Questions -

Q1. An econometrician suspects that the residuals (u_t's) of her\his 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 + 0.56x_t

(0.32) (0.14)

DW = 1.52, R² = 0.4

(standard errors in brackets)

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

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

Q4. Given the following model: y_t = α + βx_t + u_t

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

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

y_t = α + βx_t + u_t

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: β₃ = 2

(b) H₀: β₃ + β₄ = 1

(c) H₀: β₃ + β₄ = 1 and β₅ = 1

(d) H₀: β₂ = 0 and β₃ = 0 and β₄ = 0 and β₅ = 0

(e) H₀: β₂β₃ = 1.