High-dimensional Time Series Data Prediction Problems Research Based On Dynamic PCA

Under the background of big data,information content has leaped and surged.In this period of uncertainty,complexity and dynamics,much data has been generated in the form of high-dimensional time series,such as macroeconomic data,industrial process data,etc.Principal component analysis(PCA)is one of the commonly used feature extraction methods for analyzing high-dimensional time series data such as macroeconomic data.However,the role of a single macroeconomic variable in the overall macroeconomic is variable.For example,as a measure of inflation,when the CPI growth rate is less than 3%,it can be considered that the economy operates well and the price is stable.At this time,the role of CPI in the overall macroeconomic operation is relatively weak.When the CPI growth rate is more than 3% or even 5%(serious inflation),the role of CPI significantly strengthened and the position of CPI is prominent.However,in the classical PCA,the weight of a single macroeconomic variable in each principal component is unchanged,and it does not reflect the dynamic relationship of time series data and the non-synchronous correlation between the sequences.In view of the dynamic and leading lag characteristics of time series data in high-dimensional time series prediction,this paper,based on classical PCA,refers to the Di PCA algorithm,introduces the idea of sliding window into the process of ASPCA,and proposes a new ASDPCA method for feature extraction of high-dimensional time series prediction.It can solve the problem that PCA and ASPCA cannot reflect time-varying weight coefficients of principal components.The appropriate window size is the key to show the advantages of the ASDPCA method.This paper combining the adaptive window selection algorithm and the accuracy of intra-sample prediction,selects the optimal window size.Based on the optimal window size,this paper slides and extracts the principal component sequence as the prediction variable for macroeconomic variables prediction.Explicit expression of time-varying weight coefficient can help us change the perspective of economic observation,and enable us to quantitatively express and study the economic aspects of many different dimensions.Finally,this paper selects 23 commonly used macroeconomic indicators from January 2001 to December 2022,uses Chow-Lin interpolation method to align quarterly GDP data with other macroeconomic monthly data,and forecasts CPI and GDP based on ASDPCA feature extraction.The results show that: under the same cumulative contribution rate,The number of principal components extracted by ASDPCA is significantly less than that extracted by classical PCA and ASPCA;when making short-term forecasts of indicators such as CPI,whose role in the overall economic operation changes,the prediction accuracy under dimensionality reduction based on the method proposed in this paper is better than that of classical PCA and ASPCA.