Subsampling for linear processes with GARCH(1,1) noises: the case of time series regression with a unit root
2015/03/17
研討會日期 : 2015-03-17
時間 : 14:30
主講人 : Professor Chor-Yiu Sin
主持人 : Professor Le-Yu Chen
地點 : Conference Room B110
演講者簡介 : Professor Sin received his Ph.D. in Economics from University of California at San Diego,U.S.A. He is currently a Professor at National Tsing Hua University. His research fields are Time Series Analysis and Applications, Financial Econometrics.
演講摘要 : This paper considers the time series regression with a unit root. Both short-memory and long-memory linear process with possibly heavy-tailed GARCH(1,1) noises are covered. The heavy tail is characterized by α > 0, whereαis the index of regular variation; while the long-memory is characterized by the long-memory index β. Proven in the literature, the errors have finite variance iffα> 2. Following the lines in Phillips (1990), we consider a time series regression with only one lag, but here the error term follows a linear process of GARCH(1,1), rather than i,i,d., noises. Three cases are considered: (i) α< 2; (ii) α= 2; and (iii) α> 2. Case (ii) is a borderline case in which the noise process is also known as in nitevariance IGARCH(1,1). All in all, using the probabilistic results derived in Zhang, Sin and Ling (2015), we generalize the results in Chan and Zhang (2010) from an I(1)-GARCH(1,1) process to an I(1) process with a linear process of GARCH(1,1) noises. Regardless the process is of short-memory or long-memory, forα< 2, the estimated parameter converges in distribution to a functional of two dependent stable processes, one with indexαand the other with indexα/2. Forα≧2, it converges in distribution to a functional of standard Brownian motion. In all three cases, nuisance parameters are involved and for case (i), the nuisance parameters are dicult, if not impossible, to estimate. In view of this, we approximate the distribution by subsampling. An additional merit of using subsampling is that little prior knowledge onα or β is required. The subsampling procedure gives correct asymptotic size under the null of unit root, while its power goes to 1 under the alternative of no unit root. Some simulation results are also reported.
