Essay Adjusted Closing Prices – Forecasting Ability – Model Complexity – Economics Assignment Help

Assignment Task :

Question 1
1. 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. 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. 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.  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. Retain the last 10 observations for checking forecasting ability, and use the rest of your returns sample to select the optimal ARMA(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 ARMA(p, q) model that you favour the most.

6.  Perform Step 5 again, but this time use AIC to select the optimal ARMA(p, q) model. Did your conclusion change?

7. On a 3-by-3 subplot, plot the squared returns in the top row as well as ACF (2nd row) and PACF (3rd row). Based on your visual inspection of squared returns, ACF, and PACF plots, would you consider a GARCH type model?

8.  Perform Engle’s ARCH test for each of the 3 assets to reconfirm your conclusion from the above step.

9.  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. Perform Step 9 again, but this time assume Student t residuals when fitting GARCH(p, q) models. Did your conclusion change?