Homework 7 
 American Airlines - Intervention Analysis 

  On Sept. 11, 2001 terrorist attacks on the U.S. involving, among others, 
American Airlines jets produced drastic effects on many aspects of life in 
the U.S. including effects on the stock market.  AMR is the parent company 
for American Airlines.

Return to the  American Airlines volume data . 
Create a variable X1 that is 1 for the first day after Sept 11, 2001 
that the stock market was open (the first post-attack chance 
to trade) and 0 elsewhere.  Create a second variable X2 that is 1 after 
Sept. 11 and 0 elsewhere. Note that when you click on this reference, an 
ARMA(1,1) model has been fit to the pre-Sept. 11 data. 

 Questions 

 

Run a regression of Volume on X1 and X2 calling for the Durbin 
Watson statistic.  You will also get a first order autocorrelation estimate r.  
For independent residuals and large sample sizes,  the statistic 
                  Z= sqrt(n)*r/sqrt(1-r*r) 
should be approximately N(0,1) as your text mentions.  Calculate
Z and give one and two sided P-values.  What is your conclusion?

Rerun the analysis in PROC AUTOREG using 3 autoregressive lags.  
Ask for the p-values for the Durbin-Watson statistic.  Use this to answer 
the following questions: 

Estimate, and give a 95% confidence interval for the shift in 
mean from pre to post attack in the long run (ignoring the initital pulse of 
activity on reopening day).

Estimate, and give a 95% confidence interval for the mean
pre-attack volume. 

Put a 95% confidence interval on the X1 coefficient and, more 
importantly, explain clearly what that coefficient means. 


Produce the predicted values X beta (predictions ignoring the error 
autocorrelation)  Plot the data and these preditions against date, overlaid. 

Plot the residuals after Sept. 11 versus date.  Comment on any pattern 
you see.  

The analysis you have done here (level shifting dummy variables) is 
typically refered to as "intervention analysis" and can also be done in 
PROC ARIMA.   Try this: 

	PROC ARIMA; 
		I  VAR=VOLUME   CROSSCOR=(X1 X2)  NOPRINT; 
		E INPUT=(X1 X2) PLOT; 

Look at the ACF IACF etc. of these regression residuals.  Fit an 
ARMA(1,1) to the residuals by adding P=1 Q=1 ML to the estimate
statement.   Summarize your findings.

Finally, our text on page 237 suggests a model on the log scale.  Taking 
logarithms of volume, using our X2 as defined here, and omitting the dates that
the stock market was closed, fit the model from the book.  Note that we do not 
have all the data that is used in the book and thus we miss an interesting 
second event (an American jet went down off of New York shortly after 9/11/01). 
Thus we would not expect to exactly match the book coefficients and we would 
not have the variable P that the book associates with that second event. 

Turn in your COMPLETE SAS program from the enhanced editor window.



 Optional exercises (Not graded - don't hand in)
 
 Try some other error models, for example you'd naturally want to try 
whatever model you found for the pre-attack data. 
 
 Use a web site to update the data and re-analyze or go to the book data 
on our course home page and at least add those extra days. 


/***********************************************************/ 


LINKS:  SAS Online Documentation