Homework 3

Here I have assembled the North Carolina Retail Sales data for you up to May of 2007. The data can be found on our homepage
under datasets . Look for the data set ncretail_all.sas7bdat. Alternatively I have stored it as a text file.

Just to make the report complete, we start with a graph as in assignment #1. Plot the data in the Time Series Forecasting System or, if you are interested in code, plot it with PROC GPLOT or with an SGGRAPHICS procedure. If you so choose, you may want to make the label in GOPLOT on the vertical axis parallel to that axis. To do so you can use an axis statement
```
	axis1 label=(angle=90 font=centb h=1.5) offset=(3,3); 
        proc gplot; plot ____ /vaxis=axis1; 
        symbol1 v=circle c=black i=join ci=blue; 
```
Feel free to add any other graphics options you have learned to make the graph nicer.
Does anything look a bit strange to you? If you have not already done so, look at this NC Department of Revenue web page to see if there is something we should add to the model. http://www.dornc.com/publications/monthlysales.html . In particular look at the July 2005 report there or the bold "Important: Notice of Change" and mention what you find (even if you already made this note on HW1 please note it again).
Suppose I have a level shift (like the 9/11/01 effect in our airline data) that happened on some date. I can model this by creating a special predictor variable as follows: X = (date >="11sep2001"d); Changing the date from "11sep2001"d to the proper date based on the web page information, add the appropriate X variable to the data and use PROC PRINT to see what the data look like near the change point (the one you discovered when you looked at the revenue department web page). Your code could be something like this:

PROC PRINT DATA=_____; WHERE "_____"D < DATE < "_____"D ;

where you would use date constants in the blanks to pick out a few points on either side of the shift date.
If I do this kind of shift analysis in a simple linear trend case (with a shift), my model in statement in PROC REG will be something like
```
     PROC REG; MODEL Y = DATE X; 
```
Now I will get a preciction P for Y, say for example P = 10 + .01 DATE - 80 X. Before the shift date, my predictions will lie on the trend line P= 10 + .01 DATE. After the shift they lie on another line. What are the intercept _____ and slope ______ of this new line for this explanatory example
(P= 10 + .01 DATE-80 X)?
Now using the idea in (4), the X variable you created in (3), and the full data set as provided in the link in (1), fit this kind of model to the retail sales data and fill in the estimates you get from the actual retail sales data:
```
             P = _____ + ____ DATE + _____ X
```
Overlay the plot of predicted values on the plot of the original data. Using this model, what would you guess the NC retail sales was in January 1960? Explain why that is the easiest date for which to estimate sales.
If the coefficient on X were 0, there would be no shift.
- For the real data, what is the t statistic for testing the hypothesis that there was no real shift at that date. Recall that Pr>|t| is called the "P-value" and represents the probability of getting a t like you did if in fact there is no real shfit. What is the P-value for you t statistic (the one associated with the shift)? If this probability is less than some cutoff (we often use 0.05) then it is unlikely that the true process satisfies your null hypothesis (no real shift) and we reject that hypothesis.
- Using all this information, write up one or two sentence executive summary on whether or not the event you found on the web is associated with a permanent shift in the data.
- Adjust the last part of the data by that shift coefficient to estimate what would have happened without this "intervention" and make a plot of what the data would be if the state were still reporting as it did historically.
In our previous looks at the earlier part of the data, it seemed that we used seasonal dummy variables to capture the seasonal effects. Go back and create those 11 dummy variables D1 through D11 and add them to the model. Summarize the results.
(optional) Using the discussion of intervention variables from our book, fit the model in part (5) using the SAS Time Series Forecasting System (hint: Go to the "develop models" window and select "fit a custom model")