Time series

Question 1

Why is a time trend included in the model

Answer 1

To control for a deterministic time trend that might cause a spurious correlation between the two variables.

Question 2

A Breusch-Godfrey test for first-order autocorrelation has been carried out. The p-value for this test is equal to 0.0023. What do you conclude and what does it imply for the estimation results

Answer 2

The null hypothesis of no autocorrelation is rejected at the 1% level, because the p- p-value <0.01. This is evidence in favour of autocorrelation. This does not affect the parameter estimates (they are consistently estimated) but does affect its standard errors. Hence, all statistical tests based on Table 1 are invalid.
We could correct for autocorrelation using Newey-West standard errors [These are NOT “Stata” robust standard errors], or use, e.g., a prais (-winston) estimator.

Question 3

A Dickey-Fuller test has been carried out to test for a unit root in the log(AEX index). The corresponding null hypothesis is not rejected. What do you conclude, also concerning the results in Table 1?

Answer 3

if H0 is not rejected => unit root (not a trend-stationary series) => this could invalidate all results of Table 1. Arguably, we should also check for a unit root in log(Stockprice), and (1) might be a cointegrated relationship, and then all would be fine.