## Introduction to Time Series and Forecasting, Volume 1This book is aimed at the reader who wishes to gain a working knowledge of time series and forecasting methods as applied in economics, engineering, and the natural and social sciences. The book assumes knowledge only of basic calculus, matrix algebra and elementary statistics. This second edition contains detailed instructions on the use of the new totally windows-based computer package ITSM2000. Expanded treatments are also given of several topics treated only briefly in the first edition. These include regression with time series errors, which plays an important role in forecasting and inference, and ARCH and GARCH models, which are widely used for the modeling of financial time series. These models can be fitted using the new version of ITSM. The core of the book covers stationary processes, ARMA and ARIMA processes, multivariate time series and state-space models, with an optional chapter on spectral analysis. Additional topics include the Burg and Hannan-Rissanen algorithms, unit roots, the EM algorithm, structural models, generalized state-space models with applications to time series of count data, exponential smoothing, the Holt-Winters and ARAR forecasting algorithms, transfer function models and intervention analysis. Brief introductions are also given to cointegration and to non-linear, continuous-time and long-memory models. |

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### Contents

Introduction | 1 |

Seasonality | 24 |

Stationary Processes | 45 |

ARMA Models | 83 |

Spectral Analysis | 111 |

Modeling and Forecasting with ARMA Processes | 137 |

Nonstationary and Seasonal Time Series Models | 179 |

Multivariate Time Series | 223 |

Forecasting Techniques | 317 |

Further Topics | 331 |

A Random Variables and Probability Distributions | 369 |

B Statistical Complements | 383 |

Mean Square Convergence | 393 |

423 | |

429 | |

StateSpace Models | 259 |

### Other editions - View all

Introduction to Time Series and Forecasting Peter J. Brockwell,Richard A. Davis Limited preview - 2006 |

Introduction to Time Series and Forecasting Peter J. Brockwell,Richard A. Davis Limited preview - 2016 |

### Common terms and phrases

absolutely summable ACF and PACF ACVF AICC value AIRPASS.TSM applying approximately AR(p ARIMA ARMA model ARMA process ARMA(p autocorrelation function autocovariance function autoregressive best linear predictor bivariate bounds button causal click OK coefficients computed corresponding covariance matrix data set dialog box equations Example fitted model forecasts GARCH Gaussian likelihood given graph hypothesis iid noise innovations algorithm integer invertible ITSM window large-sample maximum likelihood estimators mean squared error mean-corrected minimizes moving-average multivariate obtained one-step predictors option parameters PnXn+h polynomial preliminary estimation Problem program ITSM properties random variables random vector recursions regression residuals sample ACF sample autocorrelation function sample mean seasonal component Section shown in Figure specified spectral density state-space model state-space representation stationary process stationary solution stationary time series statistic transformed transformed series TSTM uncorrelated unit root univariate white noise white noise variance Xn+h Yule-Walker zero zero-mean