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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