Using The Common Factor Test And That There Are 32

Questions -

Q1. An econometrician suspects that the residuals (ut`s) of herhis model might be auto-correlated. Explain the steps involved in testing this theory using the Durbin-Watson (DW) test.

Q2. The econometrician follows your guidance in question (4) and calculates a value for the Durbin-Watson statistic of 0.95. The regression has 60 quarterly observations and 3 explanatory variables (plus a constant term). Perform the test. What is your conclusion?

Q3. With reference to the following regression using 45 observations:

y^t= 0.98 + 0.56xt

(0.32) (0.14)

DW = 1.52, R2= 0.4

(standard errors in brackets)

i) Interpret the above R2 statistic and determine if xt is significantly different to 0 (t-statistic).

ii) Is there any evidence of 1st order autocorrelation.

Q4. Given the following model: yt= ? + ?xt + ut

Explain how you would conduct the LM test for higher order autocorrelation. If you were testing for 4th order autocorrelation and your LM statistic was 27.8, is there any evidence of 4th order autocorrelation being present?

Q5. To overcome autocorrelation in a regression, two separate models are estimated based on the original model:

yt = ? + ?xt + ut

The first attempt involves a generalised difference equation using the Cochrane-Orcutt and produces a RSS of 0.79. The second regression uses an unrestricted version of the model and produces a RSS of 0.56. Using the Common Factor test and that there are 32 observations, which is the best method for overcoming the autocorrelation?

Q6. Which of the following hypotheses about the coefficient can be tested using a t-test? Which of them can be tested using an F-test? In each case, state the number of restrictions.

(a) H0: ?3= 2

(b) H0: ?3+ ?4= 1

(c) H0: ?3+ ?4= 1 and ?= 1

(d) H0: ?2= 0 and ?3= 0 and ?4= 0 and ?5= 0

(e) H0: ?2?3= 1.