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AuthorBrockwell, Peter J. author
TitleIntroduction to Time Series and Forecasting [electronic resource] / by Peter J. Brockwell, Richard A. Davis
ImprintNew York, NY : Springer New York : Imprint: Springer, 1996
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Descript XIII, 422 p. online resource


Some of the key mathematical results are stated without proof in order to make the underlying theory acccessible to a wider audience. The book assumes a 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 introducitons are also given to cointegration and to non-linear, 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


1. Introduction -- 2. Stationary Processes -- 3. ARMA Models -- 4. Spectral Analysis -- 5. Modelling and Forecasting with ARMA Processes -- 6. Nonstationary and Seasonal Time Series Models -- 7. Multivariate Time Series -- 8. State-Space Models -- 9. Forecasting Techniques -- 10. Further Topics -- A. Random Variables and Probability Distributions -- A.1. Distribution Functions and Expectation -- A.2. Random Vectors -- A.3. The Multivariate Normal Distribution -- Problems -- B. Statistical Complements -- B.1. Least Squares Estimation -- B.1.1. The Gauss-Markov Theorem -- B.1.2. Generalized Least Squares -- B.2. Maximum Likelihood Estimation -- B.2.1. Properties of Maximum Likelihood Estimators -- B.3. Confidence Intervals -- B.3.1. Large-Sample Confidence Regions -- B.4. Hypothesis Testing -- B.4.1. Error Probabilities -- B.4.2. Large-Sample Tests Based on Confidence Regions -- C. Mean Square Convergence -- C.1. The Cauchy Criterion -- D. An ITSM Tutorial -- D.1. Getting Started -- D.1.1. Running PEST -- D.2. Preparing Your Data for Modelling -- D.2.1. Entering Data -- D.2.2. Filing Data -- D.2.3. Plotting Data -- D.2.4. Transforming Data -- D.3. Finding a Model for Your Data -- D.3.1. The Sample ACF and PACF -- D.3.2. Entering a Model -- D.3.3. Preliminary Estimation -- D.3.4. The AICC Statistic -- D.3.5. Changing Your Model -- D.3.6. Maximum Likelihood Estimation -- D.3.7. Optimization Results -- D.4. Testing Your Model -- D.4.1. Plotting the Residuals -- D.4.2. ACF/PACF of the Residuals -- D.4.3. Testing for Randomness of the Residuals -- D.5. Prediction -- D.5.1. Forecast Criteria -- D.5.2. Forecast Results -- D.5.3. Inverting Transformations -- D.6. Model Properties -- D.6.1. ARMA Models -- D.6.2. Model ACF, PACF -- D.6.3. Model Representations -- D.6.4. Generating Realizations of a Random Series -- D.6.5. Spectral Properties

Statistics Probabilities Statistics Statistical Theory and Methods Probability Theory and Stochastic Processes


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