Carbon price dynamic prediction method based on data dimension reduction and quantile

Abstract

The invention provides a dynamic carbon price prediction method based on data dimension reduction and quantiles. The method comprises the following specific steps: S1, constructing dependent variables and prediction factors of a model; the dependent variable is a carbon future return rate, and the predictive factor comprises a macroeconomic variable and a technical index. S2, performing parameter estimation by using a quantile group Lasso estimator; s3, performing prediction based on the parameter estimation value in the step S2; and S4, evaluation of a prediction result: adopting a mean square prediction error and an average absolute percentage error as evaluation indexes, and representing that the prediction precision of the prediction model is relatively high if the values of the mean square prediction error and the average absolute percentage error are relatively small. The quantile group Lasso estimator solves the problem of performing robust grouping variable selection and estimation in high-dimensional data, and is particularly suitable for the situations that error distribution is asymmetric, abnormal values exist, variables have grouping structures and analysis needs to be performed under different quantiles.

Description

Technical Field

[0001] The present invention belongs to the technical field of carbon price prediction, and in particular relates to a method for predicting carbon price dynamics based on data dimensionality reduction and quantiles. Background Art

[0002] Rising greenhouse gas concentrations lead to global warming and climate change, which may undermine the sustainability of human activities and development. In response to global climate change, the carbon market has been specially developed as an effective carbon emission reduction mechanism. It is based on the principle of "cap and trade" and achieves emission reduction by limiting carbon dioxide emissions from carbon-consuming industries.

[0003] The main methods for carbon market forecasting include time series models and statistical learning models. For example, in 2016, Balcilar et al. used the generalized autoregressive conditional heteroskedasticity (GARCH) model to study volatility in the carbon market. In 2017, Zhu and Chevallie used the support vector regression (SVR) model and found that it performed better than the traditional time series model in carbon price forecasting. In 2018, Zhu et al. used the vector autoregression (VAR) model to study the dynamics of the carbon market and found that energy prices and macroeconomic variables had a significant impact on carbon prices. Zhu et al. used the LASSO method to study carbon market forecasting factors. In 2021, Duan et al. used quantile regression to study the asymmetry of the carbon market, and found that energy prices and macroeconomic variables had a significant impact on carbon prices at extreme quantiles. In 2023, Tian et al. used the penalized quantile regression model for fiscal revenue impact analysis. However, the above methods have the following shortcomings in carbon market forecasting:

[0004] (1) Focusing on mean forecasts, it fails to capture the tail behavior and asymmetry of carbon prices;

[0005] (2) focusing on only a small number of variables and failing to fully utilize the large number of potential predictors;

[0006] (3) Even if multiple predictors are considered, the rich information in high-dimensional data cannot be fully utilized due to the limited application of variable selection methods. Summary of the invention

[0007] The purpose of the present invention is to solve the problem that the prior art fails to fully utilize a large number of potential predictive factors and fails to fully utilize the richness in high-order data.

[0008] To achieve the above objectives, the present invention provides a method for predicting carbon price dynamics based on data dimensionality reduction and quantiles, which specifically includes:

[0009] S1. Dependent variables and predictors of the constructed model

[0010] The dependent variable is the standardized carbon futures return rate, and the predictors are standardized macroeconomic variables and technical indicators.

[0011] S2. Parameter estimation using quantile group Lasso estimator

[0012] In the quantile regression with group Lasso penalty, the parameter estimator is defined as:

[0013]

[0014] in, is the parameter estimate of the quantile group Lasso model obtained using the data up to time t, b is the unknown parameter vector, λ is the regularization parameter, which controls the strength of the regularization term, is the quantile loss function at time t, p e is the logarithmic return of carbon price at time e, i is the sample factor, x i,e is the i-th predictor variable at time e, n is the number of predictors, b i is the i-th parameter in vector b, q is the number of groups, j is the length index, It is the g j The parameters in the group, and And T j is the number of parameters in the jth group;

[0015] S3. Prediction based on the parameter estimates of step S2

[0016] Use the quantile group Lasso to predict the carbon price return and obtain the prediction results:

[0017]

[0018] in is the predicted value of carbon futures return rate at time t+1, is the estimated value of the unknown parameter vector i obtained in S2, i is the sample factor, x i,l is the i-th predictor variable at time l;

[0019] S4. Evaluation of prediction results

[0020] In order to evaluate the performance of different prediction models, mean square prediction error (MSPE) and mean absolute percentage error (MAPE) were used as evaluation indicators.

[0021]

[0022] Where m is the length of the training dataset, q is the length of the out-of-sample prediction dataset, and p m+i is the actual price at time m+i, and It is the predicted price of the model at time m+i; smaller values ​​of MSPE and MAPE indicate higher prediction accuracy of the prediction model.

[0023] Furthermore, the macroeconomic variables include an energy source group, an energy price group, a stock market index group, a monetary policy group and an economic information group, and the macroeconomic variables are preprocessed by logarithmic transformation and differential transformation, namely logarithmic returns.

[0024] Furthermore, the technical indicators include moving average rule, momentum rule and volume moving average rule, as follows:

[0025] (1) Moving average rule: Generate a buy signal S at the end of time t by comparing two moving averages u,t =1 or sell signal S u,t =0:

[0026]

[0027] in,

[0028]

[0029] Where u is the number of signals, t is the time, s is the length of the short-term moving average, l is the length of the long-term moving average, and s <l,P t-i is the carbon price return rate level at time ti; i is the time factor;

[0030] (2) Momentum rule: Generate a buy signal or a sell signal by comparing the carbon price return rate at time t and time th:

[0031]

[0032] Among them, v is the quantity index of the signal, P t represents the carbon price return rate at time t, P t-h represents the carbon price return rate at time th, and h represents the period number;

[0033] (3) Volume Moving Average Rule: Generates a buy signal or a sell signal by comparing the sizes of two moving averages based on the volume factor at time t:

[0034]

[0035] and

[0036]

[0037] Among them, w is the number of signals, s is the length of the short-term moving average, and l is the length of the long-term moving average; OBVt-i is the volume factor at time ti, VOL k is the trading volume at time k; D k is a binary variable, D k The value of P k -P k-1 Decide, when P k -P k-1 >0, the value is 1. k -P k-1 When ≤0, the value is -1 ； P k is the carbon price return rate at time k, P k-1 is the carbon price return rate at time k-1.

[0038] Beneficial effects:

[0039] 1. Selection of grouping variables: The quantile group Lasso model realizes the selection of grouping variables by introducing the group Lasso penalty term under the framework of quantile regression. That is, while maintaining the correlation of variables within the group, the entire group is selected or discarded. Therefore, it can handle a large number of predictive factors of carbon prices well and thus make accurate predictions.

[0040] 2. Combination of asymmetric loss function and group selection: Although traditional quantile regression and Lasso methods can handle asymmetric error distribution and sparsity problems, they cannot simultaneously consider the group structure of variables. The quantile group Lasso model combines the asymmetric loss function of quantile regression and the group selection capability of group Lasso, so that the model can more effectively select relevant variable groups while handling asymmetric error distribution, and can provide a better solution to the problem of carbon price prediction.

[0041] 3. Group model fitting under different quantiles: Different from single quantile regression, the quantile group Lasso model can simultaneously select and estimate grouping variables under different quantiles, which helps to analyze the different effects of variable groups on carbon prices under different conditions, thereby providing more comprehensive analysis results.

[0042] 4. Robustness and sparsity: The quantile group Lasso model inherits the robustness of quantile regression, that is, it can still provide reliable estimates when there are outliers. At the same time, through the regularization effect of the group Lasso, sparsity can be achieved, especially in high-dimensional data, it can effectively select the variable group that has a significant impact on the model, reduce the complexity of the model, and effectively screen out the important factors that affect the trend of carbon prices, so as to use them for accurate prediction.

[0043] 5. Complex relationships between multiple variables: In many practical problems, there are complex relationships between different variables. The quantile group Lasso model can not only capture the nonlinear relationship between variables and the response variable, but also effectively capture the interaction between variable groups through group selection, providing a more accurate and explanatory model. The quantile group Lasso model solves the problem of robust grouping variable selection and estimation in high-dimensional data. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a flow chart of a method for data dimensionality reduction and quantile prediction provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0045] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0046] The application principle of the present invention is further described below in conjunction with the accompanying drawings and specific embodiments.

[0047] Embodiment 1:

[0048] like Figure 1 As shown, a prediction method for carbon price dynamics based on data dimension reduction and quantiles specifically includes:

[0049] S1. Dependent variables and predictors of the constructed model

[0050] Since carbon futures prices fluctuate constantly during trading hours, the dependent variable in this application is the carbon futures return rate, which is defined as the logarithmic monthly rate of change of the carbon futures closing price. Predictors include macroeconomic variables and technical indicators. The dependent variable is the target of the prediction, and the predictor is the factor used to predict the dependent variable. Both the dependent variable and the predictor are standardized. In this application, the predictor is used to predict the dependent variable.

[0051] (I) Macroeconomic variables consist of the following five groups: energy source group, energy price group, stock market index group, monetary policy group and economic information group. In order to ensure stability, macroeconomic variables have been pre-processed by logarithmic transformation and difference transformation, that is, logarithmic return. Among them,

[0052] (1) The predictors of the energy source group include crude oil production, crude oil imports, crude oil inventories, natural gas imports, and natural gas production;

[0053] (2) The predictors of the energy price group include European Brent spot price, US natural gas liquids composite price, US natural gas futures price and UK natural gas futures price;

[0054] (3) The predictors of the stock market index group include the Dow Jones Industrial Average, the UK FTSE 100 Index, the French CAC40 Index, and the German DAX Index;

[0055] (4) The predictors of the monetary policy group include money supply M2;

[0056] (5) The predictors of the economic information group include unemployment rate, inflation rate, short-term interest rate, long-term interest rate and long-term government bond yield.

[0057] (II) Technical indicators are constructed based on three technical rules: Moving Average Rule (MA), Momentum Rule (MOM) and Volume Average Rule (VOL). The details are as follows:

[0058] (1) Moving average rule: refers to a mechanical trading rule that aims to capture trends. By comparing two moving averages, a buy signal (S) is generated at the end of time t. u,t =1) or sell signal (S u,t =0):

[0059]

[0060] in,

[0061]

[0062] Where u is the number of signals, t is the time, s is the length of the short-term moving average, l is the length of the long-term moving average, and s <l,P t-i is the carbon price return rate level at time ti; i is the time factor; the MA rule is very sensitive to changes in price trends, where s = 1, 2, 3 and l = 9, 12.

[0063] (2) Momentum rule: Generate a buy signal or a sell signal by comparing the carbon price return rate at time t and time th:

[0064]

[0065] Among them, v is the quantity index of the signal, P t represents the carbon price return rate at time t, P t-h represents the carbon price return rate at time th, h represents the period number, where h=1,2,3,6,9,12.

[0066] (3) Volume Moving Average Rule: Generates a buy signal or a sell signal by comparing the size of the two moving averages based on the volume factor (OBV) at time t:

[0067]

[0068] and

[0069]

[0070] Among them, w is the number of signals, s is the length of the short-term moving average, and l is the length of the long-term moving average; OBV t-i is the volume factor at time ti, VOL k is the trading volume at time k; D k is a binary variable, D k The value of P k -P k-1 Decide, when P k -P k-1 >0, the value is 1. k -P k-1 When ≤0, the value is -1 ； P k is the carbon price return rate at time k, P k-1 is the carbon price return rate at time k-1. Similar to the moving average rule, six volume moving average indicators are used, s=1,2,3 and l=9,12.

[0071] S2. Parameter estimation using quantile group Lasso estimator

[0072] The quantile group Lasso estimator is a statistical method that combines quantile regression and group Lasso regularization. It is suitable for scenarios of variable selection and parameter estimation in high-dimensional data. This model is based on quantile regression to study the asymmetric relationship between the response variable and the explanatory variable. In the process of variable selection, group Lasso regularization is introduced to utilize the group structure information of the variables. The solution process of this estimator is achieved by balancing data fitting and regularization. In this process, the model finds the optimal parameters based on the specific quantile effects in the data and selects the variable group at the same time. Parameters refer to the unknown parameters in this estimator, and we need to use data to estimate their values. Specifically, in quantile regression with group Lasso penalty, the parameter estimator is defined as:

[0073]

[0074] in, is the parameter estimate of the quantile group Lasso model obtained using the data up to time t, b is the unknown parameter vector, λ is the regularization parameter, which controls the strength of the regularization term, is the quantile loss function at time t, p e is the logarithmic return of carbon price at time e, i is the sample factor, x i,e is the i-th predictor variable at time e, n is the number of predictors, bi is the i-th parameter in vector b, q is the number of groups, j is the length index, It is the g j The parameters in the group, and And T j is the number of parameters in the jth group;

[0075] S3. Prediction based on the parameter estimation in step S2

[0076] Use the quantile group Lasso to predict carbon price returns and obtain the prediction results

[0077]

[0078] in is the predicted value of carbon futures return rate at time t+1, is the estimated value of the unknown parameter vector i obtained in step S2, i is the sample factor, x i,t is the ith predictor variable at time t.

[0079] S4. Evaluation of prediction results

[0080] This application uses the carbon price of the European Union Carbon Emissions Trading System (ECX EUA) as an example to verify the prediction effect of the above quantile group Lasso model. This application collects the monthly carbon futures closing price observations of the ICE ECX EUA futures continuous contract from March 2009 to December 2020. These data will be used to construct the model's dependent variable, the carbon futures return, which is defined as the logarithmic monthly change in the carbon futures closing price.

[0081] This application divides the entire sample set into an in-sample training dataset and an out-of-sample prediction dataset. First, the parameter estimates of each model are obtained in the in-sample training dataset, and then they are used to obtain prediction results during the out-of-sample period. Secondly, the prediction results are compared with the true values ​​in the out-of-sample dataset. Specifically, the data from January 2010 to December 2019 is used as the in-sample dataset, and the data from January 2020 to December 2020 is used as the out-of-sample dataset. Through this segmentation method, the predictive ability of the model can be evaluated in the time dimension, so as to better understand its performance in practical applications.

[0082] In order to evaluate the performance of different prediction models, this application uses mean square prediction error (MSPE) and mean absolute percentage error (MAPE) as evaluation indicators.

[0083]

[0084] Where m is the length of the training dataset, d is the length of the out-of-sample prediction dataset, and r m+i is the actual price at time m+i, and is the predicted price of the model at time m+i. Smaller values ​​of MSPE and MAPE indicate higher prediction accuracy of the prediction model. This application compares the prediction performance of the quantile group Lasso model with the classic time series model and the traditional high-dimensional prediction model, as shown in Table 1:

[0085] Table 1 Comparison of prediction results

[0086]

[0087]

[0088] Tables (a) and (b) above report the MSPE and MAPE results of the six-month and twelve-month out-of-sample forecast tests, respectively, where the first column of each table gives the candidate forecast models. Because the competing models do not take quantiles into account, for fair comparison, this application evaluates the forecasting ability of the quantile group Lasso model at the median quantile level (i.e., 50% quantile). Since smaller MSPE and MAPE values ​​indicate that the forecasting model has higher forecasting accuracy. Therefore, the most important finding in the table is that in the six-month and twelve-month forecast tests, the MSPE and MAPE values ​​of the quantile group Lasso model are much smaller than all other models. This shows that during the test, the forecasting performance of this model is better than that of other competing models.

[0089] Although ARMA, GARCH, ARMAX(S), and GARCHX(S) models are classic and widely used time series models in economics and financial analysis, here the MSPE and MAPE values ​​are significantly larger compared to the high-dimensional forecasting model group (quantile group Lasso model, Lasso model, adaptive Lasso model, group Lasso model), which means the forecast accuracy is lower. Among the high-dimensional forecasting model group, the quantile group Lasso model performs much better. In the six-month forecast, the quantile group Lasso model has the lowest MAPE and MSPE values. In the twelve-month forecast, the model also performs well, showing its stability and reliability over different time spans.

[0090] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for predicting carbon price dynamics based on data dimension reduction and quantiles, characterized in that: Specifically include: S1. Dependent variables and predictors of the constructed model The dependent variable is the standardized carbon futures return rate, and the predictors are standardized macroeconomic variables and technical indicators. S2. Parameter estimation using quantile group Lasso estimator In the quantile regression with group Lasso penalty, the parameter estimator is defined as: in, is the parameter estimate of the quantile group Lasso model obtained using the data up to time t, b is the unknown parameter vector, λ is the regularization parameter, which controls the strength of the regularization term, is the quantile loss function at time t, p e is the logarithmic return of carbon price at time e, i is the sample factor, x i,e is the i-th predictor variable at time e, n is the number of predictors, b i is the i-th parameter in vector b, q is the number of groups, j is the length index, It is the g j The parameters in the group, and And T j is the number of parameters in the jth group; S3. Prediction based on the parameter estimates of step S2 Use the quantile group Lasso to predict the carbon price return and obtain the prediction results: in is the predicted value of carbon futures return rate at time t+1, is the estimated value of the i-th unknown parameter vector obtained in S2, i is the sample factor, x i,t is the i-th predictor variable at time t; S4. Evaluation of prediction results In order to evaluate the performance of different prediction models, mean square prediction error (MSPE) and mean absolute percentage error (MAPE) were used as evaluation indicators. Where m is the length of the training dataset, q is the length of the out-of-sample prediction dataset, and p m+i is the actual price at time m+i, and It is the predicted price of the model at time m+i; smaller values ​​of MSPE and MAPE indicate higher prediction accuracy of the prediction model.

2. The method for predicting carbon price dynamics based on data dimension reduction and quantile according to claim 1 is characterized in that: The macroeconomic variables include an energy source group, an energy price group, a stock market index group, a monetary policy group and an economic information group, and the macroeconomic variables are preprocessed by logarithmic transformation and differential transformation, namely logarithmic returns.

3. The method for predicting carbon price dynamics based on data dimension reduction and quantile according to claim 1, characterized in that: The technical indicators include moving average rule, momentum rule and volume moving average rule, as follows: (1) Moving average rule: Generate a buy signal S at the end of time t by comparing two moving averages u,t =1 or sell signal S u,t =0: in, Where u is the number of signals, t is the time, s is the length of the short-term moving average, l is the length of the long-term moving average, and s <l,P t-i is the carbon price return rate level at time ti; i is the time factor; (2) Momentum rule: Generate a buy signal or a sell signal by comparing the carbon price return rate at time t and time th: Among them, v is the quantity index of the signal, P t represents the carbon price return rate at time t, P t-h represents the carbon price return rate at time th, and h represents the period number; (3) Volume Moving Average Rule: Generates a buy signal or a sell signal by comparing the sizes of two moving averages based on the volume factor at time t: and Among them, w is the number of signals, s is the length of the short-term moving average, and l is the length of the long-term moving average; OBV t-i is the volume factor at time ti, VOL k is the trading volume at time k; D k is a binary variable, D k The value of P k -P k-1 Decide, when P k -P k-1 >0, the value is 1. k -P k-1 When ≤0, the value is -1 ； P k is the carbon price return rate at time k, P k-1 is the carbon price return rate at time k-1.

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