Chapter 10 Introduction to Time Series Modeling and

Chapter 10 Introduction to Time Series Modeling and Forecasting Copyright © 2012 Pearson Education, Inc. All rights reserved.

Section 10. 1 What Is a Time Series Copyright © 2012 Pearson Education, Inc. All rights reserved.

Section 10. 2 Time Series Components Copyright © 2012 Pearson Education, Inc. All rights reserved.

Figure 10. 1 The components of a time series Copyright © 2012 Pearson Education, Inc. All rights reserved. 4

Section 10. 3 Forecasting Using Smoothing Techniques Copyright © 2012 Pearson Education, Inc. All rights reserved.

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Figure 10. 2 MINITAB plot of quarterly power loads Copyright © 2012 Pearson Education, Inc. All rights reserved. 7

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Figure 10. 3 MINITAB plot of quarterly power loads and 4 -point moving average Copyright © 2012 Pearson Education, Inc. All rights reserved. 9

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Figure 10. 4 MINITAB printout of exponentially smoothed quarterly power loads Copyright © 2012 Pearson Education, Inc. All rights reserved. 11

Figure 10. 5 MINITAB plot of exponentially smoothed quarterly power loads Copyright © 2012 Pearson Education, Inc. All rights reserved. 12

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Section 10. 4 Forecasting: The Regression Approach Copyright © 2012 Pearson Education, Inc. All rights reserved.

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Figure 10. 6 SAS scatterplot of sales data Copyright © 2012 Pearson Education, Inc. All rights reserved. 20

Figure 10. 7 SAS printout for straight-line model of yearly sales revenue Copyright © 2012 Pearson Education, Inc. All rights reserved. continued on next slide 21

Figure 10. 7 SAS printout for straight-line model of yearly sales revenue (cont’d) Copyright © 2012 Pearson Education, Inc. All rights reserved. 22

Figure 10. 8 SAS printout for quarterly power load model Copyright © 2012 Pearson Education, Inc. All rights reserved. continued on next slide 23

Figure 10. 8 SAS printout for quarterly power load model (cont’d) Copyright © 2012 Pearson Education, Inc. All rights reserved. 24

Section 10. 5 Autocorrelation and Autoregressive Error Models Copyright © 2012 Pearson Education, Inc. All rights reserved.

Figure 10. 9 a Autocorrelation functions for several first-order auto regressive error models: Rt = f 1 Rt-1 + et Copyright © 2012 Pearson Education, Inc. All rights reserved. 26

Figure 10. 9 b Autocorrelation functions for several first-order auto regressive error models: Rt = f 1 Rt-1 + et Copyright © 2012 Pearson Education, Inc. All rights reserved. 27

Figure 10. 9 c Autocorrelation functions for several first-order auto regressive error models: Rt = f 1 Rt-1 + et Copyright © 2012 Pearson Education, Inc. All rights reserved. 28

Section 10. 6 Other Models for Autocorrelated Errors (Optional) Copyright © 2012 Pearson Education, Inc. All rights reserved.

Figure 10. 10 Autocorrelations for a firstorder moving average model: Rt = et + qet-1 Copyright © 2012 Pearson Education, Inc. All rights reserved. 30

Figure 10. 11 Autocorrelations for a fourth-order moving average model Copyright © 2012 Pearson Education, Inc. All rights reserved. 31

Section 10. 7 Constructing Time Series Models Copyright © 2012 Pearson Education, Inc. All rights reserved.

Figure 10. 12 A seasonal time series model Copyright © 2012 Pearson Education, Inc. All rights reserved. 33

Figure 10. 13 Seasonal model for quarterly data using dummy variables Copyright © 2012 Pearson Education, Inc. All rights reserved. 34

Section 10. 8 Fitting Time Series Models with Autoregressive Errors Copyright © 2012 Pearson Education, Inc. All rights reserved.

Figure 10. 14 SAS printout for model of annual sales revenue Copyright © 2012 Pearson Education, Inc. All rights reserved. 36

Figure 10. 15 MINITAB residual plot annual sales model Copyright © 2012 Pearson Education, Inc. All rights reserved. 37

Figure 10. 16 SAS printout for annual sales model with autoregressive errors Copyright © 2012 Pearson Education, Inc. All rights reserved. continued on next slide 38

Figure 10. 16 SAS printout for annual sales model with autoregressive errors (cont’d) Copyright © 2012 Pearson Education, Inc. All rights reserved. 39

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Section 10. 9 Forecasting with Time Series Autoregressive Models Copyright © 2012 Pearson Education, Inc. All rights reserved.

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Figure 10. 17 SAS printout of forecasts of annual sales revenue using straight-line model with autoregressive errors Copyright © 2012 Pearson Education, Inc. All rights reserved. 43

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Section 10. 10 Seasonal Time Series Models: An Example Copyright © 2012 Pearson Education, Inc. All rights reserved.

Figure 10. 18 Water usage time series Copyright © 2012 Pearson Education, Inc. All rights reserved. 46

Figure 10. 19 SAS printout for time series model of water usage Copyright © 2012 Pearson Education, Inc. All rights reserved. 47

Figure 10. 20 Forecasts of water usage Copyright © 2012 Pearson Education, Inc. All rights reserved. 48

Section 10. 11 Forecasting Using Lagged Values of the Dependent Variable (Optional) Copyright © 2012 Pearson Education, Inc. All rights reserved.