數學系演講公告
主 講 人：何淮中  研究員 
 (中央研究院 統計科學研究所) 
講    題：Quantiles, Long Memory and Resampling
日    期：100年03月22日（星期二）下午2:30 – 3:20
地    點：數學系(科學館S433室)

摘    要：

While there is extensive literature on the study of sample quantiles for 
stationary sequences, the corresponding work for an important class of 
nonlinear time series remains largely unaccomplished. In this talk we aim to fill 
the gap by deriving the asymptotic distributions of the sample quantile for the 
long-memory stochastic volatility (LMSV) model. We focus on the estimator 
that minimizes absolute deviation and prove the central limit theorem with 
non-root-n normalization. While the latent component of the LMSV model 
which governs the asymptotic behavior of the quantile estimate is unobserved, 
we show that a resampling scheme can be used to estimate the normalization 
constant including the variance of the limiting distribution. This result enables 
us not only to avoid the difficulty of estimating the convergence rate and the 
limiting variance both needed for constructing the confidence intervals, but 
also allows more flexibility to model the volatility process. A numerical study is 
also presented to illustrate the theory.


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