Comparison Of Parameter Estimation Methods Of Quantile Autoregressive Model And Its Application In Exchange Rate Data

As one of the common methods of macroeconomic analysis,time series analysis plays a vital role in the applied research of macroeconomic variables.Among them,Autoregression(AR)model is the theoretical basis of time series model,and Ordinary Least Squares(OLS)method is usually used to estimate AR model parameters.Since Koenker and Bassett(1978)proposed the Quantile Regression(QR)method,QR began to be widely applied in the field of macroeconomics research.Under the framework of AR model,QR method was introduced to reflect the asymmetric dynamic change characteristics of macroeconomic series,thus forming the basic idea of Quantile Autoregression(QAR)model.First of all,this paper introduces the basic form of QAR model and its stationarity characteristics,and analyzes and compares the statistical properties of relevant sample moments using Monte Carlo simulation method.Next,based on the common monotonicity characteristics of QAR model regression parameters,three QAR model parameter estimation methods,QR method and two Restricted Conditional Quantile(RCQR)method,were introduced in this paper,and applicability conditions of the three methods were further explored.For convenience,these two RCQR methods are called RCQR(a)and RCQR(b)respectively.It can be found that under the conditions of small samples and large samples,using QR method and RCQR(b)method respectively can significantly improve the estimation accuracy of QAR model.In addition,this paper also introduces the significance test of QAR model and the method of lag order selection.At last,this paper uses QAR model to analyze the dynamic series of USD/RMB exchange rate.According to the critical fractional value predicted by QAR model,the stable and non-stable time points in the exchange rate change path can be distinguished effectively.Finally,it can be found that the USD/RMB exchange rate series has significant asymmetric dynamic change characteristics.