An Introduction to Time Series Analysis and Forecasting

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ISBN: 9780127678702 | 0127678700
Cover: Hardcover
Copyright: 4/27/2000

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Providing a clear explanation of the fundamental theory of time series analysis and forecasting, this book couples theory with applications of two popular statistical packages--SAS and SPSS. The text examines moving average, exponential smoothing, Census X-11 deseasonalization, ARIMA, intervention, transfer function, and autoregressive error models and has brief discussions of ARCH and GARCH models. The book features treatments of forecast improvement with regression and autoregression combination models and model and forecast evaluation, along with a sample size analysis for common time series models to attain adequate statistical power. To enhance the book's value as a teaching tool, the data sets and programs used in the book are made available on the Academic Press Web site. The careful linkage of the theoretical constructs with the practical considerations involved in utilizing the statistical packages makes it easy for the user to properly apply these techniques.

Preface

Introduction and Overview

Purpose

(1)

Time Series

(1)

Missing Data

(1)

Sample Size

(1)

Representativenes

(1)

Scope of Application

(1)

Stochastic and Deterministic Processes

(1)

Stationarity

(2)

Methodological Approaches

(2)

Importance

(1)

Notation

(6)

Gender

(1)

Summation

(1)

Expectation

(1)

Lag Operator

(1)

The Difference Operator

(1)

Mean-Centering the Series

(1)

References

(2)

Extrapolative and Decomposition Models

Introduction

(1)

Goodness-of-Fit Indicators

(3)

Averaging Techniques

(5)

The Simple Average

(1)

The Single Moving Average

(2)

Centered Moving Averages

(1)

Double Moving Averages

(2)

Weighted Moving Averages

(1)

Exponential Smoothing

(22)

Simple Exponential Smoothing

(9)

Holt's Linear Exponential Smoothing

(6)

The Dampened Trend Linear Exponential Smoothing Model

(1)

Exponential Smoothing for Series with Trend and Seasonality: Winter's Methods

(4)

Basic Evaluation of Exponential Smoothing

(2)

Decomposition Methods

(21)

Components of a Series

(1)

Trends

(4)

Seasonality

(1)

Cycles

(1)

Background

(2)

Overview of X-11

(14)

New Features of Census X-12

(3)

References

(3)

Introduction to Box-Jenkins Time Series Analysis

Introduction

(1)

The Importance of Time Series Analysis Modeling

(1)

Limitations

(1)

Assumptions

(4)

Time Series

(7)

Moving Average Processes

(2)

Autoregressive Processes

(1)

ARMA Processes

(1)

Nonstationary Series and Transformations to Stationarity

(4)

Tests for Nonstationarity

(9)

The Dickey-Fuller Test

(3)

Augmented Dickey-Fuller Test

(1)

Assumptions of the Dickey-Fuller and Augmented Dickey-Fuller Tests

(1)

Programming the Dickey-Fuller Test

(4)

Stabilizing the Variance

(2)

Structural or Regime Stability

(1)

Strict Stationarity

(1)

Implications of Stationarity

(7)

For Autoregression

(3)

Implications of Stationarity for Moving Average Processes

(2)

References

(2)

The Basic ARIMA Model

Introduction to ARIMA

101

(1)

Graphical Analysis of Time Series Data

102

(6)

Time Sequence Graphs

102

(4)

Correlograms and Stationarity

106

(2)

Basic Formulation of the Autoregressive Integrated Moving Average Model

108

(2)

The Sample Autocorrelation Function

110

(8)

The Standard Error of the ACF

118

(1)

The Bounds of Stationarity and Invertibility

119

(3)

The Sample Partial Autocorrelation Function

122

(3)

Standard Error of the PACF

125

(1)

Bounds of Stationarity and Invertibility Reviewed

125

(1)

Other Sample Autocorrelation Functions

126

(2)

Tentative Identification of Characteristic Patterns of Integrated, Autoregressive, Moving Average, and ARMA Processes

128

(23)

Preliminary Programming Syntax for Identification of the Model

128

(4)

Stationarity Assessment

132

(2)

Identifying Autoregressive Models

134

(3)

Identifying Moving Average Models

137

(5)

Identifying Mixed Autoregressive-Moving Average Models

142

(7)

References

149

(2)

Seasonal ARIMA Models

Cyclicity

151

(3)

Seasonal Nonstationarity

154

(7)

Seasonal Differencing

161

(1)

Multiplicative Seasonal Models

162

(7)

Seasonal Autoregressive Models

164

(2)

Seasonal Moving Average Models

166

(2)

Seasonal Autoregressive Moving Average Models

168

(1)

The Autocorrelation Structure of Seasonal ARIMA Models

169

(1)

Stationarity and Invertibility of Seasonal ARIMA Models

170

(1)

A Modeling Strategy for the Seasonal ARIMA Model

171

(12)

Identification of Seasonal Nonstationarity

171

(1)

Purely Seasonal Models

171

(2)

A Modeling Strategy for General Multiplicative Seasonal Models

173

(10)

Programming Seasonal Multiplicative Box-Jenkins Models

183

(3)

SAS Programming Syntax

183

(2)

SPSS Programming Syntax

185

(1)

Alternative Methods of Modeling Seasonality

186

(2)

The Question of Deterministic or Stochastic Seasonality

188

(3)

References

189

(2)

Estimation and Diagnosis

Introduction

191

(1)

Estimation

191

(17)

Conditional Least Squares

192

(3)

Unconditional Least Squares

195

(3)

Maximum Likelihood Estimation

198

(6)

Computer Applications

204

(4)

Diagnosis of the Model

208

(7)

References

213

(2)

Metadiagnosis and Forecasting

Introduction

215

(2)

Metadiagnosis

217

(5)

Statistical Program Output of Metadiagnostic Criteria

221

(1)

Forecasting with Box-Jenkins Models

222

(22)

Forecasting Objectives

222

(2)

Basic Methodology of Forecasting

224

(1)

The Forecast Function

225

(7)

The Forecast Error

232

(1)

Forecast Error Variance

232

(1)

Forecast Confidence Intervals

233

(1)

Forecast Profiles for Basic Processes

234

(10)

Characteristics of the Optimal Forecast

244

(1)

Basic Combination of Forecasts

245

(3)

Forecast Evaluation

248

(3)

Statistical Package Forecast Syntax

251

(5)

Introduction

251

(1)

SAS Syntax

252

(2)

SPSS Syntax

254

(2)

Regression Combination of Forecasts

256

(9)

References

263

(2)

Intervention Analysis

Introduction: Event Interventions and Their Impacts

265

(2)

Assumptions of the Event Intervention (Impact) Model

267

(1)

Impact Analysis Theory

268

(12)

Intervention Indicators

268

(2)

The Intervention (Impulse Response) Function

270

(1)

The Simple Step Function: Abrupt Onset, Permanent Duration

270

(2)

First-Order Step Function: Gradual Onset, Permanent Duration

272

(4)

Abrupt Onset, Temporary Duration

276

(2)

Abrupt Onset and Oscillatory Decay

278

(1)

Graduated Onset and Gradual Decay

279

(1)

Significance Tests for Impulse Response Functions

280

(2)

Modeling Strategies for Impact Analysis

282

(6)

The Box-Jenkins-Tiao Strategy

283

(2)

Full Series Modeling Strategy

285

(3)

Programming Impact Analysis

288

(54)

An Example of SPSS Impact Analysis Syntax

290

(7)

An Example of SAS Impact Analysis Syntax

297

(17)

Example: The Impact of Watergate on Nixon Presidential Approval Ratings

314

(28)

Applications of Impact Analysis

342

(3)

Advantages of Intervention Analysis

345

(1)

Limitations of Intervention Analysis

346

(7)

References

350

(3)

Transfer Function Models

Definition of a Transfer Function

353

(1)

Importance

354

(1)

Theory of the Transfer Function Model

355

(13)

The Assumption of the Single-Input Case

355

(1)

The Basic Nature of the Single-Input Transfer Function

355

(13)

Modeling Strategie

368

(52)

The Conventional Box-Jenkins Modeling Strategy

368

(31)

The Linear Transfer Function Modeling Strategy

399

(21)

Cointegration

420

(1)

Long-Run and Short-Run Effects in Dynamic Regression

421

(1)

Basic Characteristics of a Good Time Series Model

422

(3)

References

423

(2)

Autoregressive Error Models

The Nature of Serial Correlation of Error

425

(10)

Regression Analysis and the Consequences of Autocorrelated Error

426

(9)

Sources of Autoregressive Error

435

(2)

Autoregressive Models with Serially Correlated Errors

437

(1)

Tests for Serial Correlation of Error

437

(2)

Corrective Algorithms for Regression Models with Autocorrelated Error

439

(2)

Forecasting with Autocorrelated Error Models

441

(2)

Programming Regression with Autocorrelated Errors

443

(15)

SAS Proc Autoreg

443

(9)

SPSS ARIMA Procedures for Autoregressive Error Models

452

(6)

Autoregression in Combining Forecasts

458

(4)

Models with Stochastic Variance

462

(5)

ARCH and GARCH Models

463

(1)

ARCH Models for Combining Forecasts

464

(1)

References

465

(2)

A Review of Model and Forecast Evaluation

Model and Forecast Evaluation

467

(1)

Model Evaluation

468

(1)

Comparative Forecast Evaluation

469

(7)

Capability of Forecast Methods

471

(5)

Comparison of Individual Forecast Methods

476

(1)

Comparison of Combined Forecast Models

477

(5)

References

478

(4)

Power Analysis and Sample Size Determination for Well-Known Time Series Models

Monnie McGee

Census X-11

482

(1)

Box-Jenkins Models

483

(3)

Tests for Nonstationarity

486

(1)

Intervention Analysis and Transfer Functions

487

(3)

Regression with Autoregressive Errors

490

(1)

Conclusion

491

(4)

References

492

(3)

Appendix A

495

(2)

Glossary

497

(16)

Index

513

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An Introduction to Time Series Analysis and Forecasting

Summary

Table of Contents

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