| The global economy initially recovered in 2021,but in 2022 the situation became darker and related risks began to appear.In the face of the pressure brought by various external environments to the world economy,all countries in the world should also work hard to stabilize their economies and maintain high-speed,high-quality and stable development.Macroeconomic indicators can well reflect whether a country’s economic activities are good,so they play a vital role in measuring the development of a country’s economy.Previous literature research on macroeconomics is based on vector time series analysis,or matrix direct vectorization,which will seriously lose a large amount of relevant information contained in matrix observation itself,and cut off the internal correlation of observation data.Therefore,the macroeconomic indicators are constructed into a matrix time series,and the matrix structure is used to analyze and study them,which can effectively mine the correlation between the data.Therefore,this paper selects the macroeconomic indicators of the current ten major economies,constructs them into a matrix time series,and uses the matrix structure to make qualitative or quantitative analysis and prediction of macroeconomic indicators,so as to provide new ideas for macroeconomic research.This dissertation first expounds the relevant research of macroeconomic forecasting and the development process of matrix time series,and analyzes that macroeconomic indicators can be constructed into matrix time series for research.Secondly,the estimation process of matrix time series,the projection estimation method of matrix factor model and the estimation process of cross least squares estimation method(MAR)of matrix autoregressive model are introduced in detail.Data from 2001 to 2021 from the macroeconomic indicators of the world’s top ten economies were analyzed.The data were preprocessed to construct a matrix time series,and the forward load matrix and backward load matrix were estimated by using the projection estimation method of matrix factor model,and the results showed that they were divided into four categories,the first category was gross domestic product,industrial added value,gross national income and gross national expenditure,the second category was total imports and total exports,the third category was net outflow of outward direct investment(as a proportion of GDP)and net inflow of foreign direct investment(as a proportion of GDP),and the fourth category was inflation rate and unemployment rate.Instantaneous phase synchronization is used to verify the correlation between indicators,and the first two categories have a high correlation.For the prediction of macroeconomic indicators,the cross least squares estimation method(MAR),ARIMA model and exponential smoothing method(ES)of matrix autoregressive model are used,and the prediction accuracy of the three methods is analyzed by root mean square error and mean relative error under the condition that the time series(T=15)is the same,and the results show that MAR(15)> ARIMA > ES,and analyze the indicators with larger data in the matrix time series of macroeconomic indicators that work better in MAR model forecasting.Finally,changing the timing T,not limited to MAR model order 15,can effectively improve the prediction effect of macroeconomic indicators.On this basis,the forecast for 2022 and 2023 shows that the macroeconomic indicators of various countries will increase in the future. |
