An accessible introduction to the most current thinking in and practicality of forecasting techniques in the context of time-oriented data.
Analyzing time-oriented data and forecasting are among the most important problems that analysts face across many fields, ranging from finance and economics to production operations and the natural sciences. As a result, there is a widespread need for large groups of people in a variety of fields to understand the basic concepts of time series analysis and forecasting. Introduction to Time Series Analysis and Forecasting presents the time series analysis branch of applied statistics as the underlying methodology for developing practical forecasts, and it also bridges the gap between theory and practice by equipping readers with the tools needed to analyze time-oriented data and construct useful, short- to medium-term, statistically based forecasts.
Seven easy-to-follow chapters provide intuitive explanations and in-depth coverage of key forecasting topics, including:
Regression-based methods, heuristic smoothing methods, and general time series models
Basic statistical tools used in analyzing time series data
Metrics for evaluating forecast errors and methods for evaluating and tracking forecasting performance over time
Cross-section and time series regression data, least squares and maximum likelihood model fitting, model adequacy checking, prediction intervals, and weighted and generalized least squares
Exponential smoothing techniques for time series with polynomial components and seasonal data
Forecasting and prediction interval construction with a discussionon transfer function models as well as intervention modeling and analysis
Multivariate time series problems, ARCH and GARCH models, and combinations of forecasts
The ARIMA model approach with a discussion on how to identify and fit these models for non-seasonal and seasonal time series
The intricate role of computer software in successful time series analysis is acknowledged with the use of Minitab®, JMP®, and SAS® software applications, which illustrate how the methods are imple-mented in practice. An extensive FTP site is available for readers to obtain data sets, Microsoft Office PowerPoint® slides, and selected answers to problems in the book. Requiring only a basic working knowledge of statistics and complete with exercises at the end of each chapter as well as examples from a wide array of fields, Introduction to Time Series Analysis and Forecasting is an ideal text for forecasting and time series courses at the advanced undergraduate and beginning graduate levels. The book also serves as an indispensable reference for practitioners in business, economics, engineering, statistics, mathematics, and the social, environmental, and life sciences.
Preface ix
Introduction to Forecasting 1
The Nature and Uses of Forecasts 1
Some Examples of Time Series 5
The Forecasting Process 12
Resources for Forecasting 14
Exercises 15
Statistics Background for Forecasting 18
Introduction 18
Graphical Displays 19
Time Series Plots 19
Plotting Smoothed Data 22
Numerical Description of Time Series Data 25
Stationary Time Series 25
Autocovariance and Autocorrelation Functions 28
Use of Data Transformations and Adjustments 34
Transformations 34
Trend and Seasonal Adjustments 36
General Approach to Time Series Modeling and Forecasting 46
Evaluating and Monitoring Forecasting Model Performance 49
Forecasting Model Evaluation 49
Choosing Between Competing Models 57
Monitoring a Forecasting Model 60
Exercises 66
Regression Analysis and Forecasting 73
Introduction 73
Least Squares Estimation in Linear Regression Models 75...Preface ix
Introduction to Forecasting 1
The Nature and Uses of Forecasts 1
Some Examples of Time Series 5
The Forecasting Process 12
Resources for Forecasting 14
Exercises 15
Statistics Background for Forecasting 18
Introduction 18
Graphical Displays 19
Time Series Plots 19
Plotting Smoothed Data 22
Numerical Description of Time Series Data 25
Stationary Time Series 25
Autocovariance and Autocorrelation Functions 28
Use of Data Transformations and Adjustments 34
Transformations 34
Trend and Seasonal Adjustments 36
General Approach to Time Series Modeling and Forecasting 46
Evaluating and Monitoring Forecasting Model Performance 49
Forecasting Model Evaluation 49
Choosing Between Competing Models 57
Monitoring a Forecasting Model 60
Exercises 66
Regression Analysis and Forecasting 73
Introduction 73
Least Squares Estimation in Linear Regression Models 75
Statistical Inference in Linear Regression 84
Test for Significance of Regression 84
Tests on Individual Regression Coefficients and Groups of Coefficients 87
Confidence Intervals on Individual Regression Coefficients 93
Confidence Intervals on the Mean Response 94
Prediction of New Observations 96
Model Adequacy Checking 98
Residual Plots 98
Scaled Residuals and PRESS 100
Measures of Leverage and Influence 105
Variable Selection Methods in Regression 106
Generalized and Weighted Least Squares 111
Generalized Least Squares 112
Weighted Least Squares 114
Discounted Least Squares 119
Regression Models for General Time Series Data 133
Detecting Autocorrelation: The Durbin-Watson Test 134
Estimating the Parameters in Time Series Regression Models 139
Exercises 161
Exponential Smoothing Methods 171
Introduction 171
First-Order Exponential Smoothing 176
The Initial Value, y[subscript 0] 177
The Value of [lambda] 178
Modeling Time Series Data 180
Second-Order Exponential Smoothing 183
Higher-Order Exponential Smoothing 193
Forecasting 193
Constant Process 193
Linear Trend Process 198
Estimation of [sigma subscript e superscript 2] 207
Adaptive Updating of the Discount Factor 208
Model Assessment 209
Exponential Smoothing for Seasonal Data 210
Additive Seasonal Model 210
Multiplicative Seasonal Model 214
Exponential Smoothers and ARIMA Models 217
Exercises 220
Autoregressive Integrated Moving Average (ARIMA) Models 231
Introduction 231
Linear Models for Stationary Time Series 231
Stationarity 232
Stationary Time Series 233
Finite Order Moving Average (MA) Processes 235
The First-Order Moving Average Process, MA(1) 236
The Second-Order Moving Average Process, MA(2) 238
Finite Order Autoregressive Processes 239
First-Order Autoregressive Process, AR(1) 240
Second-Order Autoregressive Process, AR(2) 242
General Autoregressive Process, AR(p) 246
Partial Autocorrelation Function, PACF 248
Mixed Autoregressive-Moving Average (ARMA) Processes 253
Nonstationary Processes 256
Time Series Model Building 265
Model Identification 265
Parameter Estimation 266
Diagnostic Checking 266
Examples of Building ARIMA Models 267
Forecasting ARIMA Processes 275
Seasonal Processes 282
Final Comments 286
Exercises 287
Transfer Functions and Intervention Models 299
Introduction 299
Transfer Function Models 300
Transfer Function-Noise Models 307
Cross Correlation Function 307
Model Specification 309
Forecasting with Transfer Function-Noise Models 322
Intervention Analysis 330
Exercises 338
Survey of Other Forecasting Methods 343
Multivariate Time Series Models and Forecasting 343
Multivariate Stationary Process 343
Vector ARIMA Models 344
Vector AR (VAR) Models 346
State Space Models 350
ARCH and GARCH Models 355
Direct Forecasting of Percentiles 359
Combining Forecasts to Improve Prediction Performance 365
Aggregation and Disaggregation of Forecasts 369
Neural Networks and Forecasting 372
Some Comments on Practical Implementation and Use of Statistical Forecasting Procedures 375
Exercises 378
Statistical Tables 387
Data Sets for Exercises 407
Bibliography 437
Index 443
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