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作者 Shao, Xiaofeng
書名 Statistical evaluation of multiresolution model output and spectral analysis for nonlinear time series
國際標準書號 9780542858970
book jacket
說明 183 p
附註 Source: Dissertation Abstracts International, Volume: 67-09, Section: B, page: 5175
Advisers: Michael Stein; Wei Biao Wu
Thesis (Ph.D.)--The University of Chicago, 2006
My dissertation has two parts, which are described as follows: Statistical evaluation of multiresolution model output. We address statistically sub-grid variability, an issue that naturally arises in multiresolution CMAQ model output. CMAQ is the main numerical air quality model used by the US EPA. For example, an 8km resolution CMAQ run does not have the sub-grid information within each 8km x 8km grid box that the 2km resolution run has. Our approach to dealing with sub-grid variability is to describe the space-time conditional distribution of high resolution output given its low resolution counterpart. A novel conditional simulation approach is proposed to produce an ensemble of high resolution runs based on the runs we have, and various criteria are used to assess whether our simulated high resolution runs capture the overall space-time variability of the original high resolution runs. The main idea of our algorithm is to apply a nonlinear filter to the high resolution runs based on the low resolution runs, then perform a time domain block bootstrap for the residuals simultaneously over space. The implications for space-time extremes are examined and a clear advantage of our approach is demonstrated over existing methods
Spectral analysis for nonlinear time series. We develop a systematic spectral theory for nonlinear processes. For short-range dependent processes, we establish the asymptotic properties of the discrete Fourier transform at Fourier frequencies, asymptotic normality of spectral density estimates, optimal rate of maximal deviation and consistency of frequency domain bootstrap. In the above work, mixing type conditions are avoided. Instead, we impose conditions only involving conditional moments, which can be easily verified for a variety of nonlinear time series models. For a class of fractionally integrated nonlinear processes, we study the asymptotic properties of the local Whittle estimator of long memory parameter. Our formulation is general enough to include various conditional heteroskedastic models and confirms the findings from finite sample simulations that the local Whittle estimator is robust to conditional heteroskedasticity. Under the same framework, we obtain the exact local asymptotic powers of nonparametric and semiparametric tests for long memory
School code: 0330
DDC
Host Item Dissertation Abstracts International 67-09B
主題 Statistics
0463
Alt Author The University of Chicago
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