Statistical Calibration Learning For Highdimensional Time Series

With the enhancement of computer computing power,the prediction of high-dimensional time series has become a very popular and important field in various fields.Macroeco-nomic data forecasting is one of the most significant directions.In the macroeconomic data,there are many important variables,such as unemployment rate,consumer price in-dex,etc.,which affect everyone's production and life and also affect national stability and social development.Macroeconomic forecasts can provide governments,banks,and in-dustry with valuable information to help them make appropriate policies.Therefore,the accurate prediction of macroeconomic variables has practical guiding significance.In this thesis,the model is improved by studying the method of high-dimensional time series prediction and the characteristics of the data.We have mainly done the following studies:(1)Through some statistical analysis,we have a preliminary understanding of the characteristics of macroeconomic data,such as weak signals,nonlinearity,correlations,etc.And we also use a few tests and visual images to visually describe the nature of the data.This section provides a reliable support for the next step of processing,analysis and forecasting.(2)Based on the data characteristics and previous studies,we verify the advantages of ARMA model,Lasso,Random Forest,Lasso ARMA,Group Lasso and the Lead-lag relationship in macro forecasting.And we demonstrate this result using r MSFE.(3)The vector autoregressive model is estimated using Reduced--Rank regression,which we can call a reduced dimensional vector autoregressive model,and this thesis details how to solve and predict this model,and gives simulation and empirical results.(4)Based on the characteristics of macroeconomic data,we illustrate how ARMA filtering is beneficial to the prediction of macroeconomic data and elaborate the mecha-nism of ARMA filtering to calibrate the machine learning model.Finally,we propose two new models,ARMA augment Lasso model and ARMA augment Random Forest model.Then we describe how the new models are built and solved,and show empirical results.