Introduction to Statistical Time SeriesWiley, 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. |
Зміст
INTRODUCTION | 1 |
ESTIMATION FOR AUTOREGRESSIVE AND MOVING | 8 |
MOVING AVERAGE AND AUTOREGRESSIVE PROCESSES | 20 |
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a₁ a₂ absolute value absolutely summable absolutely summable covariance approximately assume assumptions autocorrelations autocovariance autoregressive moving average autoregressive process autoregressive time series average time series b₁ B₂ central limit theorem Chebyshev's inequality computed Corollary correlation function covariance function covariance matrix cross covariance degrees of freedom difference equation e₁ element example filter finite moving average Fourier transform frequency given hypothesis independent 0,0² initial estimators integrable Lemma linear mean square error moving average process normal independent observations obtain order autoregressive process order in probability order moving average parameters periodogram plim polynomial predictor Proof representation roots sample satisfy Section sequence of independent sequence of random sequence of uncorrelated spectral density spectrum standard errors stationary time series statistics summable covariance function Table tion variance W₁ X₁ Y₁ Z₁ zero mean Σ α