High Dimensional Stochastic Regression With Latent Factors Based On Machine Learning Models And Its Application

With the further development of the information age,various data are widely used in all walks of life.This paper studies high-dimensional time series data.The main feature of high-dimensional data is that the data dimension is large,and there are difficulties in model identification and parameter estimation.In order to better model and estimate the high-dimensional time series data,this paper introduces the machine learning model into the potential factor model,and uses data such as daily stock returns to analyze the relevant markets of the National Securities 300 Index.Chang et al.(2015)proposed a high-dimensional random regression model with potential factors,endogenous and nonlinear.The model introduced observable factors into the model,and did not impose stationary conditions on the regression term and potential factor regression process.However,the disadvantage of the model is to use linear estimation to fit the observable factors.The traditional linear estimation has poor fitting effect on nonlinear data and other data with more complex internal relations,resulting in the impact of parameter estimation.In recent years,with the development and application of machine learning,various machine learning models have achieved a series of successes in nonlinear data modeling.Therefore,based on Chang et al.(2015)’s research,this paper estimates the observable factors using machine learning method to obtain the estimated residual part,and then estimates the potential factor process based on this residual part,Based on this,a potential factor model based on machine learning method is constructed.The machine learning method introduced in the observable factor part of the model can significantly improve its fitting ability for nonlinear data,thus improving the prediction accuracy of the residual part,and thus improving the subsequent parameter estimation accuracy.This paper carries out numerical simulation experiments on the potential factor model based on machine learning with the identification accuracy of the number of potential factors r and the estimation effect of the unknown factor load matrix as the evaluation criteria,and designs a linear numerical simulation part and two nonlinear numerical simulation parts.The results show that the potential factor model based on machine learning performs better in these three numerical simulation parts than the potential factor model based on linear estimation and polynomial estimation,especially in the nonlinear numerical simulation part,the parameter estimation is more accurate and more stable.Through the analysis of the actual data of the daily return rate of the stocks of the relevant industries of the National Securities 300 Index from January 2015 to December 2022,it is found that the potential factor model based on machine learning can well estimate the parameters,and in the comparison part of the prediction effect,both the overall prediction and the prediction by industry are better.