Quantile Regression And Its Application To Financial Time Series

Koenker and Bassett extended the median quantile regression to the general quantile regression in 1978. They used quantile regression to explore the conditional distribution of the response variable on the explanatory variables in regression models. Compared with the traditional regression methods, quantile regression has a more relaxed application conditions. The quantile regression can get more information, as it captures the feature of the distribution not only in the central of the distribution, but also in the upper and the terminal. So it has more unique advantages than the classical least square regression, especially in the process of financial data.The volatility models, the theoryof quantile regression and the quantile regression estimator for TGARCH model are discussed in this paper. The main achievements of this work are listed as follows:1. The volatility and its models are introduced,such as ARCH model given by Engle in 1978, GARCH model by Bollerslev in1986, EGARCH model by Nelson in 1991, TGARCH model by Glonsten in 1993 and Zakoian in 1994.The advantages and disadvantages of such models and the prediction are discussed.2. The theory of quantile regression is studied. First, introducing the basic definition of quantile regression according to the quantile and LSE. Then, the fundamental and inference of quantile regression are studied. Last, some test methods are presented.3. This chapter applied quantile regression to the parameter estimation of TGARCH model, which is a generalization of quantile regression theory. First, the quantile regression estimator of TGARCH model is given. And then, proof the consistency of the estimator. In the last, choosing IBM stock return as training data,according to the output result from R, verifying that the conculsion is feasible.