Investigations on Quantile Regression: Theories and Applications for Time Series Models

• Main Authors: Jau-Er Chen, 陳釗而
• Other Authors: 陳美源
• Format: Others
• Language: en_US
• Published: 2001
• Online Access: http://ndltd.ncl.edu.tw/handle/94035361688512561915

碩士 === 國立中正大學 === 國際經濟研究所 === 89 === This thesis clarifies the theoretical parts and facilitates the practical implementation of quantile regression methods. The estimation, asymptotics, statistical inferences and applications of quantile regression estimator constitute this thesis. Typically, the emphasis is put on time series models. Surprisingly, the quantile regression method had been appreciated little untile recently. Possible reasons could be that: (1) the notorious computational burden of estimation; (2) no well-established asymptotic results; and (3) lack of appropriate inference procedures.All the difficulties stem from the nondifferentiable objective function of quantile regression estimator. The possible solutions are also studied in this thesis. The linear programming has been proposed as an efficient method for estimating quantile regression estimators. The associated literature is briefly reviewed. In this thesis, the stochastic equicontinuity arguments for deriving asymptotics of estimators under nonstandard conditions are discussed. Besides, we derive the asymptotics of quantile regression estimator under i.i.d. errors by stochastic equicontinuity arguments as a prelude. The stochastic equicontinity under $\alpha$-mixing processes is also discussed. Due to the linear programming representations of quantile regression, the statistical inferences can be conducted both through primal and dual problems. In time series models, the sparsity function estimation in hypotheses testing becomes much intractable. In this thesis, the moving block bootstrapping method and rank-inverse test are designed to circumvent the direct estimation of nuisance parameters. The Monte Carlo results suggest that the rank-inverse test is the most suitable test for making inferences under AR(1)-GARCH(1,1) disturbances among the testing methods. As to the time series applications, we implements quantile regression method to construct forecasting models for exploring the loss distribution of assets. By using the capability of conditional distribution exploration, quantile regression method is used to calculate the multiperiod Value at Risk (VaR) of Nikkei 225. The back-testing results indicate that a nonparametric-like tGARCH estimator for estimating one-period-ahead volatility forecasts together with the distribution-free quantile regression method produce the highest accuracy in multiperiod VaR calculations among conventional VaR models.