## Introduction to Time Series and Forecasting, Volume 1In this book some of the key mathematical results are stated without proof in order to make the underlying theory accessible to a wider audience. The book assumes knowledge only of basic calculus, matrix algebra, and elementary statistics. The emphasis is on methods and the analysis of data sets. The logic and tools of model-building for stationary and non stationary time series are developed in detail and numerous exercises, many of which make use of the included computer package, provide the reader with ample opportunity to develop skills in this area. 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 harmonic regression, the Burg and Hannan-Rissanen algorithms, unit roots, regression with ARMA errors, structural models, the EM algorithm, 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 co integration and to nonlinear, continuous-time and long-memory models. The time series package included in the back of the book is a slightly modified version of the package ITSM, published separately as ITSM for Windows, by Springer-Verlag, 1994. It does not handle such large data sets as ITSM for Windows, but like the latter, runs on IBM-PC compatible computers under either DOS or Windows (version 3.1 or later). The programs are all menu-driven so that the reader can immediately apply the techniques in the book to time series data, with a minimal investment of time in the computational and algorithmic aspects of the analysis. |

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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 |

Introduction to Time Series and Forecasting Peter J. Brockwell,Richard A. Davis Limited preview - 2013 |

### 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