Introduction to Statistical Time Series
Wiley, 1976 - 470 стор.
The subject of time series is of considerable interest, especially among researchers in econometrics, engineering, and the natural sciences. As part of the prestigious Wiley Series in Probability and Statistics, this book provides a lucid introduction to the field and, in this new Second Edition, covers the important advances of recent years, including nonstationary models, nonlinear estimation, multivariate models, state space representations, and empirical model identification. New sections have also been added on the Wold decomposition, partial autocorrelation, long memory processes, and the Kalman filter. Major topics include: Moving average and autoregressive processes Introduction to Fourier analysis Spectral theory and filtering Large sample theory Estimation of the mean and autocorrelations Estimation of the spectrum Parameter estimation Regression, trend, and seasonality Unit root and explosive time series To accommodate a wide variety of readers, review material, especially on elementary results in Fourier analysis, large sample statistics, and difference equations, has been included.
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MOVING AVERAGE AND AUTOREGRESSIVE PROCESSES
INTRODUCTION TO FOURIER ANALYSIS
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absolute value absolutely summable analysis applied approximately associated assume assumptions autocorrelations autoregressive autoregressive process bounded called coefficients complex computed consider constant constructed contains continuous converges Corollary correlation covariance function covariance matrix cross defined definition derivative difference equation distribution function elements equation error estimator example exists expected expressed Figure filter finite fixed follows Fourier frequency given gives hypothesis independent independent 0,02 initial integrable interval least squares Lemma less limit linear matrix mean square method moving average multiple normal Note observations obtain order autoregressive parameters period periodogram plot polynomial positive prediction predictor probability Proof properties random variables realization regression representation result roots sample satisfy seasonal sequence Show simple spectral density spectrum stationary time series Statist Table Theorem theory tion transform trend uncorrelated variance vector weights write zero