Structural Model With Dynamic Factors Based On The Customer-flow Prediction

In the empirical analysis of panel data,problems are often encountered that the potential factors can not be observed.Therefore,how to fit the unknown potential factors has been great-ly concerned in recent years.In this paper,a new dynamic factor structured model is proposed based on the general linear model and the interactive effect panel data model to be applied on the customer-flow data Yti of Alibaba Koubei platform.The main research work includes the following aspects:(i)The common factor model is used to fit the unobserved variables,and the general linear model is introduced in the form of interactive effect.We propose a two-step estimation method.At the first step,by regarding the interaction effect and white noise together as residuals,we obtain the least squares estimation of the constant coefficient.At the second step,we use the covariance matrix of residuals obtained from the first step by factor analysis to estimate the common factor,factor loading matrix and the dimension r.(ii)By establishing the vector autoregressive model(VAR)of the common factor,the dynamic structure of the common factor is constructed so that the model can be predicted for the dependent variable Yti.Because of the error between the estimated value and the real value of the common factor,this paper innovatively considers the measurement error in the estimation of the dynamic structure of the factor.By using the estimation error,the autoregressive coefficient of the VAR model is estimated by the corrected Yule-Walker equation.Furthermore,in order to predict future customer flow,this paper obtains the prediction formula of Yti through the above methods.(iii)In the aspect of theoretical properties,under certain conditions,we give a proof of the nor-mal asymptotic property of regression coefficient β(see Theorem 2.1);the consistency of estima-tions of factor analysis(see Theorem 2.2,Theorem 2.3);consistency of the corrected Yule-Walker estimation of the VAR model(see Theorem 3.1,Theorem 3.2).Simulation study and real data experiments show the validity of the model proposed in this paper.In the simulation study,the model has obtained not only accurate estimations but also small prediction error results in the different(T,N)groups.In the empirical analysis,the model can effectively reduce the prediction error compared with the ordinary linear least square and the model without considering the measurement error.