Problem Set 1
Robert Kohn
UNSW School of Business
University of New South Wales
ECON 5248 2023
March 11, 2023
This problem set is to be handed in by 6 pm on Monday the 20th of
March. Apologies for its lateness.
Please look at my notes on section 5.5 of the book.
Please obtain the daily closing prices for CBA stock from 13th February
2023 to 10th of March.
Q1. (a) Please fit a random walk with drift model to the price data by esti-
mating the parameters of the model; and report these parameters.
Assume that the errors in the model are normally distributed.
(b) Please use the model to predict the close prices for the next 8
trading days.
(c) Please obtain 80% PI’s for the closing prices for the next 8 trading
days.
(d) Please use the model to generate 100 potential paths for the closing
prices for the next 8 trading days. Plot the observed data and
some of the paths selected at random, or all the paths.
(e) Use these 100 potential paths to obtain 80% predictions and PI’s
for the prices for the next 8 trading days.
(f) perform diagnostics on the model to see how well it fits the data.
That includes the Box-Ljung test on the residuals, acf plot of the
residuals, normal-quantile plot of the residuals, histogram of the
residuals.
1
Q2. An alternative model for the data is to fit a random walk with drift
to the log of the closing prices. Repeat all parts of Q1 for this model.
Note that your predictions and PI’s should be for the prices and not
the log prices.
Note that in this question you can have two predictors, the mean and
the median predictors.
Q3. Please use time series cross-validation (TSCV) to differentiate the per-
formance of the model in Q1 with the model in Q2.
Q4. Now compare the two models with respect to the actual closing prices
for the next 5 trading days, i.e., March 13 to 17th and report the results.