FORECASTING METHODS AND APPLICATIONS SPYROS MAKRIDAKIS STEVEN С WHEELWRIGHT. European Institute of Business Administration. Harvard Business School

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1 FORECASTING METHODS AND APPLICATIONS SPYROS MAKRIDAKIS European Institute of Business Administration (INSEAD) STEVEN С WHEELWRIGHT Harvard Business School. JOHN WILEY & SONS SANTA BARBARA NEW YORK CHICHESTER BRISBANE TORONTO A Wiley/Hamilton Publication

2 CONTENTS Preface PART ONE BACKGROUND AND PERSPECTIVE 2 CHAPTER 1 INTRODUCTION Needs and Uses of Forecasting Current Status of Quantitative and Technological Forecasting CHAPTER 2 FUNDAMENTALS OF QUANTITATIVE FORECASTING 2.1 Explanatory versus Time-Series Forecasting 2.2 Least Squares Estimates 2.3 Discovering and Describing Existing Relationships 2.4 Variances and Covariances 2.5 Autovariance and Autocorrelation Appendix Chapter PART TWO SMOOTHING AND DECOMPOSITION TIME-SERIES METHODS 42 CHAPTER 3 SMOOTHING METHODS 3.1 Introduction 3.2 Single Moving Averages

3 XII CONTENTS 3.3 Single Exponential Smoothing Adaptive-Response-Rate Single Exponential Smoothing Linear Moving Averages Linear Exponential Smoothing Brown's Quadratic Exponential Smoothing Selecting the Appropriate Smoothing Method for the Data Pattern Winters' Linear and Seasonal Exponential Smoothing Other Smoothing Methods General Aspects of Smoothing Methods Development of the Mathematical Basis of Smoothing Methods CHAPTER 4 DECOMPOSITION METHODS Introduction Trend Fitting The Ratio-to-Moving Averages Classical Decomposition Method Different Types of Moving Averages The Census II Decomposition Method The FORAN System PART THREE REGRESSION METHODS 144 CHAPTER 5 SIMPLE REGRESSION 5.1 General Comments on Regression Methods 5.2 Different Forms of Functional Relationships 5.3 Determining the Parameters, a and b, of a Straight Line 5.4 The Correlation Coefficient 5.5 The Significance of a Regression Equation 5.6 Trend Analysis, Time-Series Forecasting 5.7 The Regression Equation as a Model Appendix Mathematical Supplement Chapter CHAPTER 6 MULTIPLE REGRESSION 6.1 Introduction 6.2 Applying Multiple Regression

4 CONTENTS XIII 6.3 Multiple Correlation and the Coefficient of Determination 6.4 Tests of Significance 6.5 Transformations 6.6 The Assumptions of Regression Analysis 6.7 Multicollineanty 6.8 Model Specification 6.9 Lagged Variables 6.10 Dummy Variables Summary Appendix Mathematical Supplement Chapter CHAPTER 7 ECONOMETRIC MODELS AND FORECASTING 7.1 The Basis of Econometric Modeling 7.2 The Advantages and Drawbacks of Econometric Methods 7.3 Estimation Procedures Used by Econometric Models 7.4 Specification and Identification 7.5 Development and Application of Econometric Models PART FOUR AUTOREGRESSIVE/MOVING AVERAGE (ARMA) TIME-SERIES METHODS 250 CHAPTER 8 TIME-SERIES ANALYSIS 8.1 Introduction to Autoregressive Schemes 8.2 Identifying the Characteristics of a Time Series 8.3 Autocorrelation Coefficients 8.4 The Sampling Distribution of Autocorrelations 8.5 Autocorrelation Analysis 8.6 The X 2 -Test 8.7 Partial Autocorrelations 8.8 Summary of Time-Series Analysis CHAPTER 9 GENERALIZED ADAPTIVE FILTERING 9.1 Analyzing and Forecasting a Time Series 9.2 Autoregressive Models 9.3 The Method of Adaptive Filtering

5 XIV CONTENTS 9.4 Moving Average Models 9.5 Applying the Method of Adaptive Filtering in MA Models 9.6 Mixed Autoregressive Moving Average Models 9.7 Seasonal ARMA Models 9.8 Summary Comments on Generalized Adaptive Filtering Appendix Mathematical Supplement Chapter CHAPTER 10 THE BOX-JENKINS METHOD 10.1 Identification 10.2 Estimating the Parameters of an ARMA Model 10.3 Diagnostic Checking of the Estimated Model 10.4 Using an ARMA Model to Forecast 10.5 Seasonal ARMA Models 10.6 An Application of Seasonal ARMA Processes 10.7 Achieving Stationarity in Variance CHAPTER 1 1 MULTIVARIATE TIME-SERIES ANALYSIS Introduction Bivariate Time-Series Analysis Identification of an Appropriate MARMA Model and Initial Estimation of Its Parameters Estimation of the Parameters of a Specific MARMA Model and Diagnostic Checking Identification of r, s. and b by Contracting the Cross Autocorrelations of the Estimates Other Multivariate Models Conclusions PART FIVE QUALITATIVE AND TECHNOLOGICAL METHODS 432 CHAPTER 12 PREDICTING THE CYCLE 12.1 Introduction Business Cycles

6 CONTENTS 12.3 Causes of Business Cycles 12.4 Anticipatory Surveys 12.5 Leading Indicators Paired Indices 12.7 Tracking the Evolution of Cycles CHAPTER 13 SUBJECTIVE ASSESSMENT METHODS 13.1 The Basic Framework of Decision Analysis 13.2 Methods for Obtaining Subjective Assessments 13.3 Combining Subjective Assessments and Decision Analysis in Practice CHAPTER 14 QUALITATIVE AND TECHNOLOGICAL METHODS OF FORECASTING Introduction Exploratory Methods of Forecasting Normative Approaches to Technological Forecasting Summary Exercise 528 PART SIX INTEGRATING FORECASTING AND PLANNING IN THE ORGANIZATION 530 CHAPTER 15 FORECASTING AND PLANNING The Role of Forecasting in Planning Relating Forecasting and Planning in the Organization Forecasting as Input to Planning and Decision Making Contribution of Forecasting to Analysis and Understanding CHAPTER 16 COMPARISON AND SELECTION OF FORECASTING METHODS The Accuracy of Forecasting Methods Pattern of the Data and Its Effects on Individual Forecasting Methods 587

7 XVI CONTENTS 16.3 Time Horizon Effects on Forecasting Methods 16.4 The Costs of Forecasting Methods 16.5 The Ease of Application of Forecasting Methods 16.6 An Interactive Procedure for Selecting, Running, and Comparing Alternative Forecasting Methods CHAPTER 17 DATA PROCUREMENT, PREPARATION, AND HANDLING 17.1 Definition and Specification of Variables in Forecasting 17.2 Data Procurement Data Preparation 17.4 Data Management CHAPTER 18 ORGANIZATIONAL AND BEHAVIORAL ASPECTS OF FORECASTING Status of Forecasting in Business Firms Reasons for the Organizational Status of Forecasting in the Mid-1970s Organizational Steps for Improved Forecasting Organizing for Individual Forecasting Projects APPENDIX I STATISTICAL TABLES A Areas under the Normal Curve В Student f Distribution С Values of the F-Test D Values of the Durbin-Watson Statistic E Critical Points of the Chi-Squared (x 2 ) Statistic APPENDIX II APPENDIX III INDEX GLOSSARY DATA SOURCES

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