A New Adaptive Elastic Net Model With Application In Time Series Data Forecasting

Time series is the development process of random events in chronological order.At present,time series have been widely used in many fields such as hydrology,meteorology,earthquake prediction,economics and military,including temperature changes,personal health data,and futures stock prices,advertising data,etc.Time series analysis is the earliest and most common method in the field of time series.It is a method of observing,analyzing,and searching for the law of change and development of a certain time series.Common time series analysis includes AR model,MA model and their variants.With the development of cloud computing,the number of time series is rapidly expanding,and a large amount of data makes time series analysis more difficult.However,traditional time series analysis methods have certain limitations,that is,they all have the disadvantage of not being able to select variables,which makes the model more complicated.In addition,the accuracy of parameter estimation is not high,which leads to poor forecasting effects.Therefore,how to effectively analyze time series and obtain simple and effective models to generate predictive value has become a hot topic.Therefore,this article analyzes and studies time series from two aspects,including:(1)Aiming at the observation sequence with partial autocorrelation coefficient p-order truncation and autocorrelation coefficient p-order tailing,this paper proposes an improved adaptive elastic net model with partial autocorrelation coefficient(AEN-PAC).The model estimates the weights based on the partial autocorrelation coefficients and adds them to the penalty items of the adaptive elastic net to achieve the purpose of improving the elastic net,so that the model can perform variable selection and parameter estimation on time series data.The relevance is explained.In addition,we also perform special segmentation preprocessing for the time series,that is,perform segmentation processing on all data according to the model order before modeling,and then establish a segmented AEN-PAC model based on the segmented data.In order to propose an effective method to solve the model optimization problem,we respectively establish optimization algorithms for the AEN-PAC model and the segmented AEN-PAC model.Finally,simulation research and empirical analysis show that our model is more accurate in variable selection and parameter estimation than models such as adaptive elastic nets,and our model fitting error and prediction error are smaller,indicating that our model is more accurate in time feasible and advantageous in sequence prediction.(2)For the time series with partial autocorrelation coefficient q-order tailing and autocorrelation coefficient q-order censoring,this paper proposes an improved adaptive elastic net model with autocorrelation coefficient(AEN-AC)and the segmented AEN-AC model.The results of simulation and empirical analysis show that the proposed AEN-AC model has more accurate variable selection and parameter estimation results than the comparison model,so the prediction effect is better.The segmented AEN-AC model can better predict the fluctuation of time series,and the fitting error on the training set and the training error on the test set are smaller,which further shows that our model performs better in time series forecasting.This paper proposes two new adaptive elastic net models for time series data.By incorporating the correlation coefficient into the weight of the adaptive elastic net,the problem of variable selection in traditional time series analysis is solved,and a simple and effective regression model is obtained.According to simulation research and empirical analysis,the model in this paper is feasible for time series forecasting,and the prediction effect is better than the adaptive elastic net model.