)	(0.002)	(0.064)	(0.003)
Observations	1,633,802	1,783,481	1,749,531	1,672,655	1,648,740	1,304,140	1,653,857
$R^2$	0.067	0.024	0.001	0.030	0.002	0.657	0.036
Adjusted $R^2$	0.067	0.024	0.0005	0.030	0.002	0.656	0.036
Residual Std. Error	0.011 (df = 1,633,732)	0.014 (df = 1,783,409)	0.043 (df = 1,749,459)	1.787 (df = 1,672,583)	0.330 (df = 1,648,668)	2.533 (df = 1,304,068)	0.107 (df = 1,653,786)
F Statistic	1706.848 *** (df = 69; 1,633,732)	614.282 *** (df = 71; 1,783,409)	12.813 *** (df = 71; 1,749,459)	732.879 *** (df = 71; 1,672,583)	38.180 *** (df = 71; 1,648,668)	35,103.650 *** (df = 71; 1,304,068)	875.066 *** (df = 70; 1,653,786)

Note: *** p < 0.01, ** p < 0.05, * p < 0.1.

, which highlighted some of the most important variables in the model (additional tables for omitted variables will be included in the appendix). The estimated regression was based on using HAC standard errors (robust to possible presence of heteroscedasticity and autocorrelation simultaneously), as proposed by Stock and Watson (2011) [43] and Wooldridge (2010) [44].

4.1. Results of the Explanatory Variables Considered

In this section, the results of the estimation will be reviewed. Table 3 and Table 4 contain the estimation of the quarterly model 1 and the semi-annual model 2, respectively. These tables are actually a reduced version of the estimation of each model, where special attention is paid to monthly controls, device controls, and holiday controls.

Starting with the quarterly model, Table 3 presents the results of the estimations of model 1 for each house. Each column shows houses 1 to 7. Note that in some cases, there were missing observations through the meters or over time, and they were marked as N/A. Standard errors were presented in parentheses), and focusing on the regressors that measured the fixed effects of the months of the year ($months$), as well as those corresponding to weekdays ($weekdays$), it can be seen that, in general, almost all of them were significant. This indicates that each month and each day of the week had its own statistically significant behavior, different from the reference month specified as October and the reference day as Sunday. However, it is important to add that this month-effect and day-effect were practically negligible in magnitude—very close to zero in all cases—except for houses 4, 5, and 6.

Another interesting result to highlight in the quarterly model is that the variables that captured the fixed effects of each device were also all significant. This refers to the fact that each measured device in each of the analyzed households had its own statistical difference from the reference device. Nonetheless, it should be considered that the magnitude of this effect was marginal and close to zero, except for houses 4, 5, and 6. Finally, the variable that measured whether the data collected at that minute were located on a holiday ($holidays$) was significant in all households. Thus, for this group of households, the hypothesis of a difference in energy consumption during these festivities is confirmed. In particular, the magnitude of the effect was close to zero in houses 1, 2, 3, and 7; whereas in house 3, on average, $3.087$ kWh/mint more was consumed on holidays than on a working day. This effect was negative in houses 4 and 5, where, on average, 1.499 and 5.844 less was consumed, respectively, than on a working day.

At the same time, and associated with this quarterly estimation of the model, the reader can check in the Appendix A,

Table A1. Results of the Model 1 consumption by house: October 2021 to December 2021, vector of hours.

	House 1	House 2	House 3	House 4	House 5	House 6	House 7
h1	−0.0003	−0.0001 ***	0.001 ***	0.023	1.356 ***	−0.073	−0.002 ***
	(0.0005)	(0.00003)	(0.0004)	(0.423)	(0.492)	(0.074)	(0.001)
h2	−0.0001	−0.0003 ***	−0.00004	0.011	0.521	0.410 ***	−0.003 ***
	(0.0005)	(0.00002)	(0.0003)	(0.426)	(0.510)	(0.080)	(0.001)
h3	−0.002 ***	−0.0003 ***	−0.001 ***	−0.378	−9.289 ***	−0.084	−0.002 ***
	(0.0004)	(0.00002)	(0.0003)	(0.414)	(0.542)	(0.075)	(0.001)
h4	0.004 ***	−0.0004 ***	−0.001 ***	−0.182	1.172 **	−0.084	−0.0005
	(0.001)	(0.00002)	(0.0002)	(0.424)	(0.495)	(0.075)	(0.001)
h5	−0.001 **	−0.0004 ***	−0.002 ***	0.314	−1.436 ***	0.187 ***	−0.003 ***
	(0.0003)	(0.00002)	(0.0003)	(0.412)	(0.496)	(0.065)	(0.001)
h6	−0.002 ***	−0.0004 ***	−0.001 ***	0.016	−3.054 ***	−0.089	−0.003 ***
	(0.0003)	(0.00002)	(0.0002)	(0.428)	(0.542)	(0.074)	(0.001)
h7	−0.001 ***	−0.0004 ***	−0.001 ***	0.006	−0.093	−0.108	0.002 **
	(0.0004)	(0.00002)	(0.0002)	(0.428)	(0.527)	(0.075)	(0.001)
h8	−0.001 ***	−0.0003 ***	−0.001 ***	−0.025	0.082	−0.068	−0.005 ***
	(0.0004)	(0.00002)	(0.0002)	(0.428)	(0.524)	(0.074)	(0.001)
h9	−0.001 ***	−0.0003 ***	−0.0003	73.911 ***	53.812 ***	0.511 ***	−0.002 **
	(0.0003)	(0.00002)	(0.001)	(1.188)	(0.855)	(0.062)	(0.001)
h10	−0.001 **	−0.0002 ***	−0.001 *	−2.603 ***	−11.990 ***	−1.194 ***	−0.002 *
	(0.0003)	(0.00002)	(0.0003)	(0.487)	(0.517)	(0.066)	(0.001)
h11	−0.001 ***	0.0001 ***	0.0003	−2.076 ***	−1.364 ***	0.422 ***	−0.0001
	(0.0004)	(0.00003)	(0.0003)	(0.498)	(0.453)	(0.063)	(0.001)
h12	−0.001 ***	0.0002 ***	−0.001 ***	−2.079 ***	−1.297 **	6.305 ***	−0.0003
	(0.0004)	(0.00003)	(0.0003)	(0.497)	(0.541)	(0.120)	(0.001)
h13	−0.00003	0.0001 ***	−0.0002	−1.503 ***	−2.107 ***	−0.288 ***	0.001
	(0.0004)	(0.00003)	(0.001)	(0.410)	(0.502)	(0.063)	(0.001)
h14	−0.001 **	0.0002 ***	−0.001 ***	−4.271 ***	−18.526 ***	0.574 ***	0.0002
	(0.0004)	(0.00003)	(0.0003)	(0.458)	(0.596)	(0.070)	(0.001)
h15	−0.001 ***	0.0003 ***	−0.0004	−2.123 ***	5.601 ***	−0.060	0.0003
	(0.0004)	(0.00003)	(0.0004)	(0.492)	(0.517)	(0.074)	(0.001)
h16	−0.001 *	0.0001 ***	−0.001 ***	−1.947 ***	−0.897 *	0.085	−0.001
	(0.0003)	(0.00003)	(0.0003)	(0.494)	(0.527)	(0.070)	(0.001)
h17	−0.001 **	0.00002	0.001	−2.211 ***	−4.003 ***	−0.110	0.001
	(0.0003)	(0.00003)	(0.001)	(0.492)	(0.551)	(0.074)	(0.001)
h18	−0.0004	−0.00003	−0.0003	−1.907 ***	−2.064 ***	−0.110	0.0002
	(0.0004)	(0.00003)	(0.0003)	(0.497)	(0.472)	(0.074)	(0.001)
h19	−0.001	0.0001 ***	−0.001 **	−1.644 ***	0.206	−0.108	0.002 ***
	(0.0005)	(0.00003)	(0.0003)	(0.448)	(0.504)	(0.073)	(0.001)
h20	0.0004	0.0004 ***	0.0003	−1.889 ***	−0.078	−0.133 *	0.005 ***
	(0.001)	(0.0001)	(0.0004)	(0.502)	(0.521)	(0.074)	(0.001)
h21	−0.002 ***	0.001 ***	−0.001 **	−1.882 ***	−0.961 *	0.142 **	0.011 ***
	(0.0004)	(0.00003)	(0.0003)	(0.501)	(0.521)	(0.069)	(0.002)
h22	−0.0004	0.001 ***	−0.001 ***	−3.256 ***	−3.918 ***	−1.439 ***	0.001 **
	(0.0004)	(0.00003)	(0.0003)	(0.449)	(0.527)	(0.077)	(0.001)
h23	−0.003 ***	0.0002 ***	−0.0004	−0.053	−0.413	0.390 ***	0.018 ***
	(0.0004)	(0.00003)	(0.0003)	(0.535)	(0.510)	(0.066)	(0.002)
Constant	0.002 ***	0.001 ***	0.001 ***	21.487 ***	48.485 ***	−0.880 ***	0.043 ***
	(0.0003)	(0.00005)	(0.0004)	(0.731)	(1.048)	(0.092)	(0.005)
Observations	746,259	603,075	728,203	718,326	679,465	538,216	735,553
$R^2$	0.033	0.032	0.002	0.797	0.510	0.826	0.016
Adjusted $R^2$	0.033	0.032	0.002	0.797	0.510	0.826	0.016
Residual Std. Error	0.017 (df = 746,191)	0.002 (df = 603,008)	0.034 (df = 728,135)	31.749 (df = 718,258)	34.593 (df = 679,397)	2.764 (df = 538,149)	0.081 (df = 735,485)
F Statistic	378.505 *** (df = 67; 746,191)	299.483 *** (df = 66; 603,008)	20.106 *** (df = 67; 728,135)	42,075.420 *** (df = 67; 718,258)	10,554.980 *** (df = 67; 679,397)	38,638.270 *** (df = 66; 538,149)	182.887 *** (df = 67; 735,485)

*** p < 0.01, ** p < 0.05, * p < 0.1.

and

Table A2. Results of the Model 1 consumption by house: October 2021 to December 2021, vector of days.

	House 1	House 2	House 3	House 4	House 5	House 6	House 7
D2	−0.003 ***	−0.0002 ***	0.0002	6.259 ***	14.388 ***	−2.960 ***	−0.029 ***
	(0.0002)	(0.00004)	(0.0002)	(0.581)	(0.614)	(0.095)	(0.004)
D3	−0.001 ***	−0.0001 **	0.001 ***	5.791 ***	−1.271 *	−1.364 ***	−0.027 ***
	(0.0001)	(0.00004)	(0.0002)	(0.540)	(0.719)	(0.099)	(0.004)
D4	−0.002 ***	−0.0001 *	−0.0001	1.831 ***	−2.536 ***	−1.708 ***	−0.030 ***
	(0.0001)	(0.00004)	(0.0002)	(0.559)	(0.722)	(0.094)	(0.004)
D5	−0.003 ***	−0.0002 ***	0.001 ***	10.011 ***	4.514 ***	−1.853 ***	−0.030 ***
	(0.0003)	(0.00003)	(0.0002)	(0.507)	(0.669)	(0.088)	(0.004)
D6	−0.003 ***	−0.0002 ***	−0.0002	−0.176	−1.426	−0.076	−0.027 ***
	(0.0002)	(0.00004)	(0.0002)	(0.722)	(0.922)	(0.085)	(0.004)
D7	−0.001 ***	−0.0002 ***	−0.0003 **	3.015 ***	−1.635 *	0.264 ***	−0.030 ***
	(0.0002)	(0.00004)	(0.0001)	(0.649)	(0.864)	(0.099)	(0.004)
D8	−0.0002	−0.0002 ***	−0.0004 **	−0.309	−1.561 ***	0.086	−0.026 ***
	(0.0001)	(0.00004)	(0.0002)	(0.456)	(0.605)	(0.083)	(0.004)
D9	−0.003 ***	−0.0004 ***	−0.0001	6.827 ***	−1.248 **	−0.302 ***	−0.032 ***
	(0.0002)	(0.00004)	(0.0002)	(0.494)	(0.628)	(0.081)	(0.004)
D10	−0.003 ***	−0.0003 ***	0.003 ***	1.207 *	−0.747	0.251 ***	−0.028 ***
	(0.0002)	(0.00004)	(0.0005)	(0.654)	(0.857)	(0.086)	(0.004)
D11	0.008 ***	−0.0002 ***	−0.00002	2.032 ***	−0.498	2.158 ***	−0.026 ***
	(0.001)	(0.00003)	(0.0001)	(0.687)	(0.948)	(0.119)	(0.004)
D12	−0.002 ***	−0.0003 ***	0.003 ***	106.498 ***	41.317 ***	−0.712 ***	−0.029 ***
	(0.0002)	(0.00004)	(0.001)	(1.324)	(0.885)	(0.083)	(0.004)
D13	−0.003 ***	−0.0004 ***	−0.0005 ***	−5.662 ***	−3.748 ***	0.0005	−0.026 ***
	(0.0002)	(0.00004)	(0.0001)	(0.589)	(0.756)	(0.087)	(0.005)
D14	−0.002 ***	−0.0002 ***	0.0002	−2.701 ***	−2.567 ***	0.929 ***	−0.030 ***
	(0.0002)	(0.00004)	(0.0002)	(0.685)	(0.791)	(0.087)	(0.004)
D15	−0.002 ***	−0.0005 ***	−0.0003 **	0.0004	2.174 ***	−0.235 ***	−0.024 ***
	(0.0001)	(0.00003)	(0.0002)	(0.549)	(0.743)	(0.078)	(0.004)
D16	−0.003 ***	−0.0005 ***	0.001 ***	−1.582 **	−0.988	−0.823 ***	−0.024 ***
	(0.0002)	(0.00004)	(0.0003)	(0.655)	(0.765)	(0.089)	(0.004)
D17	−0.002 ***	−0.0004 ***	0.002 ***	−6.040 ***	−5.323 ***	0.313 ***	−0.026 ***
	(0.0001)	(0.00004)	(0.0004)	(0.609)	(0.813)	(0.085)	(0.004)
D18	−0.003 ***	−0.0001 ***	0.003 ***	−4.878 ***	−2.077 ***	0.341 ***	−0.028 ***
	(0.0002)	(0.00004)	(0.0004)	(0.554)	(0.710)	(0.087)	(0.004)
D19	0.001 ***	−0.0002 ***	0.001 ***	4.212 ***	2.730 ***	−0.658 ***	−0.028 ***
	(0.0001)	(0.00004)	(0.0003)	(0.613)	(0.742)	(0.084)	(0.004)
D20	−0.003 ***	−0.0003 ***	0.00003	−5.824 ***	−19.028 ***	0.098	−0.025 ***
	(0.0002)	(0.00004)	(0.0001)	(0.596)	(0.715)	(0.088)	(0.004)
D21	0.004 ***	−0.00000	0.002	−7.136 ***	8.911 ***	15.557 ***	−0.030 ***
	(0.001)	(0.00003)	(0.002)	(0.593)	(0.865)	(0.184)	(0.004)
D22	0.002 ***	−0.0004 ***	−0.0001	−0.246	5.374 ***	−0.218 ***	−0.028 ***
	(0.001)	(0.00003)	(0.0001)	(0.546)	(0.698)	(0.078)	(0.004)
D23	−0.003 ***	−0.0002 ***	−0.0002	−2.400 ***	3.319 ***	−0.405 ***	−0.029 ***
	(0.0002)	(0.00004)	(0.0003)	(0.648)	(0.783)	(0.084)	(0.004)
D24	−0.002 ***	−0.0003 ***	0.001 *	−4.987 ***	−7.983 ***	0.590 ***	−0.027 ***
	(0.0002)	(0.00004)	(0.001)	(0.603)	(0.734)	(0.078)	(0.004)
D25	−0.0004 ***	−0.00005	−0.001 ***	−4.884 ***	8.857 ***	−0.555 ***	−0.029 ***
	(0.0001)	(0.00004)	(0.0002)	(0.556)	(0.603)	(0.092)	(0.004)
D26	−0.003 ***	−0.0004 ***	0.001 ***	2.025 ***	11.593 ***	−0.285 ***	−0.030 ***
	(0.0002)	(0.00004)	(0.0002)	(0.577)	(0.688)	(0.081)	(0.004)
D27	−0.002 ***	−0.0005 ***	0.004 **	−5.125 ***	5.197 ***	−0.004	0.001
	(0.0002)	(0.00004)	(0.002)	(0.609)	(0.683)	(0.088)	(0.004)
D28	−0.001 ***	−0.0002 ***	−0.0001	−4.520 ***	1.212	1.111 ***	−0.028 ***
	(0.0002)	(0.00004)	(0.0001)	(0.586)	(0.772)	(0.089)	(0.004)
D29	−0.001 ***	−0.0003 ***	−0.0003 *	0.769	4.941 ***	−0.719 ***	−0.026 ***
	(0.0002)	(0.00003)	(0.0002)	(0.625)	(0.732)	(0.083)	(0.004)
D30	−0.003 ***	−0.0004 ***	−0.0001	9.435 ***	1.931 **	−0.349 ***	−0.029 ***
	(0.0002)	(0.00004)	(0.0002)	(0.719)	(0.799)	(0.083)	(0.004)
D31	0.004 ***	−0.0001 ***	0.001 ***	−16.381 ***	−3.371 ***	6.453 ***	−0.029 ***
	(0.0003)	(0.00004)	(0.0002)	(0.789)	(1.004)	(0.133)	(0.004)
Constant	0.002 ***	0.001 ***	0.001 ***	21.487 ***	48.485 ***	−0.880 ***	0.043 ***
	(0.0003)	(0.00005)	(0.0004)	(0.731)	(1.048)	(0.092)	(0.005)
Observations	746,259	603,075	728,203	718,326	679,465	538,216	735,553
$R^2$	0.033	0.032	0.002	0.797	0.510	0.826	0.016
Adjusted $R^2$	0.033	0.032	0.002	0.797	0.510	0.826	0.016
Residual Std. Error	0.017 (df = 746,191)	0.002 (df = 603,008)	0.034 (df = 728,135)	31.749 (df = 718,258)	34.593 (df = 679,397)	2.764 (df = 538,149)	0.081 (df = 735,485)
F Statistic	378.505 *** (df = 67; 746,191)	299.483 *** (df = 66; 603,008)	20.106 *** (df = 67; 728,135)	42,075.420 *** (df = 67; 718,258)	10,554.980 *** (df = 67; 679,397)	38,638.270 *** (df = 66; 538,149)	182.887 *** (df = 67; 735,485)

*** p < 0.01, ** p < 0.05, * p < 0.1.

, which contain information on the dummy variables that controlled the effects of each hour of the day ($hours$) and each day of the month ($day$–$month$), respectively. Beyond finding significant effects for a broad set of hours of the day, the effect was very close to zero in several households, except in the models adjusted for households 4 and 5, where the magnitude of the estimated coefficients at 09:00 a.m. was significant. Additionally it was significant in magnitude for houses 4 and 5. Specifically, it was found that consumption at $09:00$ increased on average by 73.911 kWh/mint in house 4 and 53.812 kWh/mint in house 5. Regarding the controls for each day of the month, these dummies were significant, which served to not reject the hypothesis that each day of the month had a particular behavior that differed from the first day of the month.

On the other hand, moving on to the semi-annual model, the conclusions obtained changed considerably. First, by comparing Table 3 and Table 4, it can be confirmed that the set of variables that had a significant effect was smaller than in the quarterly model. This may lead us to think that the effects previously considered were robust over a very short-term horizon, such as the quarterly one. For example, the regressors that measured the fixed effects of the months of the year ($months$) were not significant in several months within the seven households analyzed, and there was no clear pattern to affirm whether this vector had a significant effect or not. In the case of the fixed effects for weekdays ($weekdays$), there was a clearer pattern in which most of the variables in the vector were significant, confirming in this longer time window the differences in energy consumption according to the day of the week. Furthermore, the variable $holidays$ was statistically significant in all households except one, the first. This effect was practically zero in all houses, except in house 6. This means that on holidays, there was a different behavior, statistically speaking. But, in terms of its magnitude, this effect was negligible. In the sixth house, this effect was −3.080. This means that in house 6 on holidays, the consumption decreased be an average of −3.080 kWh/mint.

On the other hand, by observing

Table A3. Results of the Model 2 consumption by house: August 2021 to December 2021, vector of hours.

	House 1	House 2	House 3	House 4	House 5	House 6	House 7
h1	−0.00000	−0.0001	0.0004 **	0.035 ***	−0.002	−0.019	−0.002 ***
	(0.0004)	(0.0001)	(0.0002)	(0.005)	(0.001)	(0.038)	(0.001)
h2	0.0001	−0.0004 ***	−0.0001	−0.040 ***	−0.002	−1.608 ***	−0.003 ***
	(0.0004)	(0.0001)	(0.0001)	(0.005)	(0.002)	(0.045)	(0.001)
h3	−0.001 ***	−0.0004 ***	−0.001 ***	−0.050 ***	0.006 **	0.520 ***	0.0005
	(0.0003)	(0.0001)	(0.0001)	(0.006)	(0.003)	(0.049)	(0.001)
h4	0.004 ***	−0.0004 ***	−0.001 ***	−0.049 ***	0.014 ***	−0.002	−0.001 *
	(0.0005)	(0.0001)	(0.0001)	(0.006)	(0.003)	(0.039)	(0.001)
h5	−0.0004	−0.0004 ***	−0.001 ***	0.007	−0.005 ***	0.078 **	0.002 *
	(0.0003)	(0.0001)	(0.0001)	(0.007)	(0.001)	(0.034)	(0.001)
h6	−0.001 ***	−0.0004 ***	−0.001 ***	−0.038 ***	−0.003 *	−0.011	−0.003 ***
	(0.0003)	(0.0001)	(0.0001)	(0.005)	(0.002)	(0.039)	(0.001)
h7	−0.001 ***	−0.0004 ***	−0.001 ***	−0.033 ***	−0.004 ***	0.035	−0.003 ***
	(0.0003)	(0.0001)	(0.0001)	(0.005)	(0.001)	(0.038)	(0.001)
h8	−0.001 ***	−0.0003 ***	−0.001 ***	−0.017 ***	−0.014 ***	0.045	0.001
	(0.0003)	(0.0001)	(0.0001)	(0.006)	(0.002)	(0.035)	(0.002)
h9	−0.001 ***	−0.0002 ***	0.001 *	0.056 ***	0.008	0.350 ***	−0.0002
	(0.0003)	(0.0001)	(0.0004)	(0.013)	(0.008)	(0.032)	(0.001)
h10	−0.001 *	−0.0001	0.002 **	−0.002	0.0004	−1.431 ***	0.001
	(0.0003)	(0.0001)	(0.001)	(0.008)	(0.001)	(0.040)	(0.001)
h11	−0.001 ***	0.0005 ***	0.0005 *	0.005	0.005	0.168 ***	0.002 ***
	(0.0003)	(0.0001)	(0.0003)	(0.007)	(0.003)	(0.033)	(0.001)
h12	−0.001 **	0.003 ***	0.0001	0.027 ***	0.003 *	5.082 ***	0.002 ***
	(0.0003)	(0.0003)	(0.0001)	(0.008)	(0.002)	(0.065)	(0.001)
h13	0.001 ***	0.001 ***	0.001	0.004	−0.002	0.166 ***	0.004 ***
	(0.0003)	(0.0001)	(0.0004)	(0.005)	(0.002)	(0.031)	(0.001)
h14	−0.001 ***	0.001 ***	−0.0004 ***	0.002	0.003 *	0.406 ***	0.003 ***
	(0.0003)	(0.0001)	(0.0001)	(0.007)	(0.002)	(0.036)	(0.001)
h15	−0.001 **	0.001 ***	−0.0004 ***	−0.077 ***	0.010 ***	−0.005	0.003 ***
	(0.0003)	(0.0001)	(0.0001)	(0.006)	(0.002)	(0.035)	(0.001)
h16	−0.0004	0.001 ***	−0.0001	0.021 ***	−0.002	−0.112 ***	0.002 ***
	(0.0003)	(0.0001)	(0.0001)	(0.005)	(0.002)	(0.041)	(0.001)
h17	−0.001 *	0.001 ***	0.001	−0.014 **	−0.007 ***	−0.106 **	0.003 ***
	(0.0003)	(0.0001)	(0.0004)	(0.007)	(0.002)	(0.042)	(0.001)
h18	−0.0003	−0.001 ***	0.0003 **	0.012 *	−0.004 ***	−0.050	0.007 ***
	(0.0004)	(0.0001)	(0.0002)	(0.006)	(0.002)	(0.039)	(0.001)
h19	−0.0003	0.003 ***	0.0003 *	−0.078 ***	−0.004 ***	−0.155 ***	0.003 ***
	(0.0004)	(0.0002)	(0.0001)	(0.010)	(0.001)	(0.042)	(0.001)
h20	0.0004	0.004 ***	0.0004 ***	−0.018 ***	−0.001	0.085 **	0.007 ***
	(0.0005)	(0.0002)	(0.0002)	(0.006)	(0.002)	(0.035)	(0.001)
h21	−0.001 ***	0.004 ***	0.001 ***	−0.016 ***	0.001	0.070 *	0.012 ***
	(0.0004)	(0.0002)	(0.0002)	(0.006)	(0.006)	(0.037)	(0.002)
h22	−0.0001	0.002 ***	0.001 ***	−0.017 ***	0.003	−0.823 ***	0.061 ***
	(0.0004)	(0.0002)	(0.0001)	(0.005)	(0.002)	(0.038)	(0.003)
h23	−0.003 ***	0.001 ***	−0.0002	1.165 ***	−0.005 ***	0.046	0.014 ***
	(0.0004)	(0.0001)	(0.0001)	(0.114)	(0.001)	(0.036)	(0.001)
holidays	−0.004	0.0003 **	−0.0003 ***	0.020 ***	0.003 *	−3.080 ***	0.031 ***
	(0.0003)	(0.0001)	(0.0001)	(0.006)	(0.002)	(0.047)	(0.002)
dst	−0.0002	−0.001 ***	0.0001	0.054 ***	0.009 ***	−2.190 ***	0.019 ***
	(0.00002)	(0.0001)	(0.0002)	(0.007)	(0.002)	(0.044)	(0.002)
Constant	0.003 ***	0.006 ***	0.002 ***	0.191 ***	0.024 ***	−1.481 ***	−0.013 ***
	(0.0004)	(0.0002)	(0.0002)	(0.010)	(0.002)	(0.064)	(0.003)
Observations	1,633,802	1,783,481	1,749,531	1,672,655	1,648,740	1,304,140	1,653,857
$R^2$	0.067	0.024	0.001	0.030	0.002	0.657	0.036
Adjusted $R^2$	0.067	0.024	0.0005	0.030	0.002	0.656	0.036
Residual Std. Error	0.011 (df = 1,633,732)	0.014 (df = 1,783,409)	0.043 (df = 1,749,459)	1.787 (df = 1,672,583)	0.330 (df = 1,648,668)	2.533 (df = 1,304,068)	0.107 (df = 1,653,786)
F Statistic	1706.848 *** (df = 69; 1,633,732)	614.282 *** (df = 71; 1,783,409)	12.813 *** (df = 71; 1,749,459)	732.879 *** (df = 71; 1,672,583)	38.180 *** (df = 71; 1,648,668)	35,103.650 *** (df = 71; 1,304,068)	875.066 *** (df = 70; 1,653,786)

*** p < 0.01, ** p < 0.05, * p < 0.1.

in the Appendix A, it can be confirmed that there were no clear patterns in the significance of the variables that represented hourly controls (hours). Meanwhile,

Table A4. Results of the Model 2 consumption by house: August 2021 to December 2021, vector of days.

	House 1	House 2	House 3	House 4	House 5	House 6	House 7
D2	−0.002 ***	0.00003	0.0004 *	0.017 **	0.004 ***	−2.044 ***	−0.004
	(0.0002)	(0.0001)	(0.0002)	(0.007)	(0.001)	(0.063)	(0.003)
D3	−0.001 ***	−0.0002	0.0002 **	−0.035 ***	0.010 ***	−0.002	−0.001
	(0.0001)	(0.0001)	(0.0001)	(0.011)	(0.003)	(0.060)	(0.003)
D4	−0.002 ***	0.00002	0.0005 ***	0.062 ***	0.030 ***	−0.368 ***	−0.010 ***
	(0.0001)	(0.0001)	(0.0001)	(0.006)	(0.005)	(0.067)	(0.003)
D5	−0.002 ***	−0.0004 ***	0.0003 ***	0.0001	0.004 **	−0.251 ***	−0.025 ***
	(0.0002)	(0.0001)	(0.0001)	(0.007)	(0.002)	(0.064)	(0.003)
D6	−0.002 ***	0.0001	−0.0001	−0.029	−0.002 *	0.756 ***	−0.016 ***
	(0.0001)	(0.0001)	(0.0001)	(0.019)	(0.001)	(0.057)	(0.003)
D7	−0.002 ***	0.00000	0.001 ***	0.068 ***	0.016 ***	0.869 ***	−0.006 *
	(0.0002)	(0.0001)	(0.0002)	(0.007)	(0.003)	(0.065)	(0.003)
D8	−0.001 ***	0.0004 **	−0.0004 ***	0.050 ***	0.002	−0.117 *	−0.016 ***
	(0.0001)	(0.0002)	(0.0001)	(0.005)	(0.002)	(0.064)	(0.003)
D9	−0.002 ***	0.001 ***	−0.0001	−0.005	0.002 **	1.422 ***	−0.010 ***
	(0.0002)	(0.0002)	(0.0001)	(0.006)	(0.001)	(0.055)	(0.004)
D10	−0.003 ***	0.001 ***	0.001 ***	0.025 ***	−0.001	1.257 ***	−0.008 **
	(0.0002)	(0.0002)	(0.0002)	(0.005)	(0.001)	(0.056)	(0.004)
	(0.001)	(0.0002)	(0.0001)	(0.008)	(0.001)	(0.063)	(0.003)
D12	−0.001 ***	0.001 ***	0.001 ***	−0.015	0.012	1.575 ***	−0.003
	(0.0001)	(0.0002)	(0.0005)	(0.018)	(0.008)	(0.055)	(0.003)
D13	−0.002 ***	0.001 ***	0.001 ***	−0.053 ***	−0.005 ***	0.913 ***	−0.010 ***
	(0.0002)	(0.0002)	(0.0003)	(0.011)	(0.001)	(0.058)	(0.004)
D14	−0.002 ***	0.001 ***	0.00001	1.209 ***	−0.002	1.384 ***	−0.008 **
	(0.0001)	(0.0002)	(0.0001)	(0.115)	(0.001)	(0.056)	(0.003)
D15	−0.001 ***	0.001 ***	0.0003 ***	−0.051 ***	−0.002	2.087 ***	−0.009 **
	(0.0001)	(0.0002)	(0.0001)	(0.011)	(0.001)	(0.057)	(0.003)
D16	−0.002 ***	−0.0002	0.001 ***	−0.025 *	−0.003 ***	1.081 ***	−0.009 ***
	(0.0001)	(0.0001)	(0.0001)	(0.013)	(0.001)	(0.058)	(0.003)
D17	−0.002 ***	−0.0004 ***	−0.0001	−0.049 ***	−0.006 ***	1.859 ***	−0.007 **
	(0.0001)	(0.0001)	(0.0001)	(0.011)	(0.001)	(0.059)	(0.003)
D18	−0.002 ***	−0.0002 **	0.001 ***	0.033 ***	−0.002	1.794 ***	−0.009 **
	(0.0001)	(0.0001)	(0.0002)	(0.008)	(0.003)	(0.058)	(0.004)
D19	0.00002	0.002 ***	0.0004 ***	−0.054 ***	0.002	1.703 ***	0.054 ***
	(0.0001)	(0.0004)	(0.0001)	(0.012)	(0.001)	(0.059)	(0.005)
D20	−0.002 ***	0.0003 **	−0.0003 ***	−0.047 ***	0.008 ***	0.844 ***	−0.012 ***
	(0.0002)	(0.0002)	(0.0001)	(0.012)	(0.001)	(0.058)	(0.003)
D21	0.004 ***	0.001 ***	0.0002	0.024 ***	0.006	11.271 ***	−0.014 ***
	(0.001)	(0.0002)	(0.0003)	(0.008)	(0.004)	(0.126)	(0.003)
D22	0.002 ***	0.0002	−0.0003 ***	0.032 ***	0.011 **	1.332 ***	−0.006 *
	(0.001)	(0.0001)	(0.0001)	(0.008)	(0.004)	(0.055)	(0.003)
D23	−0.002 ***	0.0004 ***	−0.0003 ***	0.028 **	−0.002 **	1.479 ***	−0.010 ***
	(0.0001)	(0.0001)	(0.0001)	(0.014)	(0.001)	(0.056)	(0.003)
D24	−0.002 ***	0.0002 *	0.001 **	0.041 ***	−0.004 ***	1.381 ***	0.0005
	(0.0001)	(0.0001)	(0.0002)	(0.010)	(0.001)	(0.055)	(0.003)
D25	−0.001 ***	0.0003 *	0.0005	0.013	−0.004 **	1.105 ***	−0.017 ***
	(0.0001)	(0.0001)	(0.0003)	(0.012)	(0.002)	(0.057)	(0.003)
D26	−0.001 ***	0.0004 **	0.001 ***	−0.105 ***	0.007 **	1.539 ***	−0.006 *
	(0.0001)	(0.0002)	(0.0002)	(0.018)	(0.003)	(0.056)	(0.003)
D27	−0.001 ***	−0.002 ***	0.001 **	−0.046 ***	−0.0003	1.287 ***	0.018 ***
	(0.0001)	(0.0001)	(0.001)	(0.010)	(0.005)	(0.055)	(0.004)
D28	−0.001 ***	0.001 ***	0.001	−0.091 ***	−0.002 *	1.388 ***	−0.004
	(0.0002)	(0.0002)	(0.001)	(0.013)	(0.001)	(0.057)	(0.003)
D29	−0.001 ***	0.0005 ***	0.00003	0.021 ***	0.002 *	0.998 ***	0.0002
	(0.0002)	(0.0002)	(0.0001)	(0.005)	(0.001)	(0.056)	(0.004)
D30	−0.001 ***	0.0003 **	0.0001	−0.073 ***	−0.003 **	1.384 ***	−0.013 ***
	(0.0001)	(0.0001)	(0.0001)	(0.018)	(0.001)	(0.056)	(0.003)
D31	0.003 ***	−0.001 ***	−0.0001	−0.129 ***	−0.005 ***	2.143 ***	−0.019 ***
	(0.0002)	(0.0001)	(0.0001)	(0.016)	(0.002)	(0.060)	(0.003)
Constant	0.003 ***	0.006 ***	0.002 ***	0.191 ***	0.024 ***	−1.481 ***	−0.013 ***
	(0.0004)	(0.0002)	(0.0002)	(0.010)	(0.002)	(0.064)	(0.003)
Observations	1,633,802	1,783,481	1,749,531	1,672,655	1,648,740	1,304,140	1,653,857
$R^2$	0.067	0.024	0.001	0.030	0.002	0.657	0.036
Adjusted $R^2$	0.067	0.024	0.0005	0.030	0.002	0.656	0.036
Residual Std. Error	0.011 (df = 1,633,732)	0.014 (df = 1,783,409)	0.043 (df = 1,749,459)	1.787 (df = 1,672,583)	0.330 (df = 1,648,668)	2.533 (df = 1,304,068)	0.107 (df = 1,653,786)
F Statistic	1706.848 *** (df = 69; 1,633,732)	614.282 *** (df = 71; 1,783,409)	12.813 *** (df = 71; 1,749,459)	732.879 *** (df = 71; 1,672,583)	38.180 *** (df = 71; 1,648,668)	35,103.650 *** (df = 71; 1,304,068)	875.066 *** (df = 70; 1,653,786)

*** p < 0.01, ** p < 0.05, * p < 0.1.

shows that, in general, for all households, the variables corresponding to controls by day of the month (day–month) were significant. The results were expressed in absolute terms and were interpreted for the entire household. Following [45], in Appendix C, we attached the results for the variable consumption per square meter (unit of measurement used in Chile, instead of cubic feet), as well as for household per capita consumption. At the same time, it is interesting to note that the DST variable was significant in six of the seven households, with a negative impact on three and a positive impact on two of them. Thus, there was no clear pattern of behavior observed in this analysis that was correlated with the change in time zone. Finally, it can be noted that the F statistics of all of the estimated models were significant at the usual confidence levels. Therefore, the set of variables selected in both models was significant at explaining energy consumption. Table 4 presents the results of the estimations of model 2 for each house. Each column shows houses 1 to 7. Note that in some cases, there were missing observations through the meters or over time, and they were marked as N/A. Standard errors were presented in parentheses.

4.2. Quarterly Model vs. Semi-Annual Model

As observed in the previous section, when reviewing the results of the quarterly model and the semi-annual model, there was a smaller set of variables that were significant in Model 2. This is interesting and suggests that the results indicated a better explanatory power of the selected variables for the trimestral model compared with the semestral model. To better illustrate this idea,

Table 5. Comparison $R^2$ between Model 1 and Model 2 by house (Percentage $R^2$ × 100).

	House 1	House 2	House 3	House 4	House 5	House 6	House 7
Model 1	3.3	3.2	0.2	79.7	51.0	82.6	1.6
Model 2	6.7	2.4	0.1	3.0	0.2	65.7	3.6

Source: own elaboration.

is presented to the reader.

In Table 5, we can observe that the coefficient of determination R2 was notably higher in houses 4, 5, and 6, all with values greater than 50% (model 1). In other words, the proposed quarterly model explained at least 50% of the variability in household consumption for houses 4, 5, and 6. In these houses, temporal patterns primarily explained the consumption behavior using model 1. Then, when including more months from the sample and the $DST$ variable (model 2), there was a sharp decrease in $R^2$ for model 2. This last result may be confusing at first glance; $R^2$ decreased when new variables were included, which could be explained by the significant number of observations that were incorporated.

This presents significant challenges in terms of data collection, imputation techniques, and tracking of households for future research. It should be noted that as the households had different devices measured, these models were not comparable among themselves. It is also important to highlight that the imputation technique used could have affected the fit of the models in each household. In many cases, using the “Last Observation Carried Forward” method, the imputed values were repetitions of existing values. Therefore, it is most likely that in houses 1, 2, 3, and 7, there were a higher number of imputed values, which indicated the low variability of energy consumption explained by the proposed model.

Once the statistical significance of the variable vectors and the overall significance of the model were analyzed, we examined how well the adjusted model performed in explaining the observed consumption in each device. To do this, it was necessary to use the table provided earlier, in which it could be seen that the model adjusted based on 3 months of data better explained the observed variability in consumption than the model adjusted based on 6 months of data. This may be related to the fact that not all houses had statistical observations for these months, and interpolation was necessary, where the observed consumption recorded little or no variation. Furthermore, the interpolation criterion applied was the last observation carriedforward (LOCF), where, on many occasions, the last repeated value was “0”. Thus, given that an econometric estimation aims to use variations in an explanatory variable to account for variations in the dependent variable, when data with little variation were used, the explanatory power of this technique decreased.

5. Discussion

This research on load profiles has presented a comprehensive case study aimed at identifying the temporal patterns of energy consumption in a group of analyzed households. By measuring the energy consumption of six electrical devices in each of the seven households analyzed, a large dataset of over 750,000 high-frequency (minute-level) energy usage data points was collected and analyzed using econometric modeling techniques.

In each of the seven households, the energy consumption of six devices was measured, with the objective of studying specific intra-device behaviors. The evidence obtained through modeling indicated that, indeed, each device had a different self-effect from the reference device, supporting the hypothesis that energy consumption, and its determinants, can be studied at the micro-data level.

However, the estimates provided by the estimated models suggest that patterns of energy consumption vary significantly depending on the time of day, day of the week, day of the month, and month of the year. At the same time, significant differences in energy consumption were also found on holidays. These temporal patterns provide valuable information about when and how energy is consumed in households, which can contribute to the development of effective resource management strategies, as well as their interaction with social systems and policies.

Another relevant aspect of this analysis was the inclusion of a daylight saving time ($DST$) dummy variable in the estimated models. Although this variable has been used in previous studies [32] to account for seasonal variations in energy consumption, the results suggest that its effect is not uniform across all households. This underscores the importance of taking into account other explanatory factors of consumption, such as weather conditions or socio-demographic characteristics of households, when analyzing the behavior of energy consumption patterns.

The results confirm differences in hourly, daily, and monthly patterns using novel panel data methodologies. In turn, each day of the week exhibited its own behavior, and each device had its own consumption pattern. These were also subjected to a temporal sensitivity analysis, checking the fit of the model for a 3-month window versus a 6-month temporal window. The set of variables that held statistical significance were fewer in the semi-annual model. The results show that temporal patterns helped to explain consumption, with a goodness of fit ranging from 1.6% to 82% for the sevem homes when analyzing the quarterly model, versus 0.1% to 65.7% when analyzing the semi-annual model. This serves to confirm that the proposed model better explained the observed differences in consumption in the short-term temporal horizon.

6. Conclusions

Overall, this research provides evidence, using a novel approach for obtaining and disaggregating the information used as a data set, regarding the behavior of energy consumption profiles. Temporal patterns in household consumption have been confirmed, as well as the factors that influence these patterns. Taking into account multiple factors and using advanced econometric techniques, we can continue to develop more accurate models that explain energy consumption management by households, which can help reduce energy waste through appropriate regulation. This can help promote energy sustainability, incrementally improving public policies in this area.

This research is a contribution to the literature on smart meters due to the characteristics of the models implemented. It will also serve as an input for future research. In the future, the methodology and data collection will be improved to make comparisons between households in future investigations.

It is crucial to generate quality information for researching and measuring the different consumption patterns of households, in order to provide inputs that enable policymakers to formulate public policies or measures related to energy use, with a more efficient design, and with scientific information on household behavior. While the information collection was robust, it was efficient and well-designed. In addition to the identification strategy being robust and easily interpretable, it is essential to expand these types of studies to a larger number of households, in order to determine consumption profiles by administrative areas, geographical locations, and socioeconomic strata, among others.