Titlebook: Asymptotic Theory of Statistical Inference for Time Series; Masanobu Taniguchi,Yoshihide Kakizawa Book 2000 Springer Science+Business Medi

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Local Asymptotic Normality for Stochastic Processes,for the likelihood ratio of general statistical models. Once LAN is proved, the asymptotic optimality of estimators and tests is described in terms of the LAN property. In this chapter we review LeCam’s LAN theorem and show the LAN results for a wide class of vector linear processes, which are permi

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Asymptotic Theory of Estimation and Testing for Stochastic Processes,models. However, in the last twenty years a lot of more complicated stochastic process models have been introduced, such as, nonlinear time series models, diffusion processes, point processes, and nonergodic processes. This chapter is devoted to providing a modern asymptotic estimation and testing t

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Asymptotic Theory for Long-Memory Processes,nvergence is slower than that of the usual AR, MA, and ARMA processes, we call them long-memory processes (or processes with long-range dependence). The phenomenon of long-range dependence was known long before suitable statistical models were introduced. Hurst (1951) studied the records of water fl

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Statistical Analysis Based on Functionals of Spectra, constructing an estimator is to replace an unknown spectral density by the periodogram based on the data. The functional of interest is, however, not always linear with respect to the spectral density. For the nonlinear case replacing the unknown spectral density by the periodogram causes asymptoti

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Discriminant Analysis for Stationary Time Series,n 7.1 we give a basic formulation of discriminant analysis. We begin with the standard methods from classical multivariate analysis and then introduce the frequency domain approach in time series analysis (Section 7.2). Even if the Gaussianity of the process is not assumed, we can construct the Gaus

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Book 2000ral sciences. A model that describes the probability structure of a se- ries of dependent observations is called a stochastic process. The primary aim of this book is to provide modern statistical techniques and theory for stochastic processes. The stochastic processes mentioned here are not restric

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