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SAS for Forecasting Time Series, Third Edition, 3rd Edition

Book Description

To use statistical methods and SAS applications to forecast the future values of data taken over time, you need only follow this thoroughly updated classic on the subject. With this third edition of SAS for Forecasting Time Series, intermediate-to-advanced SAS users—such as statisticians, economists, and data scientists—can now match the most sophisticated forecasting methods to the most current SAS applications.

Starting with fundamentals, this new edition presents methods for modeling both univariate and multivariate data taken over time. From the well-known ARIMA models to unobserved components, methods that span the range from simple to complex are discussed and illustrated. Many of the newer methods are variations on the basic ARIMA structures.

Completely updated, this new edition includes fresh, interesting business situations and data sets, and new sections on these up-to-date statistical methods:

  • ARIMA models
  • Vector autoregressive models
  • Exponential smoothing models
  • Unobserved component and state-space models
  • Seasonal adjustment
  • Spectral analysis

Focusing on application, this guide teaches a wide range of forecasting techniques by example. The examples provide the statistical underpinnings necessary to put the methods into practice. The following up-to-date SAS applications are covered in this edition:

  • The ARIMA procedure
  • The AUTOREG procedure
  • The VARMAX procedure
  • The ESM procedure
  • The UCM and SSM procedures
  • The X13 procedure
  • The SPECTRA procedure
  • SAS Forecast Studio

Each SAS application is presented with explanation of its strengths, weaknesses, and best uses. Even users of automated forecasting systems will benefit from this knowledge of what is done and why. Moreover, the accompanying examples can serve as templates that you easily adjust to fit your specific forecasting needs.

This book is part of the SAS Press program.

Table of Contents

  1. About This Book
  2. About The Authors
  3. Acknowledgments
  4. Chapter 1: Overview of Time Series
    1. 1.1 Introduction
    2. 1.2 Analysis Methods and SAS/ETS Software
      1. 1.2.1 Options
      2. 1.2.2 How SAS/ETS Procedures Interrelate
    3. 1.3 Simple Models: Regression
      1. 1.3.1 Linear Regression
      2. 1.3.2 Highly Regular Seasonality
      3. 1.3.3 Regression with Transformed Data
  5. Chapter 2: Simple Models: Autoregression
    1. 2.1 Introduction
      1. 2.1.1 Terminology and Notation
      2. 2.1.2 Statistical Background
    2. 2.2 Forecasting
      1. 2.2.1 PROC ARIMA for Forecasting
      2. 2.2.2 Backshift Notation B for Time Series
      3. 2.2.3 Yule-Walker Equations for Covariances
    3. 2.3 Fitting an AR Model in PROC REG
  6. Chapter 3: The General ARIMA Model
    1. 3.1 Introduction
      1. 3.1.1 Statistical Background
      2. 3.1.2 Terminology and Notation
    2. 3.2 Prediction
      1. 3.2.1 One-Step-Ahead Predictions
      2. 3.2.2 Future Predictions
    3. 3.3 Model Identification
      1. 3.3.1 Stationarity and Invertibility
      2. 3.3.2 Time Series Identification
      3. 3.3.3 Chi-Square Check of Residuals
      4. 3.3.4 Summary of Model Identification
    4. 3.4 Examples and Instructions
      1. 3.4.1 IDENTIFY Statement for Series 1-8
      2. 3.4.2 Example: Iron and Steel Export Analysis
      3. 3.4.3 Estimation Methods Used in PROC ARIMA
      4. 3.4.4 ESTIMATE Statement for Series 8-A
      5. 3.4.5 Nonstationary Series
      6. 3.4.6 Effect of Differencing on Forecasts
      7. 3.4.7 Examples: Forecasting IBM Series and Silver Series
      8. 3.4.8 Models for Nonstationary Data
      9. 3.4.9 Differencing to Remove a Linear Trend
      10. 3.4.10 Other Identification Techniques
    5. 3.5 Summary of Steps for Analyzing Nonseasonal Univariate Series
  7. Chapter 4: The ARIMA Model: Introductory Applications
    1. 4.1 Seasonal Time Series
      1. 4.1.1 Introduction to Seasonal Modeling
      2. 4.1.2 Model Identification
    2. 4.2 Models with Explanatory Variables
      1. 4.2.1 Case 1: Regression with Time Series Errors
      2. 4.2.2 Case 1A: Intervention
      3. 4.2.3 Case 2: Simple Transfer Functions
      4. 4.2.4 Case 3: General Transfer Functions
      5. 4.2.5 Case 3A: Leading Indicators
      6. 4.2.6 Case 3B: Intervention
    3. 4.3 Methodology and Example
      1. 4.3.1 Case 1: Regression with Time Series Errors
      2. 4.3.2 Case 2: Simple Transfer Functions
      3. 4.3.3 Case 3: General Transfer Functions
      4. 4.3.4 Case 3B: Intervention
    4. 4.4 Further Example
      1. 4.4.1 North Carolina Retail Sales
      2. 4.4.2 Construction Series Revisited
      3. 4.4.3 Milk Scare (Intervention)
      4. 4.4.4 Terrorist Attack
  8. Chapter 5: The ARIMA Model: Special Applications
    1. 5.1 Regression with Time Series Errors and Unequal Variances
      1. 5.1.1 Autoregressive Errors
      2. 5.1.2 Example: Energy Demand at a University
      3. 5.1.3 Unequal Variances
      4. 5.1.4 ARCH, GARCH, and IGARCH for Unequal Variances
    2. 5.2 Cointegration
      1. 5.2.1 Cointegration and Eigenvalues
      2. 5.2.2 Impulse Response Function
      3. 5.2.3 Roots in Higher-Order Models
      4. 5.2.4 Cointegration and Unit Roots
      5. 5.2.5 An Illustrative Example
      6. 5.2.6 Estimation of the Cointegrating Vector
      7. 5.2.7 Intercepts and More Lags
      8. 5.2.8 PROC VARMAX
      9. 5.2.9 Interpretation of the Estimates
      10. 5.2.10 Diagnostics and Forecasts
  9. Chapter 6: Exponential Smoothing
    1. 6.1 Single Exponential Smoothing
      1. 6.1.1 The Smoothing Idea
      2. 6.1.2 Forecasting with Single Exponential Smoothing
      3. 6.1.3 Alternative Representations
      4. 6.1.4 Atlantic Ocean Tides: An Example
      5. 6.1.5 Improving the Tide Forecasts
    2. 6.2 Exponential Smoothing for Trending Data
      1. 6.2.1 Linear and Double Exponential Smoothing
      2. 6.2.2 Properties of the Forecasts
      3. 6.2.3 A Generated Multi-Series Example
      4. 6.2.4 Real Data Examples
      5. 6.2.5 Boundary Values in Linear Exponential Smoothing
      6. 6.2.6 Damped Trend Exponential Smoothing
      7. 6.2.7 Diagnostic Plots
      8. 6.2.8 Sums of Forecasts
    3. 6.3 Smoothing Seasonal Data
      1. 6.3.1 Seasonal Exponential Smoothing
      2. 6.3.2 Winters Method
      3. 6.4.1 Validation
      4. 6.4.2 Choosing a Model Visually
      5. 6.4.3 Choosing a Model Numerically
    4. 6.5 Advantages of Exponential Smoothing
    5. 6.6 How the Smoothing Equations Lead to ARIMA in the Linear Case
  10. Chapter 7: Unobserved Components and State Space Models
    1. 7.1 Nonseasonal Unobserved Components Models
      1. 7.1.1 The Nature of Unobserved Components Models
      2. 7.1.2 A Look at the PROC UCM Output
      3. 7.1.3 A Note on Unit Roots in Practice
      4. 7.1.4 The Basic Structural Model Related to ARIMA Structures
      5. 7.1.5 A Follow-Up on the Example
    2. 7.2 Diffuse Likelihood and Kalman Filter: Overview and a Simple Case
      1. 7.2.1 Diffuse Likelihood in a Simple Model
      2. 7.2.2 Definition of a Diffuse Likelihood
      3. 7.2.3 A Numerical Example
    3. 7.3 Seasonality in Unobserved Components Models
      1. 7.3.1 Description of Seasonal Recursions
      2. 7.3.2 Tourism Example with Regular Seasonality
      3. 7.3.3 Decomposition
      4. 7.3.4 Another Seasonal Model: Sine and Cosine Terms
      5. 7.3.5 Example with Trigonometric Components
      6. 7.3.6 The Seasonal Component Made Local and Damped
    4. 7.4 A Brief Introduction to the SSM Procedure
      1. 7.4.1 Brief Overview
      2. 7.4.2 Simple Examples
      3. 7.4.3 Extensions of the AR(1) Model
      4. 7.4.4 Accommodation for Curvature
      5. 7.4.5 Models with Several Lags
      6. 7.4.6 Bivariate Examples
      7. 7.4.7 The Start-up Problem Revisited
      8. 7.4.8 Example and More Details on the State Space Approach
  11. Chapter 8: Adjustment for Seasonality with PROC X13
    1. 8.1 Introduction
    2. 8.2 The X-11 Method
      1. 8.2.1 Moving Averages
      2. 8.2.2 Outline of the X-11 Method
      3. 8.2.3 Basic Seasonal Adjustment Using the X-11 Method
      4. 8.2.4 Tests for Seasonality
    3. 8.3 regARIMA Models and TRAMO
      1. 8.3.1 regARIMA Models
      2. 8.3.2 Automatic Selection of ARIMA Orders
    4. 8.4 Data Examples
      1. 8.4.1 Airline Passengers Revisited
      2. 8.4.3 Employment in the United States
  12. Chapter 9: SAS Forecast Studio
    1. 9.1 Introduction
    2. 9.2 Creating a Project
    3. 9.3 Overview of Available Modes
    4. 9.4 Project Settings
    5. 9.4.1 Model Generation
    6. 9.4.2 Goodness of Fit and Honest Assessment
    7. 9.4.2 Transformation and Outlier Detection
    8. 9.5 Creating Custom Events
    9. 9.6 Hierarchical Time Series and Reconciliation
  13. Chapter 10: Spectral Analysis
    1. 10.1 Introduction
    2. 10.2 Example: Plant Enzyme Activity
    3. 10.3 PROC SPECTRA
    4. 10.4 Tests for White Noise
    5. 10.5 Harmonic Frequencies
    6. 10.6 Extremely Fast Fluctuations and Aliasing
    7. 10.7 The Spectral Density
    8. 10.8 Some Mathematical Detail (Optional Reading)
    9. 10.9 Estimation of the Spectrum: The Smoothed Periodogram
    10. 10.10 Cross-Spectral Analysis
      1. 10.10.1 Interpretation of Cross-Spectral Quantities
      2. 10.10.2 Interpretation of Cross-Amplitude and Phase Spectra
      3. 10.10.3 PROC SPECTRA Statements
      4. 10.10.4 Cross-Spectral Analysis of the Neuse River Data
      5. 10.10.5 Details on Gain, Phase, and Pure Delay
  14. References
  15. Index