Monthly GDP Estimation And Coincident Index Based On Low-Rank Matrix Optimization

The coincident index of business cycle is an important standard to measure the current macroeconomic development.In the context of the era of big data,there are more and more factors affecting the development trend of macroeconomics.GDP is not only a key indicator to reflect the macroeconomy,but also an important reference to study the development trend of the macroeconomy.Therefore,it is meaningful to use the mixed-frequency data composed of quarterly GDP and other monthly indicator data as the research object to synthesize the coincident index of business cycle to reflect the volatility changes of the macroeconomic cycle.Based on mixed-frequency data,this paper uses matrix optimization algorithm and onefactor model,ect,to analyze relevant economic data.On this basis,the synthetic coincident index of business cycle is used to determine the turning point of business cycle.Content of the research includes two aspects of the following:Firstly,the low-rank matrix optimization model is used to complete the missing values of the low-frequency data in the mixed-frequency data,and an iterative algorithm for solving the model is designed.First,a non-convex function with matrix kernel norm and norm is used to approximate the model.Then,based on the matrix optimization methods such as the proximal point algorithm and the singular value threshold algorithm,the algorithm is designed to solve the approximate optimization model.Secondly,after completing the missing values of low-frequency data,the relevant economic data are analyzed by combining one-factor model,state space model,maximum likelihood estimation and Kalman filter.After completion,the observation transition matrix in the corresponding state space model is simpler in form.On this basis,numerical experiments are carried out using the quarterly real GDP and the four monthly economic data of the United States,the coincident index of business cycle is synthesized.Numerical comparison was made with other methods,and a line chart of the coincident index of business cycle was drawn with the national bureau of economic research business cycle reference line as a reference.Numerical experiments show that the proposed method can well determine the peak and valley points in the business cycle.The first chapter of this paper briefly introduces the relevant research work on the coincident index of business cycle.The second chapter mainly introduces several missing value completion methods,state space models and Kalman filter.The third chapter presents the lowrank matrix optimization model and algorithm for low-frequency data missing value completion.Then,based on the processed mixed-frequency data,the relevant economic data is analyzed by using one-factor model,maximum likelihood estimation,Kalman filter and Bayesian information criterion,etc;The fourth chapter applies the method to the problem of the turning point of business cycle,and lists the numerical experimental results and conclusions.Finally,the conclusion and outlook are given.