## Introduction to Statistical Time SeriesThe 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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### Contents

Moving Average and Autoregressive Processes | 21 |

Average Processes | 58 |

Introduction to Fourier Analysis | 112 |

Spectral Theory and Filtering | 143 |

Stationary Process | 149 |

Some Large Sample Theory | 214 |

Estimation of the Mean and Autocorrelations | 308 |

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### Common terms and phrases

absolute value absolutely summable Analysis approximately Assume assumptions of Theorem asymptotic autocovariance autoregressive moving average autoregressive process autoregressive time series average time series central limit theorem computed confidence interval constructed converges in distribution Corollary covariance function covariance matrix degrees of freedom denote derivatives difference equation distribution function elements example finite fixed frequency given hypothesis infinite moving average integrable least squares estimator Lemma limiting distribution maximum likelihood estimator mean function mean square error moving average process multivariate nonlinear nonsingular normal distribution normal independent observations obtain order autoregressive process order moving average ordinary least squares parameters periodogram polynomial prediction error predictor procedure random variables real numbers regression coefficients representation sample satisfy Section sequence of random spectral density stationary autoregressive stationary process stationary time series stochastic sum of squares symmetric estimator Table trend uncorrelated unit root variance vector zero mean