Time Series Analysis and Forecasting by Example

Cover......Page 1
S Title......Page 2
Editors......Page 3
Title: TIME SERIES ANALYSIS AND FORECASTING BY EXAMPLE......Page 4
ePub ISBN: 978-1-118-05695-0......Page 5
Dedication: To the memory of Søren Bisgaard......Page 6
CONTENTS......Page 7
PREFACE......Page 11
1.2 EXAMPLES OF TIME SERIES DATA......Page 14
1.3 UNDERSTANDING AUTOCORRELATION......Page 23
1.4 THE WOLD DECOMPOSITION......Page 25
1.5 THE IMPULSE RESPONSE FUNCTION......Page 27
1.6 SUPERPOSITION PRINCIPLE......Page 28
1.7 PARSIMONIOUS MODELS......Page 31
EXERCISES......Page 32
2.1 INTRODUCTION......Page 33
2.2 GRAPHICAL ANALYSIS OF TIME SERIES......Page 34
2.3 GRAPH TERMINOLOGY......Page 35
2.4 GRAPHICAL PERCEPTION......Page 36
2.5 PRINCIPLES OF GRAPH CONSTRUCTION......Page 40
2.6 ASPECT RATIO......Page 42
2.7.2 Connected Lines Graph......Page 46
2.7.5 Graph with Projected Bars (Vertical Line Plot)......Page 47
2.7.6 Area Graph......Page 48
2.7.7 Cut and Stack Graph......Page 49
Case 1. Defect Report to Upper Management......Page 50
Case 2. Temperature of an Industrial Furnace......Page 52
Case 4. Auto and Truck Production in the United States......Page 55
EXERCISES......Page 58
3.1.1 Deterministic Versus Stochastic Models......Page 59
3.1.2 Stationarity......Page 60
3.1.3 Backshift Operator......Page 62
3.1.4 Autocorrelation Function (ACF)......Page 63
3.1.5 Linear Processes......Page 65
3.2.1 Example: Temperature Readings from a Ceramic Furnace......Page 66
3.2.2 Serial Correlation......Page 67
3.2.3 Time Series Model for the Furnace Data......Page 68
3.2.4 ARMA(p, q) Models......Page 71
3.3 STATIONARITY AND INVERTIBILITY OF ARMA MODELS......Page 74
3.4.1 Periodicities in Stationary Processes......Page 78
3.4.2 Stationary or Not Stationary?......Page 79
3.5 TRANSFORMATION OF DATA......Page 81
EXERCISES......Page 85
4.2 DETECTING NONSTATIONARITY......Page 90
4.2.1 Transformation to Stationarity......Page 91
4.2.2 Using the Variogram to Detect Nonstationarity......Page 93
4.3 AUTOREGRESSIVE INTEGRATED MOVING AVERAGE (ARIMA) MODELS......Page 94
4.3.1 Model Identification and Estimation......Page 95
4.3.2 Parameter Estimation......Page 96
4.3.3 Model Diagnostic Checking......Page 97
4.3.4 Outliers......Page 99
4.3.5 Alternative Model......Page 101
4.4 FORECASTING USING ARIMA MODELS......Page 102
4.5 EXAMPLE 2: CONCENTRATION MEASUREMENTS FROM A CHEMICAL PROCESS......Page 104
4.5.1 Preliminary Time Series Analysis......Page 106
4.5.2 Diagnostic Checking......Page 109
4.5.3 Implications and Interpretations of the IMA(1, 1)Model......Page 110
4.5.4 To Be or Not To Be Stationary......Page 113
4.6 THE EWMA FORECAST......Page 114
EXERCISES......Page 115
5.1.1 Example 1: The International Airline Passenger Data......Page 121
5.1.2 Data Transformation for the Airline Passenger Data......Page 124
5.2 SEASONAL ARIMA MODELS......Page 126
5.2.1 Model Identification......Page 128
5.2.2 The Anatomy of Seasonal Models......Page 129
5.2.3 Model Fitting and Model Checking......Page 130
5.3 FORECASTING USING SEASONAL ARIMA MODELS......Page 134
5.4 EXAMPLE 2: COMPANY X’S SALES DATA......Page 136
5.4.1 Preliminary Graphical Analysis......Page 137
5.4.2 Model Identification......Page 142
5.4.4 Interlude: A Bit about the Controversy on the Sales Data......Page 144
5.4.5 Box–Cox Transformation......Page 146
5.4.6 A Second Analysis of the Sales Data: Taking Account of Outliers......Page 150
5.4.7 Final Model Checking......Page 152
5.4.8 Forecasting for the Sales Data......Page 153
5.4.8.1 An Alternative Representation of the Forecasting Model: The π Weights......Page 154
5.4.8.2 Forecasting the Seasonal ARIMA(1, 1, 0) × (0, 1, 1)12 Model......Page 157
5.4.9 An Alternative Model for the Sales Data......Page 158
EXERCISES......Page 162
6.2 FINDING THE ‘‘BEST’’ MODEL......Page 165
6.3 EXAMPLE: INTERNET USERS DATA......Page 166
6.4 MODEL SELECTION CRITERIA......Page 173
6.5 IMPULSE RESPONSE FUNCTION TO STUDY THE DIFFERENCES IN MODELS......Page 176
6.6 COMPARING IMPULSE RESPONSE FUNCTIONS FOR COMPETING MODELS......Page 179
6.7 ARIMA MODELS AS RATIONAL APPROXIMATIONS......Page 180
6.8 AR VERSUS ARMA CONTROVERSY......Page 181
6.8.1 Yet Another Model Comparison......Page 182
APPENDIX 6.1: HOW TO COMPUTE IMPULSE RESPONSE FUNCTIONS WITH A SPREADSHEET......Page 183
EXERCISES......Page 184
7.2 LINEAR DIFFERENCE EQUATIONS......Page 186
7.2.1 Linear Difference Equations and ARIMA Models......Page 188
7.3 EVENTUAL FORECAST FUNCTION......Page 192
7.4 DETERMINISTIC TREND MODELS......Page 196
7.5 YET ANOTHER ARGUMENT FOR DIFFERENCING......Page 198
7.6 CONSTANT TERM IN ARIMA MODELS......Page 199
7.7 CANCELLATION OF TERMS IN ARIMA MODELS......Page 200
7.8 STOCHASTIC TREND: UNIT ROOT NONSTATIONARY PROCESSES......Page 203
7.9 OVERDIFFERENCING AND UNDERDIFFERENCING......Page 204
7.10 MISSING VALUES IN TIME SERIES DATA......Page 206
EXERCISES......Page 210
8.2 STUDYING INPUT–OUTPUT RELATIONSHIPS......Page 212
8.3 EXAMPLE 1: THE BOX–JENKINS’ GAS FURNACE......Page 213
8.5.1 Time Series Modeling of the Input......Page 216
8.5.2 Prewhitening the Output......Page 218
8.5.3 Determining the Input–Output Relationship......Page 219
8.6 IDENTIFICATION OF THE TRANSFER FUNCTION......Page 222
8.7 MODELING THE NOISE......Page 224
8.8 THE GENERAL METHODOLOGY FOR TRANSFER FUNCTION MODELS......Page 231
8.9 FORECASTING USING TRANSFER FUNCTION–NOISE MODELS......Page 232
8.9.1 Example 2: Sales with Leading Indicators......Page 233
8.9.3 Prewhitening the Sales Series......Page 236
8.9.4 Identification of the Transfer Function......Page 239
8.9.5 Transfer Function–Noise Model......Page 240
8.9.6 Forecasting Sales......Page 241
8.10 INTERVENTION ANALYSIS......Page 247
8.10.1 Example 3: Box and Tiao Level Change......Page 248
8.10.2 Intervention Analysis of a Level Change......Page 251
8.10.3 Example 4: Crest Versus Colgate Market Share Fight......Page 253
8.10.3.2 Time Series Modeling of the Noise Process: Colgate......Page 254
8.10.3.3 Time Series Modeling of the Noise Process: Crest......Page 257
8.10.3.4 Graphical Investigation of the Intervention......Page 260
8.10.3.5 InterventionModels for the Market ShareData......Page 262
EXERCISES......Page 270
9.1.1 Review of Basic Regression Theory and Assumptions......Page 272
9.1.2 What is Spurious Relationship?......Page 273
9.1.3 Identifying Spurious Relationships......Page 278
9.2 AUTOCORRELATION IN REGRESSION......Page 280
9.2.2 Cross Correlation Analysis......Page 281
9.2.3 An Alternative Analysis: Box–Newbold’s Approach......Page 284
9.3 PROCESS REGIME CHANGES......Page 287
9.3.1 Example 2: Temperature Readings from a Ceramic Furnace......Page 288
9.4 ANALYSIS OF MULTIPLE TIME SERIES......Page 294
9.4.1 Models for Stationary Multivariate Time Series......Page 295
9.4.2 Models for Nonstationary Multivariate Time Series......Page 296
9.4.3 Model Selection Criteria for Multivariate Time Series Models......Page 297
9.4.4 Example 3: Box and Jenkins’ Gas Furnace......Page 298
9.5 STRUCTURAL ANALYSIS OF MULTIPLE TIME SERIES......Page 305
9.5.1.1 Example 4: Monitoring an Industrial Process......Page 306
9.5.1.2 PCA in Two and Three Dimensions......Page 309
9.5.1.3 PCA of the Five Temperatures......Page 311
9.5.2 Canonical Analysis of Multiple Time Series......Page 315
EXERCISES......Page 319
APPENDIX A: DATASETS USED IN THE EXAMPLES......Page 320
APPENDIX B: DATASETS USED IN THE EXERCISES......Page 336
BIBLIOGRAPHY......Page 369
INDEX......Page 373
Cataloge of Wiley Series in Probability and Statistics......Page 375