An arima prediction model optimization method suitable for right-biased distribution of power consumption data

Abstract

The application relates to an ARIMA prediction model optimization method suitable for right-skewed distribution power consumption data. The method comprises the following steps: obtaining historical time series data of resident life power consumption in a target region in a preset time period, and dividing the data into a training set and a test set; performing a normalizing transformation suitable for a right-skewed distribution on the original data of the training set, and performing stationarity inspection and difference processing to determine the optimal difference order; constructing multiple groups of ARIMA candidate models by taking the optimal difference order as a fixed parameter, and screening out an initial optimal ARIMA model; performing white noise inspection on the residual sequence of the initial model and calculating a prediction error index, and determining the optimal ARIMA model after double verification; and using the optimal model to predict the power consumption in the transformed scale to obtain an updated resident life power consumption prediction result. The method can solve the defects of traditional ARIMA models in adapting to non-normal data, improve the result precision and stability, and provide accurate decision support for power dispatching, load distribution and other work.

Description

Technical Field

[0001] This invention belongs to the field of electricity consumption prediction technology, and in particular relates to an optimization method for ARIMA prediction models applicable to right-skewed electricity consumption data. Background Technology

[0002] With the improvement of residents' living standards and the intelligent development of the power system, accurate forecasting of residential electricity consumption has become a core prerequisite for power dispatching, load allocation, and energy optimization, and is of great practical significance for ensuring the stability of power supply and improving energy efficiency. Residential electricity consumption is affected by various factors such as seasonal changes, work and rest habits, climate conditions, and holidays. Its historical time series data shows a clear right-skewed distribution characteristic—that is, electricity consumption is at a low level for most periods, while electricity consumption is significantly higher during a few peak periods (such as summer cooling and winter heating), forming a long-tailed distribution pattern.

[0003] Currently, in the field of time series forecasting, the ARIMA (Autoregressive Integral Moving Average) model is widely used in electricity consumption forecasting due to its simple structure, strong interpretability, and adaptability to linear time series data. However, the traditional ARIMA model assumes that the data follows a normal distribution, and its adaptability to right-skewed data is poor. When the traditional ARIMA model is directly applied to right-skewed residential electricity consumption data, problems such as data distribution distortion and insufficient model fitting accuracy are likely to occur, resulting in large deviations in the prediction results, which are difficult to meet the accurate requirements of actual power dispatching and management.

[0004] In existing technologies, optimization schemes for ARIMA models mostly focus on parameter tuning, difference order optimization, or fusion prediction with other machine learning models. They often ignore the core feature of the right-skewed distribution of residential electricity consumption data and fail to perform targeted optimization of the distribution pattern of the original data. As a result, the model cannot fully extract the effective information from the data during the fitting process, and the prediction accuracy is difficult to improve further.

[0005] In addition, although some optimization schemes attempt to normalize the data, the transformation methods lack specificity and fail to design appropriate transformation strategies based on the quantitative characteristics of the right-skewed distribution. Furthermore, in the model verification and iterative optimization stages, there are problems such as imprecise verification logic and lack of scientific basis for parameter adjustment, resulting in poor stability and insufficient generalization ability of the optimized model, which cannot effectively adapt to the right-skewed distribution electricity consumption data prediction needs of different regions and time periods. Summary of the Invention

[0006] Therefore, it is necessary to provide an ARIMA prediction model optimization method suitable for right-skewed electricity consumption data, which can solve the problem of poor adaptability of traditional ARIMA models to non-normal data, improve the accuracy and stability of prediction results, and effectively solve the technical defects of existing ARIMA models in predicting right-skewed electricity consumption data with insufficient accuracy and poor stability.

[0007] Firstly, this application provides an ARIMA prediction model optimization method applicable to right-skewed electricity consumption data, including:

[0008] Obtain historical time series data of residential electricity consumption in the target area within a preset time period, and divide the historical time series data into training set and test set according to time sequence.

[0009] Perform a normalization transformation on the original data sequence of the training set to adapt to the right-skewed distribution characteristics. Then, perform stationarity testing and differencing on the transformed sequence to obtain a stationary sequence and determine the optimal difference order.

[0010] Using a determined optimal difference order as a fixed parameter, multiple ARIMA candidate models with different parameter combinations are constructed based on stationary sequences. The optimal ARIMA model is initially selected through screening using multi-dimensional information criteria.

[0011] For the initial selection of the best The residual sequence of the model is subjected to white noise test. If the test results show that the residual sequence conforms to the characteristics of white noise and the prediction error index of the initially selected optimal ARIMA model is lower than the preset threshold, then the initially selected optimal ARIMA model is determined as the optimal ARIMA model.

[0012] The optimal ARIMA model after verification was used to perform time series prediction on the test set to obtain the predicted electricity consumption under the transformed scale.

[0013] Based on the electricity consumption forecast, multi-dimensional prediction accuracy indicators are calculated and the optimal ARIMA model is iteratively optimized to generate updated prediction results.

[0014] In one embodiment, a normalization transformation adapted to the right-skewed distribution characteristics is performed on the original data sequence of the training set. The transformed sequence is then subjected to stationarity testing and differencing to obtain a stationary sequence and determine the optimal differencing order, including:

[0015] Based on the original electricity consumption time series of the training set Calculate the skewness value of the sequence that characterizes the right-skewed distribution.

[0016] The formula for calculating the sequence skewness value is: .

[0017] in, Represents the original electricity consumption sequence skewness value, This represents the total number of samples in the electricity consumption sequence of the training set. express The original value of residential electricity consumption at that time. This represents the sample mean of the original electricity consumption sequence. This represents the sample standard deviation of the original electricity consumption sequence.

[0018] Based on the sequence skewness value, the original electricity consumption sequence The distribution pattern is quantitatively determined, and when the determination sequence is a right-skewed distribution... At that time, a normalization transformation method adapted to the corresponding right-skewed distribution characteristics was used to transform the original electricity consumption sequence in the training set, resulting in a transformed sequence with optimized distribution. .

[0019] For the transformed sequence Perform an ADF unit root test, based on the preset significance level and the probability value obtained from the ADF unit root test. Determine the stationary state of the transformed sequence.

[0020] Where, if the test probability value If the transformed sequence is determined to be a stationary sequence, it has reached a stationary state.

[0021] If the test probability value If the transformed sequence is determined to be non-stationary and has not reached a stationary state, then it is determined that the transformed sequence is non-stationary.

[0022] If the transformed sequence is determined If the sequence does not reach a stationary state, perform first-order differencing on the non-stationary sequence, and then perform the ADF unit root test again on the differrated sequence until the sequence test probability value is reached. It reaches a stable state.

[0023] The total number of iterations of the difference is recorded as the optimal difference order. Simultaneously output Stationary sequence after order difference .

[0024] in, The formula for calculating the order difference is: ; This represents the first-order difference operation. express Moment The order difference sequence value.

[0025] In one embodiment, using a determined optimal difference order as a fixed parameter, multiple ARIMA candidate models with different parameter combinations are constructed based on stationary sequences. The preliminary optimal ARIMA model is then selected through multi-dimensional information criteria, including:

[0026] based on Stationary sequence after order difference With the optimal difference order Iterate through the autoregressive order within the preset parameter range. Moving average order Multiple sets of integer combinations to construct Candidate models.

[0027] in, The general formula for the candidate model is: ; Indicates the autoregressive operator, Represents the moving average operator. Indicates the lag operator, This represents the independent and identically distributed random error term.

[0028] Calculate each group separately The AIC, SC, and HQC information criterion values ​​of candidate models are used as the core basis for comprehensive screening to obtain the preliminary optimal ARIMA model.

[0029] In one embodiment, the electricity consumption forecast under the transformed scale is obtained through the following process, including:

[0030] Extract the residual sequence of the initially selected optimal ARIMA model ,use Test statistic to determine the randomness of residuals; The formula for calculating the test statistic is:

[0031]

[0032] in, express Test statistic This represents the total number of samples in the model residual sequence. This indicates the maximum lag order selected for the test. Representing the residual sequence of Autocorrelation coefficient of the first-order sample This represents the degree of freedom correction term.

[0033] according to The test statistic determines the corresponding test probability value. Based on the test probability value Determine the residual sequence Is it white noise?

[0034] When the test probability value When determining the residual sequence It is white noise.

[0035] If the residual sequence If the noise is determined to be white noise and the prediction error index of the initially selected optimal ARIMA model is lower than the preset threshold, then the initially selected optimal ARIMA model is deemed valid and determined as the optimal ARIMA model.

[0036] The optimal ARIMA model was determined and used to perform time series prediction on the test set to obtain the predicted electricity consumption under the transformed scale.

[0037] In one embodiment, the optimal ARIMA model is iteratively optimized based on a multi-dimensional prediction accuracy index calculated from the electricity consumption forecast value to generate an updated prediction result, including:

[0038] Perform an inverse transformation on the predicted electricity consumption value to restore the predicted result.

[0039] The deviation of the prediction results is calculated using an accuracy evaluation algorithm to obtain prediction accuracy index data.

[0040] The prediction accuracy index data is used to determine whether the prediction result has reached the preset reliability threshold.

[0041] If the prediction result fails to reach the reliability threshold, the distribution characteristics of the prediction deviation are determined through error analysis.

[0042] Wherein, prediction bias is defined as By statistically analyzing the mean, variance, and skewness of the prediction deviation, the distribution characteristics of the deviation can be determined. This represents the actual power consumption value of the test set. This represents the predicted result after restoration.

[0043] Key influencing factors are extracted from the characteristics of the prediction deviation distribution to construct an optimized parameter set. Key influencing factors include the mean deviation and the variance correction coefficient.

[0044] Using the optimized parameter set The autoregressive order of the optimal ARIMA model Moving average order The parameters are then corrected and adjusted to obtain the revised prediction parameters.

[0045]

[0046] in, Indicates the adjusted autoregressive order. This indicates the order of the adjusted moving average. , Represents the set of optimization parameters The corresponding order correction factor, This represents the rounding function.

[0047] The electricity consumption forecast is recalculated using the adjusted forecast parameters to generate updated forecast results.

[0048] Secondly, this application also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the method described above.

[0049] Thirdly, this application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the aforementioned method.

[0050] The aforementioned method, computer equipment, and storage medium for optimizing an ARIMA prediction model for right-skewed electricity consumption data involve acquiring historical time-series data of residential electricity consumption in a target area within a preset time period. The historical time-series data is divided into a training set and a test set according to chronological order. The training set is used for model building and parameter optimization, while the test set is used for model validation and accuracy evaluation. A normalization transformation adapted to the right-skewed distribution characteristics is performed on the original data sequence of the training set to eliminate the fitting bias caused by the right-skewed distribution. A stationarity test is performed on the transformed sequence, and the non-stationary sequence is differencing based on the test results until a stationary sequence is obtained. The total number of iterations of differencing is recorded as the optimal differencing order. Using the determined optimal differencing order as a fixed parameter, based on the stationary sequence, all integer combinations of the autoregressive order and the moving average order are traversed within a preset parameter interval to construct multiple sets of different parameter combinations. For each ARIMA candidate model, multi-dimensional information criterion values ​​are calculated, and minimization of these criterion values ​​is used as the core selection criterion to obtain a preliminary optimal ARIMA model. The residual sequence of this preliminary optimal ARIMA model is extracted and subjected to a white noise test. Simultaneously, the prediction error index of this preliminary optimal ARIMA model is calculated. If the test results indicate that the residual sequence conforms to white noise characteristics and the prediction error index is below a preset threshold, then this preliminary optimal ARIMA model is determined as the optimal ARIMA model. The optimal ARIMA model is then used to perform time-series prediction on the test set to obtain electricity consumption prediction values ​​under a transformed scale. Based on the electricity consumption prediction values ​​under the transformed scale, a multi-dimensional prediction accuracy index is calculated. Combined with the deviation information fed back by the accuracy index, the parameters of the optimal ARIMA model are iteratively corrected and optimized to finally generate an updated prediction result for residential electricity consumption in the target area.

[0051] This method addresses the problem of poor adaptability of traditional ARIMA models to non-normal data by performing targeted normalization transformation on the raw data of right-skewed residential electricity consumption, thereby improving the accuracy of model fitting. The optimal difference order is determined through stationarity testing and differencing, and the optimal model is initially selected using multi-dimensional information criteria. The optimal model is then confirmed through dual verification using residual white noise testing and prediction error indices, ensuring the rigor and reliability of model selection. Iterative optimization of the model based on prediction accuracy indices enables dynamic adjustment of model parameters, further reducing prediction bias and improving the accuracy and stability of prediction results. This provides accurate and reliable decision support for power dispatching, load allocation, and other power management tasks, effectively solving the technical defects of existing ARIMA models in predicting right-skewed electricity consumption data, such as insufficient accuracy and poor stability. Attached Figure Description

[0052] To more clearly illustrate the technical solutions in the embodiments or related technologies of this application, the accompanying drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0053] Figure 1 A flowchart illustrating an ARIMA prediction model optimization method for right-skewed electricity consumption data provided in this embodiment of the invention;

[0054] Figure 2 A schematic diagram of the original time series of residential electricity consumption in Beijing from 1978 to 2023, provided for embodiments of the present invention;

[0055] Figure 3 This is a schematic diagram of the distribution histogram of the original electricity consumption sequence and the sequences after different normalization transformations provided in an embodiment of the present invention;

[0056] Figure 4 A schematic diagram comparing the original electricity consumption sequence with sequences after different normalization transformations provided in an embodiment of the present invention;

[0057] Figure 5 This is a schematic diagram of autocorrelation and partial autocorrelation analysis after second-order differencing of the original electricity consumption sequence provided in an embodiment of the present invention.

[0058] Figure 6 This is a schematic diagram comparing the white noise test of the residuals of the ARIMA model under different preprocessing methods provided in the embodiments of the present invention. Detailed Implementation

[0059] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0060] In one embodiment, such as Figure 1 As shown, this application provides an ARIMA prediction model optimization method suitable for right-skewed electricity consumption data, which may include the following steps:

[0061] Step S101: Obtain historical time series data of residential electricity consumption in the target area within a preset time period, and divide the historical time series data into training set and test set according to time order.

[0062] Specifically, historical time-series data of residential electricity consumption in the target area within a preset time period is obtained, and the historical time-series data is divided into a training set and a test set according to time sequence. The historical time-series data is the residential electricity consumption data of the target area recorded continuously in chronological order, covering the electricity consumption values ​​at each moment within the preset time period. The division process strictly follows the chronological order and does not disrupt the temporal logic to avoid data leakage. The training set is used for subsequent model construction, parameter tuning and validation, and the test set is used to test the predictive performance of the model. The typical division ratio is 70%-80% for the training set and 20%-30% for the test set. After division, the training set and test set data are output separately.

[0063] Step S102: Perform a normalization transformation to adapt to the right-skewed distribution characteristics on the original data sequence of the training set, perform stationarity testing and differencing on the transformed sequence, obtain a stationary sequence and determine the optimal differencing order.

[0064] Furthermore, a normalization transformation adapted to the right-skewed distribution characteristics is performed on the original data sequence of the training set. The transformed sequence is then subjected to stationarity testing and differencing to obtain a stationary sequence and determine the optimal differencing order. First, based on the skewness values ​​of the original training set data sequence, it is determined whether the data exhibits a right-skewed distribution. An adapted normalization transformation method is then applied to the right-skewed distribution characteristics to eliminate the fitting bias caused by the right-skewed distribution, resulting in a distribution-optimized transformed sequence. Subsequently, an ADF unit root test is performed on the transformed sequence, and the probability values ​​obtained from the test are used to determine the optimal difference order. To determine the stationarity of a sequence, if If <0.05, it is considered a stationary sequence; if If the difference is ≥0.05, perform first-order differencing on the sequence, then perform ADF unit root testing again. Repeat this process until the sequence reaches stationarity. Record the total number of differencing iterations and determine it as the optimal differencing order. Output the result. A stationary sequence after order difference.

[0065] Step S103: Using the determined optimal difference order as a fixed parameter, construct multiple ARIMA candidate models with different parameter combinations based on stationary sequences, and select the initial optimal ARIMA model through multi-dimensional information criteria.

[0066] Optionally, ARIMA, short for Autoregressive Integral Moving Average, is a classic time series analysis model for modeling, fitting, and trend prediction of non-stationary time series. It is suitable for continuous time series data such as electricity consumption, load, and weather that have time series correlation, fluctuation characteristics, and potential trends.

[0067] ARIMA consists of three core modules, each corresponding to one of the three key order parameters of the model. .

[0068] Schematic illustration: Using a determined optimal differencing order as a fixed parameter, multiple ARIMA candidate models with different parameter combinations are constructed based on stationary sequences. The preliminary optimal ARIMA model is then selected through multi-dimensional information criteria. The optimal differencing order is then used as the basis for further analysis. For a fixed value, at a preset autoregressive order Moving average order Within the parameter range, iterate through all integer combinations to construct multiple sets. Candidate Models: For each candidate model, calculate its AIC, SC, and HQC multi-dimensional information criterion values. Using the minimization of each criterion value as the core screening criterion, comprehensively consider the model fitting effect and complexity, and select the candidate model with the best fitting performance. This model is then determined as the initial optimal ARIMA model, completing the initial screening of models.

[0069] Step S104: Perform a white noise test on the residual sequence of the initially selected optimal ARIMA model. If the test results show that the residual sequence conforms to the characteristics of white noise and the prediction error index of the initially selected optimal ARIMA model is lower than the preset threshold, then the initially selected optimal ARIMA model is determined as the optimal ARIMA model.

[0070] Preferably, a white noise test is performed on the residual sequence of the initially selected optimal ARIMA model. If the test results show that the residual sequence conforms to white noise characteristics and the prediction error index of the initially selected optimal ARIMA model is lower than a preset threshold, then the initially selected optimal ARIMA model is determined as the optimal ARIMA model. First, the residual sequence generated during the fitting process of the initially selected optimal ARIMA model is extracted. ,use The randomness test is performed on the residual series by calculating the test statistic. Obtain the corresponding test probability value ,when If the value is greater than 0.05, the residual sequence is considered to meet the characteristics of white noise. Simultaneously, the prediction error indices of the initially selected optimal ARIMA model are calculated, including mean absolute error and root mean square error. If the residual sequence meets the characteristics of white noise and the prediction error indices are below a preset threshold, it indicates that the model fit is satisfactory and there is no information omission. The initially selected optimal ARIMA model is then determined as the final optimal ARIMA model. If the above conditions are not met, the process is returned to adjustment. Parameters, rebuild candidate models and filter them.

[0071] Step S105: Use the validated optimal ARIMA model to perform time series prediction on the test set to obtain the predicted electricity consumption value under the transformed scale.

[0072] The validated optimal ARIMA model is used to perform time-series predictions on the test set, obtaining the predicted electricity consumption under the transformed scale. The test set data is input into the validated optimal ARIMA model. Based on the stationary sequence variation pattern, optimal difference order, and model parameters learned during training, the model performs time-series predictions on the electricity consumption at each time point in the test set. Since the original training set data has already undergone normalization, the predicted values ​​output by the model are still under the transformed scale, thus obtaining the predicted electricity consumption under the transformed scale.

[0073] Step S106: Calculate the multi-dimensional prediction accuracy index based on the electricity consumption forecast value, iteratively optimize the optimal ARIMA model, and generate the updated prediction results.

[0074] The optimal ARIMA model is iteratively optimized based on multi-dimensional prediction accuracy indices calculated from electricity consumption forecasts to generate updated prediction results. First, multi-dimensional prediction accuracy indices, including mean absolute error and root mean square error, are calculated based on the predicted electricity consumption under different scales and the actual electricity consumption in the test set. These indices quantify the deviation between the predicted results and the actual values. Then, the autoregressive order of the optimal ARIMA model is adjusted based on the deviation information. Moving average order The model is iteratively corrected and adjusted, rebuilt, and its predictions are validated until the prediction accuracy meets the preset requirements. Finally, the updated prediction results of residential electricity consumption in the target area are generated, improving the accuracy and reliability of the predictions.

[0075] The aforementioned method for optimizing an ARIMA prediction model applicable to right-skewed electricity consumption data involves acquiring historical time-series data of residential electricity consumption within a preset time period in the target area. This data is then divided into a training set (for model construction and parameter optimization) and a test set (for model validation and accuracy assessment) in chronological order. The original training set data undergoes a normalization transformation to adapt to a right-skewed distribution, eliminating fitting bias. The transformed sequence is then subjected to stationarity testing and differencing to obtain a stationary sequence and determine the optimal differencing order. Using the optimal differencing order as a fixed parameter, multiple ARIMA candidate models are constructed by iterating through combinations of autoregressive and moving average orders. A preliminary optimal ARIMA model is selected through multi-dimensional information criteria. The residual sequence of the preliminary model undergoes a white noise test, and the prediction error index is calculated. After passing both validations, the model is determined as the optimal ARIMA model. The optimal model is then used to predict electricity consumption under a transformed scale on the test set. Based on the predicted values, an accuracy index is calculated, and the model parameters are iteratively corrected to finally generate an updated prediction result for residential electricity consumption. This method addresses the shortcomings of traditional ARIMA models in adapting to non-normal data through targeted normalization transformation, thereby improving fitting accuracy. Multi-step verification and screening ensure the model's rigor and reliability, while iterative optimization of accuracy indicators enables dynamic parameter adjustment, reducing prediction bias and improving result accuracy and stability. This provides precise decision support for power dispatching, load allocation, and other tasks, effectively solving the pain points of existing technologies.

[0076] In one embodiment, performing a normalization transformation to adapt to the right-skewed distribution characteristics on the original data sequence of the training set, and then performing stationarity testing and differencing on the transformed sequence to obtain a stationary sequence and determine the optimal differencing order may include the following steps:

[0077] Step S201, based on the original power consumption time series of the training set Calculate the skewness value of the sequence that characterizes the right-skewed distribution.

[0078] The formula for calculating the sequence skewness value is: .

[0079] in, Represents the original electricity consumption sequence skewness value, This represents the total number of samples in the electricity consumption sequence of the training set. express The original value of residential electricity consumption at that time. This represents the sample mean of the original electricity consumption sequence. This represents the sample standard deviation of the original electricity consumption sequence.

[0080] Step S202, adjust the original electricity consumption sequence based on the sequence skewness value. The distribution pattern is quantitatively determined, and when the determination sequence is a right-skewed distribution... At that time, a normalization transformation method adapted to the corresponding right-skewed distribution characteristics was used to transform the original electricity consumption sequence in the training set, resulting in a transformed sequence with optimized distribution. .

[0081] Step S203, for the transformed sequence Perform an ADF unit root test, based on the preset significance level and the probability value obtained from the ADF unit root test. Determine the stationary state of the transformed sequence.

[0082] Where, if the test probability value If the transformed sequence is determined to be a stationary sequence, it has reached a stationary state.

[0083] Step S204, if the test probability value If the transformed sequence is determined to be non-stationary and has not reached a stationary state, then it is determined that the transformed sequence is non-stationary.

[0084] Step S205, if the transformed sequence is determined If the sequence does not reach a stationary state, perform first-order differencing on the non-stationary sequence, and then perform the ADF unit root test again on the differrated sequence until the sequence test probability value is reached. It reaches a stable state.

[0085] Step S206: Record the total number of iterations of the difference as the optimal difference order. Simultaneously output Stationary sequence after order difference .

[0086] in, The formula for calculating the order difference is: ; This represents the first-order difference operation. express Moment The order difference sequence value.

[0087] Preferably, as shown in Table 1, this application provides the ADF unit root test results of the original electricity consumption sequence, the natural logarithm transformation sequence, and the square root transformation sequence under different difference orders. value):

[0088] Table 1

[0089]

[0090] Specifically, the skewness value of the original electricity consumption time series X in the training set is calculated to quantify the data distribution pattern. If the calculated skewness value is greater than 0, the electricity consumption series is determined to be right-skewed. In this case, a normalization transformation method adapted to the right-skewed distribution is used to process the original series X, resulting in the transformed series Y, thus eliminating the influence of the original data distribution bias on the modeling. Subsequently, a stationarity test is performed on the transformed series Y using the ADF unit root test method, and the test probability value is calculated. Determine the stationarity of a sequence: If If <0.05, then sequence Y is determined to be a stationary sequence, and no further differencing is required; if If the value is 0.05, then perform a first-order difference operation on the sequence Y to obtain the difference sequence. Then, perform the ADF unit root test again on the differenced series, and repeat this process until a stationary series is obtained. (in (This refers to the difference order, i.e., the optimal difference order). Based on this stationary sequence, an ARIMA model is constructed. The optimal parameter combination is selected using information criteria, the model is trained, and finally, a prediction result that conforms to the actual power consumption scenario is output.

[0091] This embodiment effectively addresses the problem of traditional ARIMA models' poor adaptation to right-skewed data. Through targeted normalization transformation, it eliminates the impact of data distribution bias on modeling. Utilizing ADF unit root testing and iterative differencing, it ensures the stationarity of the modeling data, providing a reliable foundation for model fitting. By scientifically selecting model parameters, it improves model fitting accuracy and prediction precision, effectively capturing the changing patterns of electricity consumption time series and reducing prediction bias. This method requires no complex additional algorithms; it achieves accurate prediction of right-skewed electricity consumption data solely through data preprocessing and model parameter optimization. This provides a scientific and reliable basis for decision-making in power dispatching and load allocation, while reducing the complexity of model construction and optimization. It balances practicality and operability, solving the technical pain points of insufficient accuracy and poor stability of traditional prediction methods in non-normal data scenarios.

[0092] In one embodiment, using a determined optimal difference order as a fixed parameter, multiple ARIMA candidate models with different parameter combinations are constructed based on stationary sequences. The preliminary optimal ARIMA model is then selected through multi-dimensional information criteria. This process may include the following steps:

[0093] Step S301, based on Stationary sequence after order difference With the optimal difference order Iterate through the autoregressive order within the preset parameter range. Moving average order Multiple sets of integer combinations to construct Candidate models.

[0094] in, The general formula for the candidate model is: ; Indicates the autoregressive operator, Represents the moving average operator. Indicates the lag operator, This represents the independent and identically distributed random error term.

[0095] Step S302, calculate each group separately. The AIC, SC, and HQC information criterion values ​​of candidate models are used as the core basis for comprehensive screening to obtain the preliminary optimal ARIMA model.

[0096] Preferably, as shown in Table 2, this application provides the AIC, SC, and HQC values ​​of each fitting model for the second-order difference sequence of the original electricity consumption sequence:

[0097] Table 2

[0098]

[0099] Preferably, as shown in Table 3, this application provides the AIC, SC, and HQC values ​​of each fitted model for the second-order difference sequence of the natural logarithm transformation sequence:

[0100] Table 3

[0101]

[0102] Preferably, as shown in Table 4, this application provides the AIC, SC, and HQC values ​​of each fitted model for the second-order difference sequence of the square root transform sequence:

[0103] Table 4

[0104]

[0105] Specifically, based on the optimal difference order Corresponding stationary sequence (Right now The stationary sequence after differencing (within a preset parameter range) traverses the autoregressive order. Moving average order All combinations of integers, construct multiple sets Candidate models. Among them, the autoregressive order... The degree to which the corresponding model depends on historical data, and the order of the moving average. To ensure the model's ability to smoothly correct for random errors, all candidate models are built based on stationary sequences, ensuring that the model matches the data features.

[0106] The general formula for the candidate model is: ,in For autoregressive operators, the corresponding autoregressive order is... The expression is ; For moving average operators, the corresponding moving average order is... The expression is ; for Order difference operator, For lag operators, For independent and identically distributed random error terms, satisfying , .

[0107] Calculate each group separately The candidate models were evaluated using three information criteria: AIC (Akaike Information Criterion), SC (Schwarz Criterion), and HQC (Hannan-Quinn Criterion). These three criteria comprehensively assess the model's fit and complexity, balancing the model's accuracy in fitting the data and its generalization ability, thus avoiding overfitting or underfitting. The AIC criterion aims to balance model fit with the number of parameters, quantifying the relationship between model fitting error and the number of parameters to prevent overfitting due to excessive parameters. The SC criterion, building upon the AIC criterion, adds a penalty weight for the number of parameters, favoring models with fewer parameters and lower complexity to improve generalization ability. The HQC criterion falls between AIC and SC, balancing fitting accuracy and model simplicity, reducing bias caused by using a single criterion.

[0108] During the screening process, the core criterion was minimizing all three information criteria values. The three criterion values ​​of each group of ARIMA (p,d,q) candidate models were compared and analyzed one by one: First, the AIC values ​​of all candidate models were compared, and the set of candidate models with the smallest AIC values ​​was selected. Then, within this set, the SC values ​​were compared, and the subset with the smallest SC values ​​was selected. Finally, within this subset, the HQC values ​​were compared, and the model with the smallest HQC value was selected. Simultaneously, the fitting effect and complexity of each candidate model were comprehensively considered, and models with large fitting deviations and weak generalization abilities were eliminated—models with fitting errors exceeding the preset range and criterion values ​​deviating significantly from the optimal values ​​were directly eliminated. For models with slightly different three criterion values ​​but overall optimal performance, further screening was conducted based on model parameter complexity, prioritizing models with a reasonable number of parameters, high fitting accuracy, and strong generalization ability. Finally, the preliminary optimal ARIMA models were selected, completing the initial model screening and providing a foundation for subsequent residual white noise testing and model validity verification, ensuring the reliability of subsequent model optimization and prediction.

[0109] This embodiment constructs and screens ARIMA candidate models using the above method, ensuring that the model fits the characteristics of right-skewed electricity consumption data and avoiding fitting bias caused by improper parameter selection. At the same time, by comprehensively screening through multiple criteria, it takes into account both the model's fitting effect and simplicity, reduces the model overfitting problem caused by redundant parameters, improves the model's adaptability to electricity consumption data and prediction accuracy, lays a solid foundation for subsequent model validation and error verification, ensures the reliability and practicality of subsequent prediction results, and effectively solves the problem of insufficient prediction accuracy of traditional ARIMA models in non-normal, right-skewed electricity consumption data.

[0110] In one embodiment, the electricity consumption forecast under the transformed scale is obtained through the following process, which may include:

[0111] Step S401: Extract the residual sequence of the initially selected optimal ARIMA model. ,use Test statistic to determine the randomness of residuals; The formula for calculating the test statistic is:

[0112]

[0113] in, express Test statistic This represents the total number of samples in the model residual sequence. This indicates the maximum lag order selected for the test. Representing the residual sequence of Autocorrelation coefficient of the first-order sample This represents the degree of freedom correction term.

[0114] Step S402, according to The test statistic determines the corresponding test probability value. Based on the test probability value Determine the residual sequence Is it white noise?

[0115] Step S403, when the test probability value When determining the residual sequence It is white noise.

[0116] Step S404, if the residual sequence If the noise is determined to be white noise and the prediction error index of the initially selected optimal ARIMA model is lower than the preset threshold, then the initially selected optimal ARIMA model is deemed valid and determined as the optimal ARIMA model.

[0117] Step S405: Use the determined optimal ARIMA model to perform time series prediction on the test set to obtain the predicted electricity consumption value under the transformed scale.

[0118] Preferably, as shown in Table 5, this application provides comparison data between the actual values ​​of residential electricity consumption in the test set and the predicted values ​​of each model:

[0119] Table 5

[0120]

[0121] Specifically, the residual sequence corresponding to the initially selected optimal ARIMA model is extracted. ,use Test statistics are used to quantitatively determine the random distribution characteristics of the residual sequence; calculation Test statistic, match and determine the corresponding test probability value Using a significance level of 0.05 as the criterion, when When determining the residual sequence It conforms to the characteristics of white noise. Based on the determination that the residual sequence is white noise, the prediction error index of the initially selected optimal ARIMA model is further compared. Only when the prediction error index is lower than the preset threshold can the initially selected optimal ARIMA model be determined to be effective and be identified as the optimal ARIMA model. The optimal ARIMA model determined by double verification is used to perform time series extrapolation and prediction on the test set, and the predicted electricity consumption value under the transformed scale is output.

[0122] This embodiment is illustrated by... The study examines and quantifies the autocorrelation characteristics of residuals from a statistical perspective to objectively determine whether the model has completely extracted effective information from the time-series data. Residuals satisfying the white noise standard indicate that the model has no unextracted time-series correlation features. Simultaneously, a prediction error threshold is introduced as an auxiliary constraint, constructing a dual judgment mechanism combining residual testing and error indices. This avoids model selection bias caused by relying solely on a single statistical test and standardizes the criteria for determining the optimal ARIMA model. The validated model is used to conduct time-series predictions on a test set, ensuring that the generated electricity consumption predictions under different scales possess statistical rationality and time-series adaptability.

[0123] In one embodiment, calculating a multi-dimensional prediction accuracy index based on the electricity consumption forecast value and iteratively optimizing the optimal ARIMA model to generate an updated prediction result may include the following steps:

[0124] Step S501: Perform an inverse transformation on the predicted electricity consumption value to restore the predicted result.

[0125] Preferably, the inverse transformation process corresponds to the normalization transformation method. If the Box-Cox transformation is used, the inverse transformation formula is:

[0126]

[0127] In the formula, This is the original energy scale prediction result after inverse transformation. These are the electricity consumption predictions under different scales output by the ARIMA model. The shape parameters are those of the Box-Cox transformation.

[0128] Step S502: The deviation of the prediction result is calculated using an accuracy evaluation algorithm to obtain the prediction accuracy index data.

[0129] Optionally, based on the actual values ​​of the test set, a multi-dimensional accuracy evaluation algorithm is used to calculate the deviation of the prediction results, thereby obtaining multi-dimensional prediction accuracy index data. The multi-dimensional accuracy evaluation algorithm uses Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE), and Root Mean Square Error (RMSE) as core accuracy indicators, and their calculation formulas are as follows:

[0130]

[0131]

[0132]

[0133] In the formula, To test the actual electricity consumption values, This is the original energy scale prediction result after inverse transformation. This represents the total number of samples in the test set.

[0134] Preferably, as shown in Table 6, this application provides comparative data on the prediction accuracy metrics of each ARIMA model in the test set:

[0135] Table 6

[0136]

[0137] Step S503: Determine whether the prediction result has reached the preset reliability threshold based on the prediction accuracy index data.

[0138] Step S504: If the prediction result does not reach the reliability threshold, the prediction deviation distribution characteristics are determined by error analysis.

[0139] Wherein, prediction bias is defined as By statistically analyzing the mean, variance, and skewness of the prediction deviation, the distribution characteristics of the deviation can be determined. This represents the actual power consumption value of the test set. This represents the predicted result after restoration.

[0140] Step S505: Extract key influencing factors from the prediction deviation distribution characteristics and construct an optimized parameter set. Key influencing factors include the mean deviation and the variance correction coefficient.

[0141] Step S506, using the optimized parameter set The autoregressive order of the optimal ARIMA model Moving average order The parameters are then corrected and adjusted to obtain the revised prediction parameters.

[0142]

[0143] in, Indicates the adjusted autoregressive order. This indicates the order of the adjusted moving average. , Represents the set of optimization parameters The corresponding order correction factor, This represents the rounding function.

[0144] Step S507: Recalculate the electricity consumption forecast using the adjusted forecast parameters to generate an updated forecast result.

[0145] Specifically, an inverse transformation is performed on the electricity consumption forecast value under the transformed scale. This inverse transformation corresponds to the normalization transformation adapted to the right-skewed distribution mentioned earlier, ensuring that the restored forecast result is consistent with the original residential electricity consumption scale, thus obtaining the forecast result at the original scale. An accuracy evaluation algorithm is used to calculate the deviation between the forecast result and the actual electricity consumption value in the test set, generating forecast accuracy index data. The accuracy evaluation algorithm can use Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE), and Root Mean Square Error (RMSE) as core accuracy indicators to quantify the degree of deviation between the forecast result and the actual value. Based on the generated forecast accuracy index data, it is determined whether the forecast result reaches a preset reliability threshold. This reliability threshold is set based on actual electricity forecasting needs and is used to measure the usability of the forecast result. If the forecast result does not reach the preset reliability threshold, the forecast deviation distribution characteristics are determined through error analysis. By statistically analyzing the three core dimensions of the forecast deviation—mean, variance, and skewness—the distribution pattern and characteristics of the deviation are clarified. Key influencing factors are extracted from the forecast deviation distribution characteristics. These key influencing factors include the deviation mean offset and the deviation variance correction coefficient. Based on the extracted key influencing factors, an optimized parameter set is constructed. ; Utilizing the optimized parameter set The autoregressive order of the optimal ARIMA model Moving average order The prediction parameters are then corrected and adjusted to obtain the adjusted prediction parameters. These adjusted prediction parameters are then used in conjunction with the optimal difference order. The ARIMA model was reconstructed to perform electricity consumption forecasting calculations and generate updated forecasts of residential electricity consumption in the target area.

[0146] This embodiment uses inverse transformation to restore the predicted values ​​under the transformed scale to the original electricity consumption scale, ensuring that the prediction results match the actual application scenario and avoiding scale bias from affecting subsequent accuracy evaluation and application. It quantifies the prediction deviation using mean absolute error and root mean square error, providing accurate data support for model optimization. Based on a reliability threshold, it judges the usability of the prediction results and clarifies the necessity of model optimization. When the prediction results do not meet the standards, it determines the deviation distribution characteristics by statistically analyzing the mean, variance, and skewness of the deviation, accurately extracting key influencing factors to construct an optimization parameter set, and achieving the adjustment of the autoregressive order of the ARIMA model. Moving average order The targeted correction process uses a rounding function to ensure parameter rationality and that model parameters are well-matched with bias characteristics. This entire optimization process effectively solves the problems of large prediction bias and insufficient adaptability in the optimal ARIMA model, significantly improving the accuracy and reliability of prediction results. Furthermore, it eliminates the need for complex algorithms, balancing practicality and operability, and providing accurate data for power dispatching, load allocation, and other power management tasks.

[0147] In one embodiment, such as Figure 2 As shown, this application provides the original time-series diagram of residential electricity consumption in Beijing from 1978 to 2023.

[0148] In one embodiment, such as Figure 3 As shown, this application provides distribution histograms of the original electricity consumption sequence and sequences after different normalization transformations, which may include:

[0149] Histograms of the original residential electricity consumption series, the series histograms after natural logarithmic transformation, and the series histograms after square root transformation for Beijing residents from 1978 to 2023. The original series histograms show a significant right-skewed distribution, while the series histograms after logarithmic and square root transformations are closer to a symmetrical normal distribution, which intuitively reflects the effect of the two normalization transformations on the distribution correction of right-skewed electricity consumption data.

[0150] This embodiment uses histograms to visually present the changes in distribution patterns, providing an intuitive basis for the selection of normalization transformation methods and ensuring that the transformed sequence meets the modeling requirements of the ARIMA model.

[0151] In one embodiment, such as Figure 4 As shown, this application provides a QQ comparison chart of the original electricity consumption sequence and sequences after different normalization transformations, which may include:

[0152] QQ plots of the original sequence, the natural logarithm transformed sequence, and the square root transformed sequence; the data points of the original sequence deviate significantly from the normal distribution baseline, while the data points of the sequence after normalization are closer to the baseline, quantitatively verifying that the transformation can effectively improve the non-normality of the data.

[0153] This embodiment uses a QQ plot to test the normality of the data and further confirm the effect of the right-skewed distribution correction.

[0154] In one embodiment, such as Figure 5 As shown, this application provides autocorrelation and partial autocorrelation analysis diagrams after second-order differencing of the original electricity consumption series, which may include:

[0155] The autocorrelation coefficient (AC) curve, partial autocorrelation coefficient (PAC) curve, Q statistic and probability value (significance); based on the truncation and tailing characteristics of autocorrelation and partial autocorrelation, the initial intervals for the autoregression order p and the moving average order q of the ARIMA model can be determined.

[0156] This embodiment improves the efficiency and rationality of candidate model construction by standardizing the range of model parameter values ​​through correlation analysis of stationary sequences.

[0157] In one embodiment, such as Figure 6 As shown, this application provides a comparison chart of white noise test results for ARIMA model residuals under different preprocessing methods, which may include:

[0158] Residual test plots for the original ARIMA model without transformation, the ARIMA model with natural logarithmic transformation, and the ARIMA model with square root transformation are presented. By analyzing the residual autocorrelation, partial autocorrelation distribution, and Ljung-Box Q test probability values, it is determined whether the residuals are white noise. The residual test results for the model corresponding to the square root transformation are the best.

[0159] This embodiment verifies the effectiveness of the optimal ARIMA model through multi-model comparison and testing, ensuring that the model fully extracts effective information from the data.

[0160] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0161] In one embodiment, a computer device is provided, including a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the steps of the ARIMA prediction model optimization method for right-skewed electricity consumption data as described above.

[0162] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps in the above method embodiments.

[0163] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The components described as separate parts may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this disclosure according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0164] The above-described embodiments are merely illustrative of several implementation methods of the embodiments of this application, and their descriptions are relatively specific and detailed. However, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the embodiments of this application, and these modifications and improvements all fall within the protection scope of the embodiments of this application.

Claims

1. An optimization method for ARIMA prediction models applicable to right-skewed electricity consumption data, characterized in that, The method includes: Obtain historical time series data of residential electricity consumption in the target area within a preset time period, and divide the historical time series data into a training set and a test set according to the time sequence. Perform a normalization transformation to adapt to the right-skewed distribution characteristics on the original data sequence of the training set, perform stationarity testing and differencing on the transformed sequence, obtain a stationary sequence and determine the optimal differencing order; Using the determined optimal difference order as a fixed parameter, multiple ARIMA candidate models with different parameter combinations are constructed based on the stationary sequence, and the initial optimal ARIMA model is obtained by screening through multi-dimensional information criteria. A white noise test is performed on the residual sequence of the initially selected optimal ARIMA model. If the test results show that the residual sequence conforms to the characteristics of white noise and the prediction error index of the initially selected optimal ARIMA model is lower than a preset threshold, then the initially selected optimal ARIMA model is determined as the optimal ARIMA model. The optimal ARIMA model after verification is used to perform time series prediction on the test set to obtain the predicted electricity consumption under the transformed scale. Based on the predicted electricity consumption, a multi-dimensional prediction accuracy index is calculated to iteratively optimize the optimal ARIMA model and generate updated prediction results.

2. The method according to claim 1, characterized in that, The process of performing a normalization transformation on the original data sequence of the training set to adapt to the right-skewed distribution characteristics, performing stationarity testing and differencing on the transformed sequence to obtain a stationary sequence and determine the optimal differencing order includes: Based on the original electricity consumption time series of the training set Calculate the skewness value of the sequence that characterizes the right-skewed distribution; The formula for calculating the sequence skewness value is as follows: ; in, Represents the original electricity consumption sequence skewness value, This represents the total number of samples in the electricity consumption sequence of the training set. express The original value of residential electricity consumption at that time. This represents the sample mean of the original electricity consumption sequence. The sample standard deviation represents the original electricity consumption sequence; Based on the sequence skewness value, the original electricity consumption sequence The distribution pattern is quantitatively determined, and when the determination sequence is a right-skewed distribution... Then, a normalization transformation method adapted to the right-skewed distribution characteristics is used to transform the original electricity consumption sequence in the training set to obtain the transformed sequence with optimized distribution. ; For the transformed sequence Perform an ADF unit root test, and compare the results with the probability values ​​obtained from the ADF unit root test based on a preset significance level. Determine the stationary state of the transformed sequence; Where, if the test probability value If so, the transformed sequence is determined to be a stationary sequence, reaching the stationary state; If the test probability value If so, the transformed sequence is determined to be a non-stationary sequence and has not reached the stationary state; If the transformed sequence is determined If the stationary state is not reached, first-order differencing is performed on the non-stationary sequence, and the ADF unit root test is performed again on the differrated sequence until the sequence test probability value is reached. To reach the aforementioned stable state; The total number of iterations of the difference is recorded as the optimal difference order. Simultaneously output Stationary sequence after order difference ; in, The formula for calculating the order difference is: ; This represents the first-order difference operation. express Moment The order difference sequence value.

3. The method according to claim 1, characterized in that, The process involves using the determined optimal difference order as a fixed parameter, constructing multiple sets of ARIMA candidate models with different parameter combinations based on the stationary sequence, and selecting the initial optimal ARIMA model through multi-dimensional information criteria, including: based on The stationary sequence after order difference With the optimal difference order Iterate through the autoregressive order within the preset parameter range. Moving average order Multiple sets of integer combinations to construct Candidate models; Among them, the The general formula for the candidate model is: ; Indicates the autoregressive operator, Represents the moving average operator. Indicates the lag operator, This represents the independent and identically distributed random error term; Calculate the values ​​of each group separately. The AIC, SC, and HQC information criterion values ​​of the candidate models are used as the core basis for comprehensive screening to obtain the preliminary optimal ARIMA model.

4. The method according to claim 1, characterized in that, The predicted electricity consumption value under the transformed scale is obtained through the following process, including: Extract the residual sequence of the initially selected optimal ARIMA model. ,use The test statistic determines the randomness of the residuals; The formula for calculating the test statistic is: in, express Test statistic This represents the total number of samples in the model residual sequence. This indicates the maximum lag order selected for the test. Representing the residual sequence of Autocorrelation coefficient of the first-order sample This indicates the degree of freedom correction term; According to the above The test statistic determines the corresponding test probability value. Based on the test probability value Determine the residual sequence Is it white noise? When the test probability value When, determine the residual sequence The white noise; If the residual sequence If the noise is determined to be white noise and the prediction error index of the initially selected optimal ARIMA model is lower than a preset threshold, then the initially selected optimal ARIMA model is determined to be valid and is identified as the optimal ARIMA model. The determined optimal ARIMA model is used to perform time series prediction on the test set to obtain the predicted electricity consumption value under the transformed scale.

5. The method according to claim 1, characterized in that, The process of calculating multi-dimensional prediction accuracy indices based on the predicted electricity consumption value and iteratively optimizing the optimal ARIMA model to generate updated prediction results includes: Perform an inverse transformation on the predicted electricity consumption value to restore the predicted result; The deviation of the prediction results is calculated using an accuracy evaluation algorithm to obtain prediction accuracy index data; Based on the prediction accuracy index data, determine whether the prediction result reaches the preset reliability threshold; If it is determined that the prediction result does not reach the reliability threshold, the prediction deviation distribution characteristics are determined by error analysis method; Wherein, prediction bias is defined as The distribution characteristics of the prediction deviation are determined by statistically analyzing the mean, variance, and skewness of the prediction deviation. This represents the actual power consumption value of the test set. This represents the predicted result after restoration; Key influencing factors are extracted from the predicted deviation distribution characteristics to construct an optimized parameter set. The key influencing factors include the mean deviation and the variance correction coefficient. Using the optimized parameter set The autoregressive order of the optimal ARIMA model Moving average order Make corrections and adjustments to obtain the adjusted prediction parameters; in, Indicates the adjusted autoregressive order. This indicates the order of the adjusted moving average. , Represents the set of optimization parameters The corresponding order correction factor, This represents the rounding function; The electricity consumption forecast is recalculated using the adjusted forecast parameters to generate an updated forecast result.

6. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 5.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 5.

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