DSCI 5340: Predictive Modeling and Business Forecasting Spring 2013 – Dr. Nick Evangelopoulos

1. DSCI 5340: Predictive Modeling and Business ForecastingSpring 2013 – Dr. Nick Evangelopoulos Lecture 11: General Box-Jenkins Approach, Interventions (Ch. 12) Material based on: Bowerman-O’Connell-Koehler, Brooks/Cole

2. Homework in Textbook Page 523 Ex 11.6 through 11.9

3. EX 11.6 and 11.7 Page 523 • Least squares estimates of q1 and q1,12 are -.18157 and .38802, respectively (see Lag column). Note that in the model there is another negative sign that needs to be included with these coefficients, except for the multiplicative term. • P-values are .02 and <.0001. Since they are less than .05, consider the coefficients to be significant. Note there is no significance test for the multiplicative part.

4. EX 11.8 Page 523 • All ChiSq p-values are large, which implies an adequate fit. One should also look at the individual autocorrelations to see if there are any moderately large values.

5. EX 11.9 Page 523 To obtain a 99% prediction interval, first find SE179(178). Note Margin of Error = (406.8397 – 401.5445)/2 = 5.2972/2 = 2.6476. Approximate t(df = 178-2)[a/2=.025] by Z.025 = 1.96; Note that Z.005 = 2.576. SE179(178) = 2.6476/1.96 = 1.3508 (same as value on page 523 in output). Lower Limit for 99% PI: 404.1921 – 2.576*1.3508 = 400.712 Upper Limit for 99% PI: 404.1921 + 2.576*1.3508 = 407.672

6. General Box Jenkins Approach • Identification • Fitting • Diagnostics • Refitting if necessary • Forecasting

7. Different Names for the Chi-Square Goodness of Fit Test • Box Statistic • Ljung-Box Statistic • Ljung-Box-Pierce Q Statistic • Portmanteau Test

8. Seasonal ARIMA Models • Basic concept is to add extra terms to model that take into account a persistent seasonal pattern • For example, a AR model for monthly data may contain information from lag 12, lag 24, etc. • i.e. Yt = A1Yt-12 +A2 Yt-24 + et • This is referred to as an ARIMA(0,0,0)x(2,0,0)12 model • General form is ARIMA(p,d,q)x(ps,ds,qs)s • This combines both non-seasonal and seasonal terms • This provides a broader class of models so the challenge is to select a model from a larger class.

9. Box Cox Transformation:Determine l to Maximize R-square Box-Cox is a family of power transformations: Y = Yλ, Such that R-squared is maximized (or, equivalently, SSE is minimized) λ = 2 Y* = Y2 λ = 0.5 Y* = √Y λ = 0 Y* = logeY (by definition) λ = -0.5 Y* = 1/(√Y) λ = -1 Y* = 1/Y

10. Independent Variables Can Be Added to Box-Jenkins Models • Independent variables are appropriate when their coefficients are not changing much over time. • The error term to the prediction model is treated as the new Y variable for the Box-Jenkins model

11. Box Jenkins Operators

12. Examples of Operators for Selected Conditions

13. Autoregressive Operators

14. General Box Jenkins Model

15. Stationarity & Invertibility Conditions Sum of coefficients for any one operator must be less than 1.

16. Guidelines for Fitting Box Jenkins Models

17. Intervention Models: Directory Assistance example

18. Estimation of Intervention Model

19. General Intervention Model Include the following statements in proc arima: identify var=y(1,12) crosscor=(S(1,12)) estimate q=(12) Input = (0$/(1)S) ;

21. Shift and Pulse Interventions Shift Dummy Variable Pulse (Additive) Dummy Variable

22. Homework in Textbook Page 524 Ex 11.10 and 11.11 Page 534 Ex 11.15

23. Please complete SETE! (my.unt.edu) The Spring 2013 Student Evaluation of Teaching Effectiveness is open and will remain open through the middle of May. Students can access the SETE via the my.unt portal. Very Important for Instructors!!!