Sas for Forecasting Time Series

by Brocklebank, John C., Ph.D.; Dickey, David A.

• ISBN13: 9781590471821
• ISBN10: 1590471822
• Edition: 2nd
• Format: Paperback
• Copyright: 2003-05-01
• Publisher: SAS

Summary

In this second edition of the indispensable SAS for Forecasting Time Series, Brocklebank and Dickey show you how SAS performs univariate and multivariate time series analysis. Taking a tutorial approach, the authors focus on the procedures that most effectively bring results: the advanced procedures ARIMA, SPECTRA, STATESPACE, and VARMAX. They demonstrate the interrelationship of SAS/ETS procedures with a discussion of how the choice of a procedure depends on the data to be analyzed and the results desired. With this book, you will learn to model and forecast simple autoregressive (AR) processes using PROC ARIMA, and you will learn to fit autoregressive and vector ARMA processes using the STATESPACE and VARMAX procedures. Other topics covered include detecting sinusoidal components in time series models, performing bivariate cross-spectral analysis, and comparing these frequency-based results with the time domain transfer function methodology. Intermediate to advanced data analysts who use SAS software to perform univariate and multivariate time series analyses. This book is an ideal supplemental text for students in undergraduate- and graduate-level statistics courses. Book jacket.

Author Biography

John C. Brocklebank, Ph.D., Research and Development Director of Analytic Solutions at SAS, joined SAS in 1981 and has been a SAS user since 1978. Dr. Brocklebank received his Ph.D. in statistics and mathematics from North Carolina State University in 1981. He is often invited to conferences to speak about time series and statistical methods David A. Dickey, Ph.D., is Professor of Statistics at North Carolina State University, where he teaches graduate courses in statistical methods and time series. An accomplished SAS user since 1976 and a prolific author, Dr. Dickey is the co-inventor of the Dickey-Fuller test used in SAS/ETS software. He received his Ph.D. in statistics from lowa State University in 1976. He is a fellow of the American Statistical Association

Table of Contents

Preface	p. vii
Acknowledgments	p. ix
Overview of Time Series	p. 1
Introduction	p. 1
Analysis Methods and SAS/ETS Software	p. 2
Options	p. 2
How SAS/ETS Software Procedures Interrelate	p. 4
Simple Models: Regression	p. 6
Linear Regression	p. 6
Highly Regular Seasonality	p. 13
Regression with Transformed Data	p. 21
Simple Models: Autoregression	p. 27
Introduction	p. 27
Terminology and Notation	p. 27
Statistical Background	p. 28
Forecasting	p. 29
Forecasting with PROC ARIMA	p. 30
Backshift Notation B for Time Series	p. 40
Yule-Walker Equations for Covariances	p. 41
Fitting an AR Model in PROC REG	p. 45
The General ARIMA Model	p. 49
Introduction	p. 49
Statistical Background	p. 49
Terminology and Notation	p. 50
Prediction	p. 51
One-Step-Ahead Predictions	p. 51
Future Predictions	p. 52
Model Identification	p. 55
Stationarity and Invertibility	p. 55
Time Series Identification	p. 56
Chi-Square Check of Residuals	p. 79
Summary of Model Identification	p. 79
Examples and Instructions	p. 80
IDENTIFY Statement for Series 1-8	p. 81
Example: Iron and Steel Export Analysis	p. 90
Estimation Methods Used in PROC ARIMA	p. 95
ESTIMATE Statement for Series 8	p. 97
Nonstationary Series	p. 102
Effect of Differencing on Forecasts	p. 104
Examples: Forecasting IBM Series and Silver Series	p. 105
Models for Nonstationary Data	p. 113
Differencing to Remove a Linear Trend	p. 123
Other Identification Techniques	p. 128
Summary	p. 140
The ARIMA Model: Introductory Applications	p. 143
Seasonal Time Series	p. 143
Introduction to Seasonal Modeling	p. 143
Model Identification	p. 145
Models with Explanatory Variables	p. 164
Case 1: Regression with Time Series Errors	p. 164
Case 1A: Intervention	p. 165
Case 2: Simple Transfer Function	p. 165
Case 3: General Transfer Function	p. 166
Case 3A: Leading Indicators	p. 166
Case 3B: Intervention	p. 167
Methodology and Example	p. 167
Case 1: Regression with Time Series Errors	p. 167
Case 2: Simple Transfer Functions	p. 179
Case 3: General Transfer Functions	p. 183
Case 3B: Intervention	p. 213
Further Examples	p. 223
North Carolina Retail Sales	p. 223
Construction Series Revisited	p. 231
Milk Scare (Intervention)	p. 233
Terrorist Attack	p. 237
The ARIMA Model: Special Applications	p. 239
Regression with Time Series Errors and Unequal Variances	p. 239
Autoregressive Errors	p. 239
Example: Energy Demand at a University	p. 241
Unequal Variances	p. 245
ARCH, GARCH, and IGARCH for Unequal Variances	p. 249
Cointegration	p. 256
Introduction	p. 256
Cointegration and Eigenvalues	p. 258
Impulse Response Function	p. 260
Roots in Higher-Order Models	p. 260
Cointegration and Unit Roots	p. 263
An Illustrative Example	p. 265
Estimating the Cointegrating Vector	p. 270
Intercepts and More Lags	p. 273
PROC VARMAX	p. 275
Interpreting the Estimates	p. 277
Diagnostics and Forecasts	p. 279
State Space Modeling	p. 283
Introduction	p. 283
Some Simple Univariate Examples	p. 283
A Simple Multivariate Example	p. 285
Equivalence of State Space and Vector ARMA Models	p. 294
More Examples	p. 298
Some Univariate Examples	p. 298
ARMA(1,1) of Dimension 2	p. 301
PROC STATESPACE	p. 302
State Vectors Determined from Covariances	p. 305
Canonical Correlations	p. 305
Simulated Example	p. 307
Spectral Analysis	p. 323
Periodic Data: Introduction	p. 323
Example: Plant Enzyme Activity	p. 324
PROC SPECTRA Introduced	p. 326
Testing for White Noise	p. 328
Harmonic Frequencies	p. 330
Extremely Fast Fluctuations and Aliasing	p. 334
The Spectral Density	p. 335
Some Mathematical Detail (Optional Reading)	p. 339
Estimating the Spectrum: The Smoothed Periodogram	p. 340
Cross-Spectral Analysis	p. 341
Interpreting Cross-Spectral Quantities	p. 341
Interpreting Cross-Amplitude and Phase Spectra	p. 344
PROC SPECTRA Statements	p. 346
Cross-Spectral Analysis of the Neuse River Data	p. 350
Details on Gain, Phase, and Pure Delay	p. 354
Data Mining and Forecasting	p. 359
Introduction	p. 359
Forecasting Data Model	p. 360
The Time Series Forecasting System	p. 362
HPF Procedure	p. 368
Scorecard Development	p. 375
Business Goal Performance Metrics	p. 376
Graphical Displays	p. 376
Goal-Seeking Model Development	p. 381
Summary	p. 383
References	p. 385
Index	p. 389
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