The Analysis Of Multivariate Long Memory Time Series With Approximate Factor Model

Financial time series is one important branch on time series,so the method of the research is based on the time series.Meanwhile,financial data has its own specific properties,such as fat-tail distribution,autocorrelation,volatility clustering,long memory and so on.Researches on long memory originated in the natural sciences,and developed in the economic,financial fields.This paper is focused on multivariate long memory time series.The aims of the essay are analyzing the multivariate long memory time series with approximate factor model and determining the number of factors in this data.In order to solve this problem,we develop a new model called approximate factor model with long memory.Then a new approach of determination of the number of factor in this model is also introduced.Theory and simulation both show the consistency of our estimator.In simulations,the estimator exhibits robustness under different long memory parameters.In empirical application,we investigate the linkage between international stock markets and determine the number of factors in 20 industry sector indexes.The main contribution of this paper is developing a new model called approximate factor model with long memory,and it is an extension of approximate factor model.Meanwhile,a new approach of determination of the number of factors is also introduced.This approach is really based on a two-step procedure.The first step is relying on a persistent-nonpersistent decomposition.In the second step,we propose a criteria based on BIC and IC to determine the factor number of nonpersistent part obtained by first step.In simulation,our factor estimate will allow for consistent estimation of r.The simulation results show that,when the long memory parameter is large,our method can accurately estimate the number of real factors,and far better than choosing factors by IC,AIC and BIC.When the long memory parameter is small,our method is slightly inferior to IC,but it is still possible to estimate the number of factors accurately.In conclusion,our approach is better than using IC,AIC or BIC to select the factor numbers and has robustness among different long memory parameters.