## Higher order asymptotic theory for time series analysisThis book gives higher order asymptotic results in time series analysis. Especially, higher order asymptotic optimality of estimators and power comparison of tests for ARMA processes are discussed. It covers higher order asymptotics of statistics of multivariate stationary processes. Numerical studies are given, and they show that the higher order asymptotic theory is useful and important for time series analysis. Also the validities of Edgeworth expansions of some estimators are proved for dependent situations. Many results will serve as the basis for the further theoretical development and their applications. |

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### Contents

A SURVEY OF THE FIRSTORDER ASYMPTOTIC | viii |

HIGHER ORDER ASYMPTOTIC THEORY | 11 |

VALIDITY OF EDGEWORTH EXPANSIONS | 62 |

Copyright | |

7 other sections not shown

### Other editions - View all

Higher Order Asymptotic Theory for Time Series Analysis Masanobu Taniguchi No preview available - 1991 |

### Common terms and phrases

9qML AMU estimators ancillarity ancillary statistic approximations Assumptions 2.2.1 asymptotic cumulants asymptotic expansion autoregressive process Bartlett's adjustment class of tests coefficients confidence interval defined denote density matrix derive the Edgeworth difficult to show Edgeworth expansion eigenvalues estimator 9n evaluate the asymptotic Fisher information following lemma function Gaussian ARMA processes Gaussian stationary process given higher order asymptotic hypothesis H implies Lemma likelihood function likelihood ratio test maximum likelihood estimator multivariate time series OOO OOO OOO order asymptotic efficiency order asymptotic theory process Xt Proof quasi-maximum likelihood estimator random variables respect to 9 sample covariance matrix satisfies Assumption second-order AMU second-order asymptotically efficient series analysis spectral density stochastic expansion Suppose that Assumptions T(gn Taniguchi third-order AMU third-order asymptotic properties third-order asymptotically efficient trials simulation uniformly unknown parameter Validity of Edgeworth vector Wald's test