Practical Time Series Analysis Using SAS

一又二分之一

Contents
Part 1: Time Series as a Subject for Analysis .................................. 1
Chapter 1 Time Series Data .......................................................... 3
1.1 Time Series Questions............................................................. 3
1.2 Types of Time Series: Theoretical Considerations ......................................................................... 4
1.3 Types of Time Series: Practical Considerations ............................................................................. 4
1.4 Time Series Procedures in SAS ........................................................................................................... 5
1.5 References for Data Used in this Book .............................................................................................. 6
Part 2: Time Series in SAS ............................................................... 7
Chapter 2 Datetime Variables in SAS ................................................................... 9
2.1 Datetime Variables ................................................................................................................................ 9
2.2 Output Formats ..................................................................................................................................... 9
2.3 Importing Datetime Variables ........................................................................................................... 12
2.4 Handling Datetime Variables ............................................................................................................ 14
2.5 Time Series Data Sets ........................................................................................................................ 16
Chapter 3 Aggregation Using PROC TIMESERIES ............................................... 19
3.1 Aggregation ......................................................................................................................................... 19
3.2 PROC TIMESERIES ............................................................................................................................. 19

Chapter 4 Interpolation Using PROC EXPAND .................................................... 23
4.1 Interpolation of Time Series ............................................................................................................... 23
4.2 PROC EXPAND .................................................................................................................................... 23
Part 3: Forecasting ........................................................................ 27
Chapter 5 Exponential Smoothing of Nonseasonal Series .................................. 29
5.1 Simple Exponential Smoothing ......................................................................................................... 29
5.2 Double Exponential Smoothing ......................................................................................................... 30
5.3 Forecasting Danish Fertility by Exponential Smoothing ................................................................. 33
5.4 Forecast Errors ................................................................................................................................... 38
5.5 Forecast Errors for the Prediction of Danish Fertility ..................................................................... 39
5.6 Moving Average Representations ..................................................................................................... 40
5.7 Calculating Confidence Limits for Forecasts................................................................................... 42
5.8 Applying Confidence Limits for Forecasts ....................................................................................... 42
5.9 Confidence Limits for Forecasts of Danish Fertility ........................................................................ 43
5.10 Determining the Smoothing Constant ............................................................................................ 46
5.11 Estimating the Smoothing Parameter in PROC ESM .................................................................... 47
5.12 Holt Exponential Smoothing and the Damped-Trend Method ..................................................... 49
5.13 Forecasting Fertility by the Damped-Trend Method in PROC ESM ............................................ 50
5.14 Concluding Remarks about Exponential Smoothing for Forecasting ......................................... 53
Chapter 6 Forecasting by Exponential Smoothing of Seasonal Series ................ 55
6.1 Seasonal Exponential Smoothing ..................................................................................................... 55
6.2 Using the Winters Method for Seasonal Forecasting ..................................................................... 56
6.3 Forecasting the Number of Overnight Stays by US Citizens at Danish Hotels ............................ 57
6.4 Forecasting Using Additive Seasonal Exponential Smoothing with PROC ESM ......................... 61
6.5 Forecasting US Retail E-Commerce Using the Winters Method ................................................... 63
6.6 Forecasting the Relative Importance of E-Commerce by PROC ESM .......................................... 67
6.7 Forecasting the Relative Importance of E-Commerce Using a Transformation in PROC ESM ................. 70
Chapter 7 Exponential Smoothing versus Parameterized Models ....................... 75


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一又二分之一

7.1 Exponential Smoothing Expressed as Autoregressions ................................................................. 75
7.2 Autoregressive Models ....................................................................................................................... 76
7.3 Fitting Autoregressive Models ........................................................................................................... 77
7.4 Autocorrelations .................................................................................................................................. 78
7.5 ARIMA Models ..................................................................................................................................... 79
7.6 Estimating Box-Jenkins ARIMA Models in SAS............................................................................... 81
7.7 Forecasting Fertility Using Fitted ARMA Models in PROC VARMAX ............................................ 82
7.8 Forecasting the Swiss Business Indicator with PROC ESM .......................................................... 86
7.9 Fitting Models for the Swiss Business Indicator Using PROC VARMAX ...................................... 90
art 4: Seasonal Adjustments........................................................ 97
Chapter 8 Basic Adjustments Using the Census X11 Method ............................. 99
8.1 Seasonality .......................................................................................................................................... 99
8.2 Seasonal Adjustment Using Census X11 ....................................................................................... 101
8.3 Seasonal Adjustment of US E-Commerce ..................................................................................... 103
8.4 Seasonal Adjustment of UK Unemployment .................................................................................. 108
Chapter 9 Additional Facilities in PROC X12 .................................................... 115
9.1 Model Fitting and Forecasting Using PROC X12 ........................................................................... 115
9.2 Seasonal Adjustment of US E-Commerce Data Using the Additional Features in PROC X12 ...... 116
9.3 Seasonal Adjustment of the Number of Overnight Stays ............................................................. 121
Part 5: Unobserved Components Models ..................................... 129
Chapter 10 Models with Unobserved Components ........................................... 131
10.1 Formulation of the Basic Model .................................................................................................... 131
10.2 ARIMA Representation ................................................................................................................... 132
10.3 Extensions of the Model ................................................................................................................. 132
10.4 Estimation of Unobserved Components Models ......................................................................... 134
10.5 State Space Models in SAS ............................................................................................................ 135
Chapter 11 Analysis of Danish Fertility Using PROC UCM ................................ 137
11.1 Component Estimation ................................................................................................................... 137
11.2 Outlier Detection ............................................................................................................................. 139
11.3 Extensions of the Model ................................................................................................................. 142
Chapter 12 Analysis of US E-Commerce Using PROC UCM .............................. 149
12.1 Estimation of the Components ...................................................................................................... 149
12.2 Regression Components ................................................................................................................ 155
12.3 Model Fit .......................................................................................................................................... 158
Chapter 13 An Analysis of the Arctic Ice Coverage Series Using Unobserved Components ... 161
13.1 The Time Series ............................................................................................................................... 161
13.2 Aggregation to Yearly Averages .................................................................................................... 161
13.3 Aggregation to Monthly Averages ................................................................................................. 168
13.4 Aggregation to Weekly Averages .................................................................................................. 173
13.5 Aggregation to a Series Observed Every Second Day ................................................................ 179
13.6 Analysis of the Daily Series ............................................................................................................ 181
13.7 Concluding Remarks ...................................................................................................................... 185
References ...................................................................................................... 187
Index ............................................................................................................... 189

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