# Introduction to Time Series and Forecasting [With CDROM] / Edition 2

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$98.00 (Save 17%) How NOOK Study eTextbooks work NOOK Study eTextbooks from Barnes & Noble are read with the NOOK Study eReader for your PC and Mac. Learn about NOOK Study ## More About This Textbook ### Overview This is an introduction to time series that emphasizes methods and analysis of data sets. The logic and tools of model-building for stationary and non-stationary time series are developed and numerous exercises, many of which make use of the included computer package, provide the reader with ample opportunity to develop skills. Statisticians and students will learn the latest methods in time series and forecasting, along with modern computational models and algorithms. Read More Show Less ### Product Details • ISBN-13: 9780387953519 • Publisher: Springer-Verlag New York, LLC • Publication date: 3/28/2002 • Series: Springer Texts in Statistics Series • Edition description: 2nd ed. 2002. Corr. 9th printing 2010 • Edition number: 2 • Pages: 469 • Sales rank: 673,875 • Product dimensions: 8.20 (w) x 9.42 (h) x 1.44 (d) ### Table of Contents Preface 1 INTRODUCTION 1.1 Examples of Time Series 1.2 Objectives of Time Series Analysis 1.3 Some Simple Time Series Models 1.3.3 A General Approach to Time Series Modelling 1.4 Stationary Models and the Autocorrelation Function 1.4.1 The Sample Autocorrelation Function 1.4.2 A Model for the Lake Huron Data 1.5 Estimation and Elimination of Trend and Seasonal Components 1.5.1 Estimation and Elimination of Trend in the Absence of Seasonality 1.5.2 Estimation and Elimination of Both Trend and Seasonality 1.6 Testing the Estimated Noise Sequence 1.7 Problems 2 STATIONARY PROCESSES 2.1 Basic Properties 2.2 Linear Processes 2.3 Introduction to ARMA Processes 2.4 Properties of the Sample Mean and Autocorrelation Function 2.4.2 Estimation of$\gamma(\cdot)$and$\rho(\cdot)$2.5 Forecasting Stationary Time Series 2.5.3 Prediction of a Stationary Process in Terms of Infinitely Many Past Values 2.6 The Wold Decomposition 1.7 Problems 3 ARMA MODELS 3.1 ARMA($p,q$) Processes 3.2 The ACF and PACF of an ARMA$(p,q)$Process 3.2.1 Calculation of the ACVF 3.2.2 The Autocorrelation Function 3.2.3 The Partial Autocorrelation Function 3.3 Forecasting ARMA Processes 1.7 Problems 4 SPECTRAL ANALYSIS 4.1 Spectral Densities 4.2 The Periodogram 4.3 Time-Invariant Linear Filters 4.4 The Spectral Density of an ARMA Process 1.7 Problems 5 MODELLING AND PREDICTION WITH ARMA PROCESSES 5.1 Preliminary Estimation 5.1.1 Yule-Walker Estimation 5.1.3 The Innovations Algorithm 5.1.4 The Hannan-Rissanen Algorithm 5.2 Maximum Likelihood Estimation 5.3 Diagnostic Checking 5.3.1 The Graph of$\t=1,\ldots,n\
5.3.2 The Sample ACF of the Residuals
5.3.3 Tests for Randomness of the Residuals
5.4 Forecasting
5.5 Order Selection
1.7 Problems
6 NONSTATIONARY AND SEASONAL TIME SERIES
6.1 ARIMA Models for Nonstationary Time Series
6.2 Identification Techniques
6.3 Unit Roots in Time Series Models
6.3.1 Unit Roots in Autoregressions
6.3.2 Unit Roots in Moving Averages
6.4 Forecasting ARIMA Models
6.5 Seasonal ARIMA Models
6.5.1 Forecasting SARIMA Processes
6.6 Regression with ARMA Errors
1.7 Problems
7 MULTIVARIATE TIME SERIES
7.1 Examples
7.2 Second-Order Properties of Multivariate Time Series
7.3 Estimation of the Mean and Covariance Function
7.3.2 Estimation of $\Gamma(h)$
7.3.3 Testing for Independence of Two Stationary Time Series
7.4 Multivariate ARMA Processes
7.4.1 The Covariance Matrix Function of a Causal ARMA Process
7.5 Best Linear Predictors of Second-Order Random Vectors
7.6 Modelling and Forecasting with Multivariate AR Processes
7.6.1 Estimation for Autoregressive Processes Using Whittle's Algorithm
7.6.2 Forecasting Multivariate Autoregressive Processes
7.7 Cointegration
1.7 Problems
8 STATE-SPACE MODELS
8.1 State-Space Representations
8.2 The Basic Structural Model
8.3 State-Space Representation of ARIMA Models
8.4 The Kalman Recursions
8.5 Estimation for State-Space Models
8.6 State-Space Models with Missing Observations
8.7 The EM Algorithm
8.8 Generalized State-Space Models
1.7 Problems
9 FORECASTING TECHNIQUES
9.1 The ARAR Algorithm
9.1.1 Memory Shortening
9.1.2 Fitting a Subset Autoregression
9.1.3 Forecasting
9.1.4 Running the Program ARAR
9.2 The Holt-Winters Algorithm
9.3 The Holt-Winters Seasonal Algorithm
9.4 Choosing a Forecasting Algorithm
1.7 Problems
10 FURTHER TOPICS
10.1 Transfer Function Models
10.1.1 Prediction Based on a Transfer-Function Model
10.2 Intervention Analysis
10.3 Nonlinear Models
10.3.1 Deviations From Linearity
10.3.2 Chaotic Deterministic Sequences
10.3.3 Distinguishing Between White Noise and IID Sequences
10.3.4 Three Useful Classes of Nonlinear Models
10.4 Continuous-Time Models
10.5 Long-Memory Models
10.4 Problems

APPENDIX
Appendix A Random Variables
A.1 Distribution Functions and Expectation
A.2 Random Vectors
A.3 The Multivariate Normal Distribution
A.3 Problems
Appendix 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.4.2 Large-Sample Tests Based on Confidence Regions

Appendix C Mean Square Convergence
C.1 The Cauchy Criterion

Appendix D An ITSM Tutorial
D.1 Getting Started
D.2 Preparing Your Data for Modelling
D.3 Finding a Model for Your Data
D.4.3 Testing for Randomness of the Residuals
D.5 Prediction
D.6 Model Properties
D.6.4 Generating Realizations of a Random Series
Bibliography
Index

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• Anonymous

Posted November 4, 2006

#### When is an Introduction not an Introduction

In the process of building a website targeted to those good folks that are striving valiantly to make a living through Internet marketing, you might think that an early objective would be to assemble a library of good reference material. After all, if you are planning on providing sensible information to your readers, then you should have a few good text books on hand to refer to when you need to be sure that some little tidbit of information might actually work. Well, at least I did. So, I have been scouring the Internet for textbook on the subject of Forecasting, which we share a common interest in. I have purchased a few and, for the most part, they are really quite informative and will be useful when the time comes. There is, however, an exception to this. One book I purchased bears the title 'Introduction to Time Series and Forecasting, Brockwell, Peter J and Richard A Davis'. Being an intelligent sort of chap, I naturally took the word 'Introduction' to mean just that. You know, you've been introduced to people before and becoming introduced usually means that 1. You look at the face. 2. You grasp their hand and shake firmly and 3. You exchange pleasantries, such as 'Hello, it's nice to meet you'. Now, I never blame the person making the introduction if the relationship doesn't work out. After all, it's not their fault that two people hopefully sharing a common interest (after all, why bother making an introduction?) aren't all that compatible. There are likely to be many reasons for the incompatibility, the first of which could be that people travel in different circles and your circle isn't ever going to be part of their circle. Sort of an exclusionary relationship, you might say. And, not to be overly judgmental of others, of course, there may be plenty of good reasons for that. If everyone existed in one social circle, after all, the world would be beyond boring. Anyways, the text book is a wonderful creation, that is, if you're a post-graduate or doctoral candidate. Upon opening the cover, expecting to be warmly introduced, I was rather amazed at the depth of equations and formulas gracing practically every page. I felt intimidated immediately. Remember the movie 'The Ring'? This had to be rocket science, or more correctly, forecasting science at its most extreme! Wow! I should have really paid more attention during my statistics classes. So, I quickly closed the cover and tried to get a refund from the seller. Note the word Tried here. They didn't want it back either. The good Post-Grand and PhD. candidates of the science of forecasting probably don't need an 'Introduction' to Time Series and Forecasting. Next time I buy a book, I think I'll look for something with 'Sandbox' in the title. May all your Forecasts be Good Forecasts.