The Study On Theory And Application Of Quantile Autoregression Model

Since quantile regression methods were proposed by Koenker and Bassett in1978, a significant number of quantile regression models have emerged, one of which is the quantile autoregression (QAR) model. QAR model is very popular due to advantages such as high operability for testing and estimation, and can capture non-normal distribution and asymmetry dynamic in financial time series. Furthermore, it is the theoretical starting point for the application of quantile regression in time series analysis. Since then, QAR model and its many refinements have ranked among the most fecund areas of theoretical as well as applied econometrics.The basic idea of QAR model is to integrate the quantile regression and autoregression model, in which autoregressive coefficients may take distinct values over different quantiles of the innovation process, by this means that quantile regression methods can provide an alternative way to study asymmetric dynamics and local persistence in time series. However, there are some problems in QAR models. Further studies are needed. The shortcoming of identifiability and possible misspecification of models suggest that extra care should be taken in improving the estimation and diagnose test for QAR models. With regard to theoretical research, several main contributions are included in this paper, as follows:First, based on the basic QAR model, the research summarizes the ergodic and stationary conditions, analyzes the statistical properties of sample moments via Monte Carlo simulations, introduces the modeling strategies of the QAR model, and we finish by briefly summarizing some recent research areas.Second, since quantile regression curves are estimated individually, the quantile curves can cross, leading to an invalid distribution for the response. There are three methods for estimator QAR model, such as classical regression quantile (QR), the first restricted conditional quantile regression (RCQR1) and the second restricted conditional quantile regression (RCQR2). This paper discussed unbiasedness, consistency and finite sample properties of the three estimators. The analysis of accuracy and stability shows that the QR estimator performs best for finite sample properties, while the accuracy and robustness of RCQR2estimator has shown significant improvement in asymptotic properties.Third, the empirical power and size of the quasi likelihood ratio (QLR) statistics for testing hypothesis about a single population parameter are analyzed via Monte Carlo simulations as well. A simple sequential test is proposed to determine the autoregressive order of the QAR model. Based on the Monte Carlo simulation method, the paper analyses the accuracy of the order selection for QAR model by means of sequential test and information criteria, such as SIC and AIC. Monte Carlo results indicate that sequential test procedures, especially for the Kolmogorov-Smirnov test based on QLR statistics supAn, have power gains over the conventional SIC and AIC.An empirical application of the QAR model to investigate inflation persistence and asymmetric dynamics in China further illustrates the potential of this model. Empirical results show that Chinese inflation has strong persistence, which monotonically increase as the quantiles get large. Unit root tests suggest that the inflation rates are not only global sustainability but also exhibit asymmetric in their dynamic adjustments, in which large negative shocks or deceleration stage tend to induce strong mean reversion, and on the contrary, large positive shocks or acceleration stage tend to induce nonstationarity process. Based on QAR model we can separate periods of nonstationarity from stationary ones and construct an inflation rate ceiling. We make out-of-sample forecast of such a ceiling and present the inflation rate ceiling as an inflation-warning system which could be used by policy makers.