Probabilistic Forecasting of Electricity Demand Incorporating Mobility Data

Round 1

Reviewer 1 Report

This paper shows the forecasting on electricity demand with mobility data.

I think that this topic  is very interesting and useful in real fields.

I like to talk several points for future improvements of this issue.

1. you may consider mobile traffic data such mobile phone and ev data.

2. More newly developed-statistcal methods for density estimation may be applied.

Author Response

1. you may consider mobile traffic data such mobile phone and ev data.

Australian EV uptake rates are concerningly low at 2 percent of all car sales compared to adoption approaching 10 percent internationally (International Energy Agency, 2022). https://arxiv.org/abs/2206.03277

- Added as a Future work (line 112, 113)

2. More newly developed-statistcal methods for density estimation may be applied.

k-nearest neighbors algorithm for density forecasting could be used as a future work. Due to time constraint, this method could not be applied

 

Reviewer 2 Report

I  think your paper is very interesting.  I have two questions.

1. Will mobility data be provided online when incorporated into the forecasting system?  If not, shouldn't we consider delays in data system input?

2. How many hours ago is your system predictive value?

 

Author Response

1. Will mobility data be provided online when incorporated into the forecasting system?  If not, shouldn't we consider delays in data system input?

Response 1: In this work, the offline method is used to make training as straightforward as possible. (Line 450)

2. How many hours ago is your system predictive value?

Response 2: one day (line 688)

 

Reviewer 3 Report

Comments:

1.       Section 3.1, this paper deals with time series with covariates prediction, the time series model should be included in the baseline models because it is the classic statistical prediction model for such type of data.

2.       Section 2.4.1, additional results on the full model should be included in the paper to validate the claim that Spearman correlation coefficients help prevent overfitting and change sensitivity in terms of the metrics defined in Section 2.3. There are papers studying the overfitting problem for the Gaussian Process model that should be included in the results or discussed here.

3.       Section 2.1, line 227, it seems in your X (input), the historical data (y_{t-1}, …y_{t}) is not included. Please provide more details on the input of your model in the paper, are they only the selected features in Section 2.4.1? In literature, there are papers about time series modeling using the Gaussian process. Why did you not use them? Please discuss.

4.       Section 3, line 400-line 405, how you use the kernel density method based on the PI from GP is unclear and needs more details. Suppose based on historical data and covariates, you have PI for y_{t+1} (formula (7), (8)), and how the KDE are used here? It seems the output of the data at time t is scalar, which is the electric demand, not a distributional outcome, how do you compare the PI with the true distribution (which you do not have in the data)?

Minor comments:

1.       Line 310, “dfining”->”defining”.

 

2.       Line 336, what is the formula for the predicted CDF F(x), do you assume the demand at time t follows normal distribution in (5)?

Author Response

1. Section 3.1, this paper deals with time series with covariates prediction, the time series model should be included in the baseline models because it is the classic statistical prediction model for such type of data.

Response 1: time series model should be included in section 3.1 , Figure 4. Day ahead time series forecasting results of different method for three scenarios

1. Section 2.4.1, additional results on the full model should be included in the paper to validate the claim that Spearman correlation coefficients help prevent overfitting and change sensitivity in terms of the metrics defined in Section 2.3. There are papers studying the overfitting problem for the Gaussian Process model that should be included in the results or discussed here.

Response 2: Updated section 2.3, 2.31, result (section 3 added

Table 4.Training set error on three scenarios)

2.3.2. k-fold cross validation section added to discuss and validate GPR overfitting 

Relevant sections have been updated also to reflect the discussion; updated Figure 2. The flowchart of the GPR-KDE probability density forecasting model. to reflect k-fold cross validation

line 181-186

1. Section 2.1, line 227, it seems in your X (input), the historical data (y_{t-1}, …y_{t}) is not included. Please provide more details on the input of your model in the paper, are they only the selected features in Section 2.4.1? 

response: Updated section 2.1

In literature, there are papers about time series modeling using the Gaussian process. Why did you not use them? Please discuss.

response: line 91, 93, 121-126, 131-134, 139-141

1. Section 3, line 400-line 405, how you use the kernel density method based on the PI from GP is unclear and needs more details. Suppose based on historical data and covariates, you have PI for y_{t+1} (formula (7), (8)), and how the KDE are used here? It seems the output of the data at time t is scalar, which is the electric demand, not a distributional outcome, how do you compare the PI with the true distribution (which you do not have in the data)?

Response: updated section 2.2 Probability density prediction based on kernel density estimation

update line 259-271, 285-293

update section 3.3 Probabilistic Density Prediction

Minor comments:

1. Line 310, “dfining”->”defining”.

Response: corrected

2. Line 336, what is the formula for the predicted CDF F(x), do you assume the demand at time t follows normal distribution in (5)?

Response: 

 If the forecast variable  equals the observation , then the value jumps from zero to one. The squared difference between the two CDFs is averaged over the number of observation pairs. The smaller the CRPS metric, the better the accuracy of the PDF. (line 372- 376)

 

Round 2

Reviewer 3 Report

Section 2.2, line 282, the X is already used in Section 2.1 as the input of the Gaussian Process, It should be y_i (same as the output of GP), here.

Section 3.3, lines 595-599, the Gaussian process already has the predicted distribution (you have to use it in the confidence formula), what is the reason for using KDE to fit the histogram by the confidence interval?

Author Response

Section 2.2, line 282, the X is already used in Section 2.1 as the input of the Gaussian Process, It should be y_i (same as the output of GP), here.

Response 1: updated section 2.2 line 290 - 306  

Section 3.3, lines 595-599, the Gaussian process already has the predicted distribution (you have to use it in the confidence formula), what is the reason for using KDE to fit the histogram by the confidence interval?

Response: updated section 2.2 line 284-289

Applying KDE on the predicted distribution from GPR gives a smooth curve estimation of the underlying PDF. It is helpful for creating a more accessible and understandable representation of the distribution, including by plotting a histogram with a fitted density curve. The KDE smooth the distribution and estimates the PDF continuously, eliminating the separate-out impact of the histogram bins.