Introduction to Time Series Analysis and Forecasting / Edition 1

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Overview

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 performanceover 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 discussion on 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 sof

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Editorial Reviews

From the Publisher
"This would be an appropriate source for use in a first course in time series analysis. It might also be useful as a reference for researchers who want to apply time series analysis to their data sets." (CHOICE, October 2008)

"The result is a book that can be used with a wide variety of audiences, with different interests and technical backgrounds, whose common interests are understanding how to analyze time-oriented data and constructing good short-term statistically based forecasts." (Mathematical Reviews, 2008m)

"The book is great for readers who need to apply the methods and models presented but have little background in mathematics and statistics." (MAA Reviews,  July 2008)

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Product Details

Meet the Author

Douglas C. Montgomery, PhD, is Regents' Professor and ADU Foundation Professor of Engineering  at Arizona State University. With over 35 years of academic and consulting experience, Dr. Montgomery has authored or coauthored over 250 journal articles and 13 books. His research interests include design and analysis of experiments, statistical methods for process monitoring and optimization, and the analysis of time-oriented data.

Cheryl L. Jennings, PhD, is a Process Design Consultant with Bank of America. An active member of both the American Statistical Association and the American Society for Quality, her areas of research and profession interest include Six Sigma, modeling and analysis, and process control and improvement.

Murat Kulahci, PhD, is Associate Professor of Informatics and Mathematical Modelling at the Technical University of Denmark. The author of over 30 journal articles, Dr. Kulahci’s research interests include time series analysis, design of experiments, and statistical process control and monitoring.

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Table of Contents

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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