ECO321 Intro to Econometrics Homework 3

ECO321 Intro to Econometrics Homework 3

Subject: Economics    / Accounting   
Question
Please, type in your response, the output should be presented in neat tables, not
copied straight from Stata. Describe every step and report every result. You
have full 6 days to submit it. Please, submit via Blackboard by clicking on the
assignment and uploading your document. Thank you.
1. Download your dataset. It is in Stata format, so you can open it directly. It
has 4 variables only:
crsp – value-weighted index returns
div – dividend paid on the stocks in
crsp time – time variable.
For this part of exercise you will use data only up to October 1976. First,
plot your value-weighted index returns against time.
a) Can you say by looking at the picture whether these data are stationary?
Define stationarity in its weak form. Find out using formal test whether
crsp is stationary or not.
b) Try to model your returns using autoregressive model. Choose correct
lag using proper measures. Are your coefficients significant? (make sure
you use robust in your command line). What can you tell about your fit
statistics? Is your result consistent with efficient markets hypothesis
suggesting that stock prices follow random walk? What is random walk.
Describe this process.
2. Plot dividends against time.
a) Find out using formal test whether dividends are stationary or not.
b) Model your returns using an ADL model. Choose correct lags. Are your
coefficients significant? What do you think about your model?
3. Use your final model to predict returns past October, 1976 up till December
of 2002. Make a graph of both, predicted value and actual returns for this
time window (October, 1976 to December, 2002). Does your model do a good
job predicting returns? Create a variable which is a difference between
actual returns and predicted value (pricing error, sort of). Summarize it.
Does your model on average underestimate or overestimate returns? If you
applied your model in practice, would it on average be profitable?