Introduction to Statistical Time SeriesThe subject of time series is of considerable interest, especiallyamong researchers in econometrics, engineering, and the naturalsciences. As part of the prestigious Wiley Series in Probabilityand Statistics, this book provides a lucid introduction to thefield and, in this new Second Edition, covers the importantadvances of recent years, including nonstationary models, nonlinearestimation, multivariate models, state space representations, andempirical model identification. New sections have also been addedon the Wold decomposition, partial autocorrelation, long memoryprocesses, 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 samplestatistics, and difference equations, has been included. |
Contents
Moving Average and Autoregressive Processes | 21 |
Introduction to Fourier Analysis | 112 |
Spectral Theory and Filtering | 143 |
Some Large Sample Theory | 214 |
Estimation of the Mean and Autocorrelations | 308 |
The Periodogram Estimated Spectrum | 355 |
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Common terms and phrases
a₁ absolute value absolutely summable Analysis approximately Assume asymptotic autocorrelation autocovariance autoregressive moving average autoregressive process autoregressive time series average time series B₁ B₂ central limit theorem computed constructed converges in distribution Corollary correlation covariance function covariance matrix derivatives difference equation distribution function e₁ elements example filter finite follows frequency given hypothesis infinite moving average integrable k-dimensional least squares estimator Lemma limiting distribution linear maximum likelihood estimator moving average process multivariate nonlinear nonsingular normal independent observations obtain order autoregressive process order moving average ordinary least squares parameters periodogram plim polynomial prediction error predictor procedure Proof random variables real numbers representation residuals result sample satisfy Section sequence of uncorrelated spectral density stationary process stationary time series Statist stochastic Table trend unit root variance vector w₁ weights X₁ Y₁ Y₂ Z₁ zero mean Σ Σ σ²
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