Questions -

Q1. A researcher is attempting to form an econometric model to explain daily movements of stock returns. A colleague suggests that she might want to see whether her data are influenced by daily seasonality.

a) How she go about doing this?

b) The researcher estimates a model with the dependent variable as the daily returns on a given share traded on the London stock exchange, and various macroeconomic variables and accounting ratios as independent variables. She attempts to estimate this model, together with five daily dummy variables (one for each day of the week), and a constant term, using EViews. EViews then tells her that it can't estimate the parameters of the model. Explain what has probably happened and how she can fix it.

c) A colleague estimates instead the following model for asset returns, r_t is as follows (with standard errors in parentheses)

r^{^}_t = 0.0034 - 0.0183D1_t + 0.0155D2_t - 0.0007D3_t - 0.0272D4_t + other variables

(0.0146) (0.0068) (0.0231) (0.0193)

The model is estimated using 500 observations. Is there significant evidence of any day-of-the-week effects after allowing for the effects of the other variables?

d) Distinguish between intercept dummy variables and slope dummy variables, giving an example of each.

Q2. a. Explain the term 'parameter structural stability'.

b. A financial econometrician thinks that the stock market crash of October 1987 fundamentally changed the risk-return relationship given by the CAPM equation. He decided to test this hypothesis using a Chow test. The model is estimated using monthly data from January 1980 to December 1995, and then two separate regressions are run for the sub-periods corresponding to data before and after the crash. The model is; rt = α + βR_mt + u_t

So that the excess return on a security at time t is regressed upon the excess return on a security at time t. The results for the three models estimated for a given stock as follows:

1981M₁ - 1995M₁₂

r_t = 0.0215 + 1.49r_mt, RSS = 0.189, T = 180

1981M₁ - 1987M₁₀

r_t = 0.0163 + 1.308r_mt, RSS = 0.079, T = 82

1981M11 - 1995M12

r_t = 0.0360 + 1.613r_mt, RSS = 0.82, T = 98

c. What the null and alternative hypothesis that are being tested here, in terms of α and β?

d. Perform the test. What is your conclusion?