Example 6. Regression with Serially Correlated Errors: Expenditure Data

The following data is available from the first quarter (Q1) 1952 to the fourth quarter (Q4) 1956 on the following variables:
T: Time period
Y: Consumer expenditure in the U.S. (in billions of dollars)
X: Money stock (in billions of dollars)

Source: Chatterjee, S. and Price, B. Regression Analysis by Example. John Wiley & Sons: New York.

Table 6: Expenditure Data

 T      Y      X
 1  214.6  159.3
 2  217.7  161.2
 3  219.6  162.8
 4  227.2  164.6
 5  230.9  165.9
 6  233.3  167.9
 7  234.1  168.3
 8  232.3  169.7
 9  233.7  170.5
10  236.5  171.6
11  238.7  173.9
12  243.2  176.1
13  249.4  178.0
14  254.3  179.1
15  260.9  180.2
16  263.3  181.1
17  265.6  181.6
18  268.2  182.5
19  270.4  183.3
20  275.6  184.3

Questions:

1. Define and discuss serial correlation in the errors. How can its presence be detected?
   
   
2. What is the effect on the regression of ignoring the serial correlation in the errors?
   
   
3. How can we carry out a regression analysis for data observed over time?

Keywords: Durbin-Watson statistic, Cochrane-Orcutt procedure, generalized least squares, autoregressive time series regression models