Nonparametric Multiplicative Error Model And Its Application Research On Trading Volume

The main research object of Financial Econometrics is nonnegative financial time series, such as volatility, financial duration, range, volume and so on. Scholars have proposed a series of models for these financial time series. There are autoregressive conditional heteroskedasticity model (ARCH), generalized autoregressive conditional heteroskedasticity models (GARCH), autoregressive conditional duration model (ACD), conditional autoregressive range model(CARR) etc. The GARCH model and ACD model have more research results. However, these models are focused on the specific nonnegative financial time series. In order to analyse all nonnegative financial time series, Engle (2002) proposed a general model-multiplicative error model (MEM). GARCH model, ACD model and CARR model are the special cases of MEM.Compared with parametric multiplicative error model, nonparametric multiplicative error model has its advantages. It’s prone to have parameters misspecification problems in the parametric multiplicative error model, while nonparametric multiplicative error model can make up for this defect. Moreover, in the case of data process is complicated, the performance of nonparametric multiplicative error model is usually better than the performance of parametric multiplicative error model. Reviewing domestic and foreign literature about MEM, we found that no one has yet researched the nonparametric multiplicative error model.In view of this, this paper mainly devotes to the study of nonparametric multiplicative error model and tries to enrich the system of multiplicative error model. This paper primarily contains three parts:model theory, simulation test and empirical analysis. Model theory, we introduce the:GARCH model, ACD model, CARR model and parametric multiplicative error model, compare the similarities and differences between these models, and introduce the maximum likelihood estimation method which is the commonly used estimation method of parametric multiplicative error model. Then we present the nonparametric multiplicative error model. According to the iterative algorithm which is proposed by Buhlmann, McNeil and developed by Cosma, Galli, the feasible algorithm for nonparametric multiplicative error model estimation is given and the consistency of the algorithm is proved. Simulation experiments, in the three cases which are different sample sizes, different distributions of error term, different processes of conditional mean, we use the monte carlo technique to generate simulated data. Based on the simulated data, we establish parametric and nonparametric multiplicative error model and compare the result of the estimation. Empirical analysis, we apply the nonparametric multiplicative error model to Chinese securities market and analysis the trading volume of Shanghai composite index and Shenzhen component index. The results of the simulation experiments and empirical analysis indicate that the nonparametric multiplicative error model often yields better estimates.This topic is the subtopic of national natural science fund "multiplicative error modeling and application research on normegative financial time series in the emerging order driven market"(71101118).