Download Nonlinear Time Series by Jianqing Fan, Qiwei Yao PDF

By Jianqing Fan, Qiwei Yao

This e-book offers the modern statistical tools and thought of nonlinear time sequence research. The vital concentration is on nonparametric and semiparametric concepts built within the final decade. It covers the options for modelling in state-space, in frequency-domain in addition to in time-domain. to mirror the mixing of parametric and nonparametric tools in examining time sequence info, the e-book additionally provides an updated publicity of a few parametric nonlinear versions, together with ARCH/GARCH types and threshold types. A compact view on linear ARMA types can also be supplied. information coming up in genuine purposes are used all through to teach how nonparametric techniques will help to bare neighborhood constitution in high-dimensional info. very important technical instruments also are brought. The publication should be necessary for graduate scholars, application-oriented time sequence analysts, and new and skilled researchers. it is going to have the worth either in the statistical group and throughout a wide spectrum of alternative fields reminiscent of econometrics, empirical finance, inhabitants biology and ecology. the must haves are uncomplicated classes in likelihood and records. Jianqing Fan, coauthor of the very popular e-book neighborhood Polynomial Modeling, is Professor of information on the college of North Carolina at Chapel Hill and the chinese language college of Hong Kong. His released paintings on nonparametric modeling, nonlinear time sequence, monetary econometrics, research of longitudinal facts, version choice, wavelets and different elements of methodological and theoretical data has been well-known with the Presidents' Award from the Committee of Presidents of Statistical Societies, the Hettleman Prize for inventive and Scholarly success from the college of North Carolina, and through his election as a fellow of the yankee Statistical organization and the Institute of Mathematical information. Qiwei Yao is Professor of records on the London college of Economics and Political technology. he's an elected member of the overseas Statistical Institute, and has served at the editorial forums for the magazine of the Royal Statistical Society (Series B) and the Australian and New Zealand magazine of data.

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Taniguchi and Kakizawa (2000) present a wealth of modern asymptotic theory of inference for various time series models, including (linear) ARMA processes, long-memory processes, nonlinear time series, continuous-time processes, nonergodic processes, diffusion processes, and others. Brillinger (1981) and Priestley (1981) offer wide coverage as well as in-depth accounts of the spectral analysis of time series. Early monographs on nonlinear time series include Priestley (1988). Tong (1990) provides comprehensive coverage of parametric nonlinear time series analysis.

For other parametric models, we refer to Chapter 3 of Tong (1990). We always assume {εt } ∼ IID(0, σ 2 ) instead of WN(0, σ 2 ) when we introduce various nonlinear time series models in this section. Technically, this assumption may be weakened when we proceed with theoretical explorations later on. However, as indicated in a simple example below, a white noise process is no longer a pertinent building block for nonlinear models, as we have to look for measures beyond the second moments to characterize the nonlinear dependence structure.

Therefore, a purely nondeterministic stationary Gaussian process is always linear in the sense that it can be written as an MA(∞) process with normal white noise. A particularly simple case is a q-dependent stationary Gaussian process in the sense that Xt and Xt+k are independent for all k > q. 6). Therefore {Xt } ∼ MA(q). On the other hand, if, given {Xt−1 , · · · , Xt−p }, Xt is independent of {Xt−k , k > p}, it is easy to see that εt ≡ Xt − E(Xt |Xt−1 , · · · , Xt−p ) is independent of {Xt−k , k ≥ 1} since Cov(εt , Xt−k ) = 0 for k ≥ 1.

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