agree to share your work on Dropbox with the rest of the class with your identification intact (“I-am- proud-of-my-work!” option) [default option if you forget to mention it in your e-mail submission];
economics
Description
Please submit your answers by midnight (11:59pm) on Friday, 27th March 2020 via vitali.alexeev@uts.edu.au. Your discussion
of results (50% of the marks) and
working code (the other 50%) should be contained
in a single Jupyter Notebook or MATLAB live script using markup
functionality or commentary. You don’t need to provide data. In marking
your empirical project, I will be executing your MATLAB scripts or Python
notebooks, so please make sure that the code is working to avoid a loss of 50% marks for code that
does not compile or throws an error on execution.
Late penalty: -2% for each hour past
deadline.
When submitting your files via e-mail, please:
1. Use the file-naming convention: LASTNAME, FIRSTNAME - PROJECT
1.
2. Indicate whether you:
(a)
agree to share
your work on Dropbox with the rest of the class with your identification intact
(“I-am- proud-of-my-work!” option) [default option if you forget to mention it in your e-mail submission];
(b)
agree to share
your work on Dropbox with the rest of the class but with your identification removed (“I-am-happy-to-share-but-I-feel-shy” option);
(c) do not like to share your work with anyone.
Question 1
1. [1 mark]
Obtain adjusted closing
prices from 01-Jan-2015
to 18-Mar-20201 for
• the DJIA index (Yahoo ticker: ^DJI),
•
gold mining company, Freeport-McMoRan
Inc. (FCX), and
•
Walmart Inc, (WMT).
2.
[3 marks]
Before you can proceed with time
series modeling, you have to make
sure that your data are stationary (does not contain unit root). Perform the following:
(a)
Check your price series for
stationarity using ADF and KPSS tests.
(b)
Convert your
closing prices to log returns and check your
return series for stationarity using ADF and KPSS tests.
(c)
What do you conclude?2 Did you use constant only or constant and a trend model as as your benchmark and why?
3.
[1 mark] Plot cumulative returns for all three assets on the same graph originating at $100
(the progression of the $100 invested
on 1-Jan-2015 to 18-Mar-2020). Make sure your x-axis represents dates and the legend with the names of the three assets is visible.
4.
[1 mark] On a
3-by-3 subplot, plot the returns in the top row as well as ACF (2nd row) and PACFs (3rd row). Based on your visual inspection of returns, ACF, and PACF plots, would you consider
an ARMA model?
5.
[4 marks]
Retain the last 10 observations for checking forecasting ability, and use the rest of your returns sample to select the optimal ARM A(p, q) model based on BIC for each of the three assets. Set maximum
model complexity to 5 (that is, p = 0...5, q = 0...5) and assume
Gaussian residuals (this is commonly the
default setting in any software).
(a)
Construct a 3D plot with p and
q
values on x and y axes
and BIC on z axis.
(b) What values of
p, q are optimal based on BIC?
(c)
What values of p, q are optimal if you are
interested in accuracy of 10-day forecasts from these models based on RMSE?
(d)
 |
Discuss your findings and propose the final ARM A(p, q) model that you favour the most.
1Note, that if you are using getMarketDataViaYahoo() function in MATLAB, set the end request date to one day later than the desired end date for your data, e.g. 16-Mar-2019.
This function seems
to return one observation
less than you request.
2In econometrics, “conclusions” are based on hypothesis tests with
analyses of p-values and chosen level of significance.
6.
[1 mark]
Perform Step 5 again, but this time use AIC to select the optimal ARM A(p, q)
model. Did your conclusion change?
7.
[1 mark] On a
3-by-3 subplot, plot the squared returns in the top row as well as ACF (2nd row) and PACFs (3rd row). Based on
your visual inspection of squared returns, ACF, and PACF plots,
would you consider a GARCH type model?
8.
[1 mark]
Perform Engle’s ARCH test for each of the 3 assets to reconfirm your conclusion
from the above step.
9.
[4 marks]
Retain the last 10 observations for checking forecasting ability, and use the rest of your returns sample to select the optimal GARCH(p, q) model based on
BIC for each of the three assets. Set maximum model complexity to 5 (that is, p = 0...5, q = 0...5) and assume Gaussian residuals (this is commonly the default setting in any software).
(a)
Construct a 3D plot with p and
q
values on x and y axes
and BIC on z axis.
(b) What values of
p, q are optimal based on BIC?
(c)
What values of p, q are optimal if you are
interested in accuracy of 10-day forecasts from these models based on RMSE?
(d) Discuss your findings
and propose the final model that you favour the most.
10.
[1 mark]
Perform Step 9 again, but this time assume Student t residuals when fitting GARCH(p, q) models. Did your conclusion change?
Note: you can substantially
simplify/reduce your code if you use/define functions as many of the steps in
this empirical project are repetitive with only few parameters varied.
