Detection of Trends and Anomalies with MACD and RSI Market Indicators for Temperature and Precipitation

Abstract

The changes in climatological variables are a critical concern for climatologists, hydrologists, and water resources managers. In the face of global climate change, a more profound understanding of the recent changes in climatological conditions of a specific region is becoming increasingly urgent. To this end, hydro-climatological time series are being investigated in various ways, from traditional approaches to state-of-the-art techniques. This manuscript investigates the trend changes of surface temperature and total precipitation hydro-climatological parameters over a long period, using two of the most popular market price trend detection indicators, MACD and RSI. The RSI indicator evaluation methodology has been modified for the hydro-climatological time series. Minimum, maximum, mean surface temperatures, and precipitation parameters were analyzed. The length of the data sets is 122 years, starting in 1901 and ending in 2022. The application of these indicators to the mentioned parameters underscores their potential as powerful tools in the detection of climatological trends and trend variability over time, highlighting the need for proactive climate management strategies. The results revealed that the MACD and RSI indicators are effective tools not only for trend detection but also for determining climatological anomalies. These tools can be used to complement traditional statistical trend analysis. Moreover, their visual capabilities allow the methods to offer a more comprehensive understanding of climate management strategies.

1. Introduction

In the last three decades, Türkiye has entered a highly volatile climate regime in terms of hydro-climatology, with successive periods of drought, flash floods. While TSMS data reveals a country average temperature increase of approximately +1.3 °C between 1990 and 2022, the years 2008, 2010, and 2018 stand out as extreme examples where both temperature and precipitation anomalies peaked simultaneously [1]. These unusual behaviors are considered to be the sharpest consequences of global climate change reflected in the region.

Trend investigation approaches are used to determine the ongoing or past trends in climatological and marketing trends. Due to global climate change, many recently published studies focus on the effects of regional climate change in terms of trend investigation. In recent publications on the topic of climatological trend investigation, it is possible to observe that most of the studies are based on statistical approaches such as Mann–Kendall (MK), Spearman’s rho, and Şen’s slope. Additionally, some state-of-the-art techniques, such as the innovative Şen trend test, were proposed and widely used in trend detection of climatological variables. Gocic and Trajkovic [2] searched for the statistically significant negative or positive trends of the air temperature, relative humidity, and precipitation parameters of the 12 weather stations of Serbia by using MK and Şen’s slope methods. They found the MK test and Şen’s slope agreed well with their case. Mallick et al. [3] applied a few well-known statistical tools to the annual rainfall of the Asir region. They chose MK, modified MK, pre-whitening MK, and innovative Şen trend techniques for the trend investigation of annual rainfall. The authors indicated that the innovative Şen trend test was the best trend detection technique among all techniques used. In another recently published work by [4], the authors also used the MK tests and innovative Şen trend test techniques for various hydro-climatological variables. They found annual rainfall, extreme temperatures, relative humidity, and stream flow parameters, which have statistically increasing trends, while evapotranspiration and sunshine duration parameters have decreasing trends. Zhang et al. [5] proposed an improved seasonal MK trend test. They have compared their proposal with the traditional approaches. Ashraf et al. [6] tested MK, Spearman’s rho, and innovative Şen trend methods for streamflow variations. They performed the study on an annual, seasonal, and monthly basis. For 240 monthly time series, they detected 134 statistically significant trends in the MK test, 138 in the Spearman’s rho test, and 159 in the innovative Şen trend test. Güçlü Y.S. [7] presented an improved visualization that was applied to 50 years of precipitation records from various meteorological stations in Türkiye and, unlike the Şen method, also shows the dimension (quantity) of the data. In another study performed for the Corbes River, non-parametric Mann–Kendall and Şen methods were used to test spatial and temporal variability and trends in rainfall and river flow [8]. The study examined the 40-year period between 1960 and 2000. It was found that there was a decreasing trend in annual precipitation, while river flow was generally dominated by decreasing trends, but most slopes were statistically insignificant [8]. Gomis-Cebolla et al. [9] aimed to assess the quality of ERA5 and ERA5-Land reanalyzed precipitation data by comparing it with high-resolution observations. They found that reanalysis products are in general agreement with observations and successfully represent spatial patterns and temporal trends [9]. In another interesting trend investigation study, the researchers looked for an asymmetric trend in the diurnal cycle in global cloud cover, especially in low-level clouds [10]. The authors conclude that this trend in cloudiness could be a factor exacerbating global warming [10]. Dai [11] analyzed global hydroclimatic changes between 1950 and 2018 using updated land precipitation, runoff, and improved Palmer Drought Severity Index data. The study found increases in precipitation in several continents and decreases in others. As can be interpreted from the previous studies, recently published works show differences when investigating ongoing climatological trends from region to region. Therefore, the performance of each technique, whether traditional or relatively new, should be evaluated according to the hydro-climatological conditions of the region. More studies about the applications of the widely used trend detection methods can be found in [12,13,14,15,16].

The above-mentioned traditional trend analyses have been carried out for different climatic data in various regions of Türkiye. In these studies, rainfall and temperature parameters were generally investigated, and Mann–Kendall, Spearman’s rho test, and the innovative Şen trend approaches were used. For example, in a study conducted in the Hirfanlı Dam Basin, increasing trends in temperature series were detected using these methods [17]. Similarly, in another study conducted in the Black Sea Region of Türkiye, Mann–Kendall and Şen trend methods were compared on annual total precipitation data, and both methods were found to show similar trends [18]. In a study conducted in Diyarbakır, trend changes in average temperature data were investigated with the monthly innovative Şen trend test method [19]. Although different results were found in the trend analyses of air temperature and precipitation for different regions of Türkiye, it was generally observed that there was an increasing trend in air temperature and a decreasing trend in total precipitation. In some studies, regional trend differences were reported [20]. Extensive trend analyses on Türkiye’s climate reveal various results with different time periods and methodologies. For example, Hadi and Tombul [21], in their long-term spatio-temporal analysis covering the period 1901–2014, found that annual regional temperature showed a statistically significant upward trend across Türkiye (0.88 °C per century), but annual regional precipitation did not show a statistically significant upward trend (0.11 mm per year). On a regional basis, they reported that annual precipitation decreased in Southeastern Anatolia and Mediterranean regions, while it increased in Marmara and Black Sea regions. For temperature, they observed an increasing trend in all regions. They also stated that seasonal temperature trends generally show an increase. They emphasized that the trends increased significantly after the mid-1990s. This suggests that the post-1985 period should be analyzed separately after the economic and industrial developments in Türkiye. In a study focusing on the period 1980–2019, Yetik et al. [22] examined precipitation trends in Türkiye using Spearman rank correlation and Mann–Kendall tests. The study found that there was no significant increase or decrease in annual total precipitation values on a regional basis. However, it revealed that the greatest change was observed on a seasonal basis, especially during the winter months. Furthermore, a decrease in precipitation was found in 80 out of 81 provinces in Türkiye in November. Gümüş et al. [23] conducted a trend analysis of six climate variables in the Southeastern Anatolia Region (GAP) for the period 1966–2020. Their study showed increasing trends in mean, minimum, and maximum temperatures, while for precipitation, they found a decreasing trend consistent with the ITA method. While the Mann–Kendall test showed significant trends for precipitation, relative humidity, and wind speed at a limited number of stations, the ITA method detected a consistent decreasing trend at most stations. This suggests that ITA may be more accurate in some cases. Streamflow trends are also an important indicator for understanding Türkiye’s hydro-climatological changes. Kahya and Kalaycı [24] examined a 31-year period for monthly streamflow data from 26 basins in Türkiye. Their study revealed a general decreasing trend in the basins of Western Türkiye and parts of Southeastern Anatolia, while there was no trend in the basins of Eastern Türkiye. It was emphasized that such marked changes in hydrological variables can be considered as a reflection of climate changes other than anthropogenic effects.

On the other hand, MACD (Moving Average Convergence–Divergence) and RSI (Relative Strength Index) are two very popular indicators used to detect ongoing trends in stock markets. Recently, the efficiency and usability of both tools were investigated for different markets. Chong et al. [25] applied the MACD and RSI techniques to the London Stock Exchange FT30 Index, and they found that the MACD and RSI are better indicators than the buy-and-hold strategy in many cases. Sami et al. [26] evaluated the performance of the MACD and RSI strategies for various stocks. They made predictions for the 26 stocks, and they observed that 56% of the MACD and 81% of the RSI predictions were correct. Thus, they suggested both indicators as powerful tools in the case of price trend detection. Gold [27] published a study that searched for the viability of multiple market price investigation indicators, including the MACD and RSI. He indicated that the return efficiency has mixed outputs, but it can be improved by including some factors, like volume and momentum. Chong et al. [28] re-investigated the performance of the MACD and RSI oscillators for five OECD countries’ markets. They found that both techniques can supply a good profit to their users. Cohen and Cabiri [29] compared the technical oscillators with the traditional buy-and-hold strategy. They indicated that the RSI is the second-best oscillator in the case of price trend detection and taking a profit. They also underlined that the MACD and RSI techniques perform better than indices during the bear markets.

Based on the explanation above, the objective of this study is to apply two very popular market price detection tools to the hydro-climatological time series. Since there are many published works about the trend detection of the hydro-climatological time series, according to the knowledge of the author, these tools, namely the MACD (Moving Average Convergence–Divergence) and RSI (Relative Strength Index), were never tested in such time series. This study has the potential to be a pioneering study for the application of the mentioned indicators to the hydro-meteorological time series, not only for the determination of trends but also for the determination of trend variability historically. Successful application of the mentioned approaches can also be a good alternative for the investigation of climatological anomalies from the perspective of global climate change. Trend analysis of hydro-climatological time series is of great importance for understanding and making decisions on the impacts of climate change. While traditional analysis techniques are often limited to local or specific parameters, this study’s methods (MACD and RSI) have the potential to cover a wider range of hydroclimatic conditions and geographical areas than ever before. In particular, this generalization of the applicability of market analysis techniques such as MACD and RSI to hydro-climatological data is a first in the literature. Traditional approaches, such as Mann–Kendall and Spearman’s rho tests, have some limitations in the application of trend investigation of hydro-climatological time series [30]. In the traditional approaches, generally, the users should check the data sets for seasonality effects or normal distribution conditions [31]. Furthermore, the outputs of the traditional approaches are usually presented as numerical outputs, and it is difficult to visualize them. The proposed methods in this study (MACD and RSI) do not have the mentioned limitations. The users can directly start to work on the dataset if they have a continuous hydrometeorological dataset. In relatively new techniques, such as the innovative Şen trend test, it is possible to visualize results and give the trend decision graphically. However, in this approach, the users can only check the ongoing trends. It is not possible to check for recent trends or trend detection points on the same graph. The MACD and RSI are oscillator-based indicators designed to capture momentum and turning points in financial series, while Mann–Kendall and Şen’s slope test uses ordinal statistics to determine whether the series has a monotonic slope and the magnitude of that slope. The MK and Şen’s slope strategy treats each observation with equal weighting, while MACD measures the acceleration of the slope using the difference between short (e.g., 12-year) and long (e.g., 26-year) exponential moving averages. RSI, on the other hand, scales consecutive rises and falls on a 0–100 scale and shows the relative speed of change and extreme situations (overbought/oversold). This goes beyond the “trend on/trend off” judgment of conventional tests and allows us to determine when and how strongly the trend is gaining momentum. The MACD identifies turning points at the intersection with the signal line (9 EMA). Bar charts visualize the intensity of the momentum. RSI signals acceleration–deceleration periods and extreme divergences by looking at the time it stays above or below the 50 reference line. Although there are no studies in the literature that directly analyze climatic trends with MACD or RSI, there are studies that use these indicators in forecasting models. Anuradha et al. [32] used technical indicators such as MACD, RSI, and ADX (Average Directional Movement) for rainfall forecasting through a hybrid model including DBN and LSTM methods. In another study, it was used as a model input feature to detect potential trend changes and abnormalities by adapting the MACD indicator innovatively to wind energy time series [33].

Briefly, the availability of market-based techniques such as MACD and RSI in hydro-climatological data allows for much more sophisticated analysis by expanding the range of both regions and parameters. This represents a new approach to support decisions on climate change. The findings are expected to directly contribute to strengthening early warning systems and updating adaptation strategies for hydrologists, water resources managers, agricultural planners, and climate policy makers.

2. Methodology

In this study, two very powerful market trend investigation tools, namely MACD and RSI, were applied to the minimum, maximum, mean annual average surface temperature, and annual precipitation of Türkiye. The definition of the data set, the study area, and the applied methodology are explained in that part. A summary of the works carried out in this manuscript is presented in Figure 1.

As it is presented in Figure 1, a data set downloaded for Türkiye consisting of 122 yearly data points was used for MACD, RSI, MK, and innovative Şen trend test. The results are compared with each other. The trends were identified, and the advantages of the newly proposed approach were discussed.

2.1. Study Area and the Data Set

For analyzing the effectiveness of the MACD and RSI indicators for the trend investigation of hydro-climatological time series, long-term records of Türkiye were used. The data set used was downloaded from the World Bank Climate Change Knowledge Portal [34]. The dataset was downloaded by using the World Bank Climate Change Knowledge Portal interface, but it is originally from the CRU TS v4.07 [35]. This data set is a gridded data set, and it is available for countries and regions. Version v4.07 was released on 19 April 2023, and it covers the period 1901–2022 [35]. Observed annual average mean surface temperature (T_mean), observed annual average maximum surface temperature (T_max), observed annual average minimum surface temperature (T_min), and observed annual precipitation (P) hydro-climatological time series starting from 1901 were utilized for trend investigations. The given hydro-climatological annual time series ends in 2022. So, the length of the data set is 122 years for each parameter. The location of the study area is shown in Figure 2. The map of the region was created using QGIS open-source software version 3.26.2.

The Turkish State Meteorological Service (TSMS) describes the climatology of Türkiye in four main classes. According to the general classification of the TSMS, there is a continental climate in the inner regions, a Mediterranean climate on the Mediterranean coast, a Marmara (Transition) climate in the northwestern part, and a Black Sea (Humid) climate in the north [36]. An overview of the current climatology of Türkiye for the period of 1991–2022 was obtained from CCKP [34,35] and shared in Figure 3.

Figure 3 shows the yearly distribution of the minimum, maximum, and mean observed surface temperature of Türkiye for the period of 1901–2022. In Figure 3, the distribution of annual observed precipitation (mm) is given with bars. The given graphs in Figure 3 were drawn based on the Climate Change Knowledge Portal climatology data.

The statistical description of the data set is given in

Table 1. Statistical definition of the data set.

	Max.	Min.	Mean	Standard Deviation	Skewness Coefficient
Observed annual average minimum surface temperature (°C) (Tmin)	7.4	3.8	5.4	0.7	0.4
Observed annual average maximum surface temperature (°C) (Tmax)	19.0	15.2	16.9	0.7	0.5
Observed annual average mean surface temperature (°C) (Tmean)	13.2	9.6	11.1	0.7	0.5
Observed annual precipitation (mm) (P)	743.9	439.4	597.7	59.6	0.1

. The minimum value of T_min for the 1901–2022 period was observed as 3.8 °C. The maximum value of T_max for the mentioned period was observed as 19 °C, while the mean of the T_mean was observed as 11.1 °C. The standard deviation and skewness coefficients of all three forms of surface temperature are calculated almost the same. The skewness coefficient of a time series indicates how much the distribution of values deviates from symmetry. In other words, it is the third standardized moment that indicates whether it is “skewed” to the right or left. Table 1 was shared to identify the data used statistically instead of sharing the data pages.

The yearly data set for the period of 1901–2022 was obtained from the Climate Change Knowledge Portal website [34]. According to the given explanations about the data set, historical data is produced by the Climatic Research Unit (CRU), and the resolution of the data is 0.5° × 0.5° (50 km × 50 km) [35]. The developer of the CRU is the University of East Anglia. The mentioned data set with the given resolution is a reliable data source for climatological research.

2.2. Moving Average Convergence–Divergence (MACD)

The Moving Average Convergence–Divergence technique was originally developed by Gerald Appel in 1979 [37]. The MACD can be explained as both a momentum and trend indicator that is widely used for analyzing stock prices. While the momentum indicators are simply interested in the speed and power of the price, the trend indicators are interested in price movement directions [38]. The MACD has both momentum and trend detection abilities. The calculations of the MACD are based on the Exponential Moving Averages (EMA). Generally, for analyzing stock prices, 12 days and 26 days are considered the standard periods. As it is a common application, in this study, 12 and 26 time steps were used for analyzing hydro-climatological time series. However, instead of using daily closing prices, annual averages were used. This point makes the presented study a unique research in the climatological trend investigation field. To be able to draw the MACD graph, EMA 26 for the given records (can be temperature or precipitation), and EMA 12 must be calculated. Then, the MACD line values can be obtained by extracting EMA 26 from EMA 12. After obtaining the MACD line values, the signal line values can be calculated by calculating EMA 9 for the MACD line values. In the calculations of EMA values, the first value was considered as the simple average of previous records. The calculation of the EMA is given in Equation (1) [39].

$${EMA}_{current}=\left({Value}_{current}\ast \left({\displaystyle \frac{SmoothingFactor}{1+timesteps}}\right)\right)+{EMA}_{current-1}\ast \left(1-\left({\displaystyle \frac{Smoothingfactor}{1+timesteps}}\right)\right)$$

(1)

There are many possibilities for choosing the smoothing factor in the calculation of EMA; however, generally, it is considered 2. So, in this study, the smoothing factor was taken as 2 as it has a common usage. Generally, the calculation of the EMA and, therefore, the calculation of the MACD is based on the closing daily stock prices. However, in this study, for EMA calculations, instead of daily closing prices, annual averages were taken into account.

In a common usage of the MACD for stock price analysis, it is calculated as given in Equation (2) [40].

$$MACD=12dailyEMA-26dailyEMA$$

(2)

To process the signal line, the 9-day EMA of MACD must be calculated. Then, the bar charts can be obtained by subtracting the signal line values from the MACD values [41]. An example view of the MACD graph is given in Figure 4. It is possible to see the drawn MACD line, signal line, and bar charts based on the EMA calculations.

The MACD graphs can be evaluated in the following two main ways: The MACD line crossing the center line (zero line) and the MACD line crossing the signal line. In Figure 4 evaluations were demonstrated. The triangular marks on the figure show the trend change points according to the center line. For example, the red triangle on the figure shows the start point of a downward trend according to the center line evaluation. The green cross mark shows the upward trend point according to the signal line cross evaluation type. Similarly, the green triangle shows the upward trend starting point according to the center line evaluation, while the red cross mark shows the start point of the downward trend according to the signal line cross-evaluation. The bar charts are showing the momentum of the occurred trends. For traders, center line crosses, or signal line crosses, can be points of sell or buy. The traders can build their investment strategies on center line cross, signal line cross, or both. However, in this study, the center line crosses and the signal line crosses were used to detect the hydro-climatological trend change points and the historical trend periods.

The 12–26-year EMA pair was used in the study as part of the idea to start with, directly preserving the “default” (MACD-classic) setting of the indicator in the financial literature. Thus, the extent to which a finance-based tool can produce meaningful outputs without additional period adjustments to the climate series was tested. However, the choice of the 12–26-period EMA is not entirely unfounded. The temperature and precipitation are not parameters that show abrupt changes in annual averages by nature. Therefore, 12 years for the short-term EMA and 26 years for the long-term EMA are considered reasonable. For different climatic conditions and different seasonal averages (seasonal, monthly, etc.), calibrations may need to be performed by changing the short and long-term EMA values.

2.3. Relative Strength Index (RSI)

J. Welles Wilder developed the RSI indicator in 1978 [42]. It is a momentum indicator primarily used to determine a stock’s overbought or oversold prices, enabling more secure investment. In the originally developed version of the RSI, if the stock prices are over the 70 percent line, the condition of the stock is overbought. If the stock prices are under the 30 percent line, then it means that the condition of the stock is oversold. Therefore, these definitions can help traders change or maintain their positions based on the RSI indicator. The calculation of the RSI is based on the average losses and gains. The RSI formula is given in Equation (3) [43].

$$RSI=100-({\displaystyle \frac{100}{\left(1+\frac{Averagegaininupwardperiods}{Averagelossindownwardperiods}\right)}})$$

(3)

The RSI is the Relative Strength Index. The average gain and loss must be calculated for a certain period. Generally, in-stock overbought or oversold evaluations, this period is accepted as 14 days. In this study, the period for calculations was accepted as 14, but the periods are annual averages of hydro-climatological variables instead of daily closing stock prices. When computing the average loss and average gain, it is crucial to account for the fact that periods with price declines are factored as zero in the computation of average gain. In contrast, periods with price increases are factored as zero in the computation of average loss. A typical RSI graph is given in Figure 5.

An RSI graph exists from the distribution of the RSI values from zero to one hundred over the calculation period. In Figure 5, the deep line is the RSI 30 line, and the top line is the RSI 70 line. Both lines are reference lines for traders. In Figure 5, it is possible to notice that around the 40th day, the RSI values are approaching the RSI 30 line. So, for that part of the graph, it can be said that the stock is oversold. In the same graph, around the 115th day, the RSI values are approaching the RSI of 70. For this part of the graph, it can be said that the stock is overbought. The RSI helps traders identify the conditions of overbought or oversold stock, so they can make the decision to buy or sell their shares. However, in its current form, the RSI indicator is not very useful for the detection of hydro-climatological trends. The main reason is that the hydro-climatological time series is not as volatile as the stock prices are. To handle this problem, the RSI was slightly modified by adding an RSI 50 line and a linear regression line on it. The definition of ongoing trends over time can be completed by using the slope of the linear regression line. If the slope of the regression line added to the RSI values is positive, then we can say that there is an increasing trend, and similarly, if the slope is negative, then we can say that there is a decreasing trend. Unfortunately, this will only help us to determine the trends for the whole period. We will not be able to use it to see partial changes over time by evaluating the linear slope of the RSI values. To be able to see the partial changes and the extremums, the modified version of the RSI graph, which has RSI 50, can be used. Simply, if the volatility of the values is not high, then the hydro-climatological time series must be distributed around the RSI 50 line. The distribution of the calculated values around the RSI 50 line can be evaluated to partially determine the upward or downward trends. Figure 4 and Figure 5 were not created based on a certain dataset, which means these figures were created based on random data. These figures are only for representing the general look of the MACD and RSI approaches.

2.4. Mann–Kendall Test

The Mann–Kendall test is a test that is widely used in trend analysis and is independent of the distribution of the data. There is no requirement for the data to fit a normal distribution. It is also relatively effective against missing data and outliers. The method is based on a study by Mann in 1945 [44]. It was later included in rank analysis in a study conducted by Kendall [45].

2.5. Innovative Şen Trend Test

In this method, developed by Zekai Şen [46], the time series is divided into two equal parts in terms of the number of observations. Both parts are sorted separately in ascending order. The first half is placed on the x-axis and the second half on the y-axis. A 45° (1:1) line on the graph represents the “no trend” state. The trend is evaluated by looking at the distribution of the points around the line [46].

3. Results and Discussions

3.1. MACD and RSI Results

The MACD and the RSI indicators were applied individually to the observed annual average minimum surface temperature (T_min), observed annual average maximum surface temperature (T_max), observed annual average mean surface temperature (T_mean), and observed annual precipitation (P) of Türkiye. Türkiye was selected as a case study to show the applicability of the MACD and RSI to the hydrological data. So, the data set could be more regional or even global in scale. The main concern of this research is not the region but to show the usage and effectiveness of the methods for climatological variables.

The observed annual average minimum surface temperature (Tmin) MACD results were analyzed according to the given graph in Figure 6. The MACD graph was evaluated based on both the centerline cross (blue line crossing the black line) and the signal line cross (blue line crossing the red line). According to the centerline cross-evaluation, an increasing trend of T_min can be seen starting from 1936. This trend looks significant until 1949. In 1949, a short-term decreasing trend until 1952 can be observed in Figure 6. A new upward trend started continuously in 1952, and it was significant until 1973. In 1973, it was possible to see a statistically significant downward trend starting, and it remained until 1979. In 1979, another increasing trend of T_min started, and it went on until 1988. However, if we consider the bar charts’ heights, we cannot say this increasing period is significant. In 1988, we can observe a decreasing trend until 1995 according to the centerline evaluation criterion. The most striking aspect of the graph in Figure 6 starts after 1995. According to the centerline criteria, an increasing trend started in 1995, and it is statistically extremely significant until 2022, when the data set ends. The start of the trend periods is marked, and the year of the trend start is written in Figure 6.

Based on the second evaluation criterion, which is the MACD line crossing the signal line, an increasing trend can be seen starting from 1937. This trend was not very powerful, and it ended in 1941. In 1941, a decreasing trend started, and it has been significant since 1953, even though there are two insignificant increasing trends during this period. In 1953, an increasing trend existed, and it continued until 1972. In this period, in 1964, a decreasing trend occurred for a short period, and it lasted until 1966. As the period is too small, it is not possible to call this period a trend. A similar situation occurred from 1966 to 1967, 1967 to 1970, and 1970 to 1971. There are increasing and decreasing trends during the abovementioned periods. So, if we examine the period starting in 1964 and ending in 1972, we cannot mention statistically significant trends based on the signal line crossing evaluation. In 1972, a statistically significant decreasing trend started, and it was significant until 1978. For the period 1978 to 1987 an increasing trend existed; however, it was not significant. In 1987, we can observe a decreasing trend until 1994. After that year, an extremely significant trend can be seen until 2022, even though there was a small decrease inside this last trend period.

The RSI indicator results of the T_min parameter are presented in Figure 7. As mentioned in the methodology section, the RSI indicator is slightly modified by adding the RSI 50 line to evaluate hydro-climatological variables. The RSI 50 line was accepted as the critical line for evaluations. The linear regression line was added to the distribution of RSI value. The slope of the regression line was calculated as 0.0288 for the T_min parameter. The slope of the regression line is positive, and it indicates a significantly increasing trend. Also, the extremum years, both for the lowest and the highest, were written on the given graph. According to this evaluation, 1933 and 1992 were found to be relatively low for minimum surface temperature. The relatively extreme high values were found for 1955, 2010, and 2018. Another important output of the T_min RSI evaluation is that most of the values are above RSI 50, which means T_min is increasing.

The maximum surface temperature MACD results are given in Figure 8. The MACD results for T_max were evaluated similarly to the T_min parameter. According to the centerline evaluation criteria, a downward trend was seen for 1949–1952. Subsequently, an increasing trend can be observed starting from 1952 and ending in 1972. In 1972, a decreasing trend started, and it was strong until 1998. In 1998, a statistically significant trend started, and it has been ongoing until the end of the data set.

According to the signal line evaluation approach, a decreasing trend started in 1941, and it was in force until 1952. The periods between 1952–1967 and 1978–1994 are not obvious. There are both increasing and decreasing trends in very short periods. So, for the signal line evaluation, these zones were called mixed zones, as they did not have significant trends for a long period. These mixed zones were marked with green circles in Figure 8. After the second mixed zone, a rising trend can be seen in 1994. This trend is significant until the end of the data set.

Figure 9 represents the RSI graph created based on maximum surface temperature data. According to the proposed RSI evaluation approach, a generally increasing trend was found for T_max. The slope of the linear regression line of RSI T_max was calculated as 0.069, which is much higher than the slope value calculated for T_max. The lowest extremum years were 1920 and 1992, and the highest extremum years were 1999 and 2010.

The MACD graph of the mean surface temperature is shared in Figure 10. According to the centerline evaluation, an increasing trend was found for the period of 1934–1948. Subsequently, a short-term downward trend was detected for the period of 1948–1951. After that short decreasing period, an upward trend was seen starting in 1951 and ending in 1972. Following the upward trend, a long-term decreasing trend was observed for the period of 1972–1995. Similar to the minimum and maximum surface temperature evaluations in the last period, a significantly increasing trend was detected for T_max.

The evaluation based on the MACD line crossing signal line showed that there are mixed zones, which include both decreasing and increasing trends in the short term. This evaluation exhibited an increasing trend from 1936 to 1945. After that, a decreasing trend started, and it remained in force until 1954. For the periods of 1951–1971 and 1978–1991, there are mixed trends. These mixed zones were marked with green circles in Figure 10. The most significant decreasing trend was found for the period of 1971–1978, and the most significant upward trend started after 1994, and it is still significant.

The RSI approach was applied to the mean surface temperature data set, and the results are presented in Figure 11. Due to the calculated linear regression slope value (0.0505), it can be said that there is a statistically increasing trend of T_mean. The calculated slope value is less than the calculated T_max value, but it is higher than the T_min slope value. The RSI T_mean evaluation shows that some extremely low values were recorded in 1920, 1933, and 1992. Also, there are some extremely high values for 1955, 2010, and 2018.

The MACD graph of the precipitation parameter is shared in Figure 12. At first glance at the precipitation results, it is possible to observe that the number of increasing and decreasing trends is higher than the surface temperature results. The most significant upward trends of centerline evaluation were found for the 1936–1949, 1963–1972, and 2009–2021 periods. The most significant downward trends of centerline evaluation results were found for the 1956–1963, 1972–1979, 1983–1987, and 1989–1996 periods. The signal line evaluation detected rising significant trends for the 1935–1945, 1962–1972, and 2009–2019 periods. The same evaluation criteria detected serious decreasing trends in the periods of 1945–1962 and 1972–1978. All increasing and decreasing trend periods for precipitation were shared in

Table 2. Results of RSI analysis for all parameters.

Parameter	Lowest Extremums	Highest Extremums	Slope Value	General Trend
Minimum Surface Temperature (°C)	1933 1992	1955 2010 2018	0.0288	Increasing
Maximum Surface Temperature (°C)	1920 1992	1999 2010	0.0690	Increasing
Mean Surface Temperature (°C)	1920 1933 1992	1955 2010 2018	0.0505	Increasing
Precipitation (mm)	1932 2008	1931 1963 2009	−0.0133	Decreasing

for each evaluation criterion separately.

The modified RSI application detected increasing trends for min., max., and mean surface temperature parameters. However, the RSI found a decreasing trend for precipitation. The results of the RSI precipitation are shared in Figure 13. The slope of the linear regression line added to the RSI values was calculated as −0.0133 for precipitation. Relatively, the lowest extremum RSI values were found in 1932 and 2008. The highest extremum values of precipitation were found in 1931, 1963, and 2009.

The results obtained from the RSI analysis are given in Table 2. The highest slope value was calculated for the maximum surface temperature parameter. The only negative slope value was calculated for precipitation. The year 2010 was found to be the most common extreme (highest) year of all kinds of temperatures. The year 1992 was found to be common for the lowest extremes of all temperature classes.

Table 3. Results of the MACD analysis for all parameters.

Minimum Surface Temperature (°C)
MACD Crossing Center Line			MACD Crossing Signal Line
Upward Trend Periods	Downward Trend Periods	Mixed	Upward Trend Periods	Downward Trend Periods	Mixed
1936–1949 1952–1973 1979–1988 1995–Ongoing	1949–1952 1973–1979 1988–1995	-	1937–1941 1953–1972 1978–1987 1994–Ongoing	1941–1953 1972–1978 1987–1994	-
Maximum Surface Temperature (°C)
MACD crossing center line			MACD crossing signal line
Upward Trend Periods	Downward Trend Periods	Mixed	Upward Trend Periods	Downward Trend Periods	Mixed
1952–1972 1998–Ongoing	1949–1952 1972–1998	-	1994–Ongoing	1941–1952 1967–1978	1952–1967 1978–1984
Mean Surface Temperature (°C)
MACD crossing center line			MACD crossing signal line
Upward Trend Periods	Downward Trend Periods	Mixed	Upward Trend Periods	Downward Trend Periods	Mixed
1934–1948 1951–1972 1995–Ongoing	1948–1951 1972–1995	-	1936–1945 1994–Ongoing	1945–1954 1991–1994 1971–1978	1954–1971 1978–1991
Precipitation (mm)
MACD crossing center line			MACD crossing signal line
Upward Trend Periods	Downward Trend Periods	Mixed	Upward Trend Periods	Downward Trend Periods	Mixed
1936–1949 1951–1956 1963–1972 1979–1983 1987–1989 1996–2007 2009–2019	1949–1951 1956–1963 1972–1979 1983–1987 1989–1996 2007–2009	-	1935–1945 1962–1972 1978–1983 1987–1989 1999–2007 2009–2019	1945–1962 1972–1978 1983–1987 1989–1999 2007–2009	-

gives the results of precipitation, minimum, maximum, and mean surface temperature parameters for MACD. It was created to compare all parameters for both MACD crossing the centerline and MACD crossing signal line evaluations. The mixed trends were evaluated only for the MACD crossing signal line criterion of mean and max. surface temperature analysis. Table 3 shows that numerically, more trends were detected for precipitation. However, these trends were mostly short-term trends. This proposed MACD approach will let users not only detect the ongoing trends but also analyze the recent trends from a perspective of relativity. It is also possible to see the extreme points on the MACD graphs. One of the main outputs of the MACD analysis of signal line crossing for all kinds of temperatures is that there is a significantly ongoing increasing trend, which started in 1994.

A summary table was prepared to show the key years in each parameter. The sudden changes, anomalies, and the start year of long-term trends are presented in

Table 4. A summary of key years.

Summary of Key Years
Year	Parameter	Evaluation Criteria	Explanation
1952	Tmin	MACD line crossing zero line	An increasing trend for a long period (until 1973)
1995	Tmin	MACD line crossing zero line	An increasing trend with a high momentum, and it is still valid in 2022
1935	Tmin	RSI	Lowest RSI value for the whole period
2010	Tmin	RSI	Highest RSI value for the whole period
1972	Tmax	MACD line crossing zero line	A decreasing trend for a long period (until 1998)
1998	Tmax	MACD line crossing zero line	An increasing trend with a high momentum, and it is still valid in 2022
1920	Tmax	RSI	Lowest RSI value for the whole period
2010	Tmax	RSI	Highest RSI value for the whole period
1934	Tmean	MACD line crossing zero line	A partly increasing trend for a long period (until 1972) There is only a short decreasing period between 1948–1951
1972	Tmean	MACD line crossing zero line	A decreasing trend for a long period (until 1995)
1995	Tmean	MACD line crossing zero line	An increasing trend with a high momentum, and it is still valid in 2022
1920	Tmean	RSI	Lowest RSI value for the whole period
2010	Tmean	RSI	Highest RSI value for the whole period
1936	Precipitation	MACD line crossing zero line	It is the start point of longest increasing trend
1931	Precipitation	RSI	Highest RSI value for the whole period
1932	Precipitation	RSI	Lowest RSI value for the whole period

.

3.2. Mann–Kendall Test Results

The Mann–Kendall test was applied to the same data set by selecting the alpha value as 0.05, which makes the confidence interval 95%. The Mann–Kendall test results of T_min, T_max, T_mean, and precipitation are presented in

Table 5. Mann–Kendall test results.

Parameter	MK Value	z-Stat	Trend	Direction
Tmin	2708	5.991	Yes	Positive
Tmax	2160	4.778	Yes	Positive
Tmean	2480	5.486	Yes	Positive
Precipitation	71	0.155	No	-

.

In the Mann–Kendall test, increasing trends are detected for all forms of temperature. However, any significant trends are found within the 95% confidence interval.

3.3. Innovative Şen Trend Test Results

As it is described in the methodology section, the innovative Şen trend method is a graphical-based trend investigation approach. The graphs of each parameter are drawn and presented in Figure 14.

For the evaluation of the innovative Şen trend test, three classifications were determined, as can be seen from Figure 14. These classifications depend on the user experience and help to catch the extremum conditions. In this approach for T_min, an increasing trend of around 5% in the medium class was determined. In the high class, the increase rose to 10%. For the T_max parameter, it can be seen that most of the values are around the “no trend” line in the medium class. In high class, an increasing trend is visible around the 5% line. In Figure 14c, it can be seen that there is no certain trend in the low class for T_mean. In the medium class, a slowly increasing trend is visible, and finally, in the high class, there is an increasing trend of more than 5%. The precipitation results are presented in Figure 14d. In the low class, a decreasing trend of around 5 percent was observed. In the middle class, there are partly decreasing and increasing trends, but these are not significant. Finally, in the high class, there is an increasing trend, but it ends up with no trend.

3.4. Discussions

It should be kept in mind that the MACD and RSI values are calculations based on relativity (EMA calculations/average gain or loss). As mentioned in the methodology section, users need to decide the length of the time series of EMA calculations. For example, for calculations of MACD in this study, we used the 12- and 26-year previous records and subsequently calculated the 9-day EMA of MACD for the signal line. For the RSI, we used the 14-year length of records.

The National Oceanic and Atmospheric Administration (NOAA) emphasizes that in climate change investigations, anomalies are more important than absolute temperature values due to indirect effects, such as elevation, urban area, etc., on absolute temperature [47]. According to NOAA’s explanation, the MACD and RSI can be very useful tools to investigate trend variabilities and anomalies. Additionally, one of the advantages of RSI and MACD will be that, by using these tools, the users will not need to define an interval for anomaly detection, as both methods use historical data for an exact time length, and they give relative outputs.

According to the Turkish State Meteorological Service (TSMS) published report on the climatology of Türkiye for 2022, they reported some yearly anomalies [1].

In Figure 15, the yearly calculated anomalies of Türkiye for the mean surface temperature can be seen. The TSMS used the 1991–2020 period as normal, and they calculated anomalies from 1970 to 2022. If we examine the extremum values in Figure 15, we will see that they were extremely high in 2010 and 2018. Furthermore, the values were extremely low in 1976 and 1992. If we check the MACD and RSI outputs, we will see that these indicators are catching the same extremum values correctly without an assumption on a normal period. Additionally, the proposed MACD and RSI approaches have the ability to present the recent and ongoing trends graphically. In the same report written by the TSMS Research Department Hydrometeorology Division [1], there is a similar graph for precipitation anomalies. In this report, extremely high records of precipitation are found for 2009 and 2018, and extremely low values are found for 2008 and 2013. Again, if one checks the MACD and RSI results, he/she will see that the proposed approaches are able to detect the same anomalies.

In this study, in addition to testing MACD and RSI for climatic data with an innovative approach, the classical methods of Mann–Kendall and innovative Şen trend test analysis were also performed with the same data. Mann–Kendall analyses revealed significantly increasing trends for all three versions of the temperature parameter. No trend was detected for precipitation. Similarly, innovative Şen trend analysis also showed increasing trends for the temperature parameter. For precipitation, a partially increasing and partially decreasing distribution is observed in different classifications and ends on the no-trend line. As such, the Mann–Kendall and innovative Şen trend testing methods largely corroborate the MACD and RSI results. However, it should be noted that the RSI method detected a downtrend in the general precipitation trend, albeit with a low slope. In addition to their performance in capturing the general trend, it is understood that it is not possible to capture turning points and historical changes in classical methods. The classical methods MACD and RSI have made it possible to capture the historical changes of the time series and the trends in the process. It has been shown that the MACD approach in particular can be as effective in trend visualization as the innovative Şen trend test, which is known to have a strong visualization performance. Finally, with the MACD approach, it is very easy to follow the momentum change of the trend with histogram bars positioned above and below the x = 0 line.

It is not enough for a hydro-climatological trend to be statistically significant; it is also very important to reveal the physical and social impacts of these trends. In particular, the impacts of climate change on agriculture, water resources management, and the energy sector constitute a critical area of study [48]. In this section, the physical implications of the findings are discussed, and the contributions of the study to decision makers and application areas are emphasized. The findings of the study showed that the increasing temperature trends detected after 1994 may have multifaceted impacts on agricultural productivity. In particular, the increase in minimum temperatures can have direct impacts on plant growth and harvest times. The outputs of extreme temperatures (peaks recorded in 2010 and 2018) are likely to increase energy demand and increase drought risk to high levels in the respective years. The decrease in precipitation between 1956 and 1963 may have had significant impacts on dam occupancy rates and river flows. The post-2009 precipitation increases may have increased flood risks and created critical situations in terms of infrastructure management. At this point, the extreme climate event reports presented by NOAA [48] are consistent with the findings of the study. The temperature increases recorded in 2010 and 2018 and the precipitation increase recorded in 2009 can be linked to global extreme weather events. These findings suggest that climate anomaly patterns can be analyzed more precisely with techniques such as MACD and RSI.

The physical evaluations revealed that the study is not merely a statistical analysis but also offers critical outputs that can be applied in real-world scenarios. By delving into the physical meanings of MACD (Moving Average Convergence–Divergence) and RSI (Relative Strength Index) indicators, the discussion highlights how these methods do not just provide predictability but also ensure ease of application for decision makers. This dual functionality is essential, as it allows decision makers to leverage these indicators effectively in various hydrometeorological contexts, enhancing their capacity to make informed choices. Furthermore, understanding the underlying physical interpretation of these indicators can aid in recognizing climatological trends and potential precaution plans, ultimately leading to improved performance in water management activities.

This study examines the applicability of MACD and RSI indicators, which are commonly used in financial analysis, for the trend analysis of hydro-climatological data. The findings demonstrate that these techniques effectively detect trends and anomalies in climate data. In particular, the MACD indicator is valuable for identifying long-term climate trends, while the RSI indicator effectively detects short-term anomalies and extreme values. These results provide a new perspective on analyzing climate data.

4. Conclusions

Trend investigation methods are very useful tools for detecting recent changes or ongoing trends of hydro-climatological time series. Traditional methods, such as Mann–Kendall and Spearman’s rho test, are widely used and accepted in climatological research. Recently, some innovative trend investigation approaches, like the innovative Şen trend test, were introduced and used for hydro-climatological trend investigations. In this study, a unique and different strategy was developed to analyze hydro-climatological trends and define the anomalies over time. For this purpose, two of the very well-known market trend investigation indicators were selected and, for the first time, applied to the hydro-climatological time series for direct trend detection. The MACD and RSI indicators were tested by accepting the yearly minimum, maximum, mean surface temperature, and yearly precipitation records as time series. Actually, there is no problem with accepting the mentioned records as time series, but in this case, the assumption was that the market or stock prices are time series, as they have continuity except for the closed days of the markets. So, if the MACD and RSI are powerful tools for the detection of trends in stock prices, then they should be powerful for the detection of trends in hydro-climatological time series. The implementation of MACD and RSI showed that both indicators have satisfactory results and can be used for the detection of hydro-climatological trends based on the tested dataset. Also, it is seen that the proposed approaches can be used to determine anomalies. Furthermore, MACD and RSI not only present the ongoing trends but also the recent trends of the time series. In this paper, for the first time, the usability of MACD and RSI indicators in hydro-climatological time series is tested with the data obtained for Türkiye. From the data covering the years 1901–2022, the following conclusions were reached in general.

• Minimum, maximum, and average surface temperatures have shown a significant upward trend since the mid-1990s.
• In all temperature types, due to the relativity, 1992 stands out as the low extreme period and 2010 as the high extreme period.
• In precipitation, a slight decreasing trend was observed in the long term. The negatively sloping regression line in the RSI graph shows that precipitation values generally tend to decrease over time.
• MACD analyses revealed partial fluctuations and short-term trend changes, emphasizing how strong the increases or decreases in recent years have been compared to the past.
• The 50 reference lines and extreme values in the RSI approach indicated that significant deviations (anomalies) can be detected in both temperature and precipitation.
• The application of the Mann–Kendall and innovative Şen trend test showed that both techniques are in agreement with the ongoing trends in general. These results do not disprove the results of the MACD and RSI for the whole period. On the contrary, the results of these methods support the results of MACD and RSI when considering the whole period.
• It is worth noting that MACD and RSI do not only detect the current trend. They also detect extremum points and historical trends of the given climatological time series.

5. Limitations of the Research

Both approaches must be tested under different climatological time series. New developments and modifications can be made based on further analysis outputs of different time series. The MACD and RSI methods used in this study were found to be effective in detecting trends, momentum, and anomalies in the indicated temperature and precipitation patterns. However, it remains to be confirmed whether this proposed approach will work for data sets with different climatic characteristics. Moreover, the proposed method can be considered as a complementary and supportive alternative to traditional methods. In future studies, a sensitivity analysis can be conducted for MACD using different short and long-term EMA values. Different data sets can be analyzed with traditional methods, and the results can be compared with MACD and RSI to statistically demonstrate the reliability of the proposed method.