Assignment Part 1: Perform all of the steps listed below to complete this part, which involves a time series data set. Use either complete sentences or point-form answers in your responses; just be sure your meaning is clear.
Question 1: Go to Kitco website and download the data set for the AM Gold Fix price in US dollars from January 2, 2003, to December 30, 2005. (Just click the Table tab and enter the appropriate dates.) Clean up the data set so that it is a continuous daily time series with 751 data points. Show the first five data points and the last five data points.
Question 2: Test for stationarity in the daily returns time series by following the five steps outlined in Lesson 7, Note 8. Set the correlogram to 15 lags, and look at the same time for a drift or time trend in the time series. When performing the Augmented Dickey-Fuller test, you may choose between three lag lengths: 5 days (business week), 10 days (business bi-week) or 20 days (business month). Provide the logic behind your choice of lag length for the test. State your conclusion on whether the time series is stationary or not. If you conclude that the series is non-stationary, use differencing to obtain a stationary series, then use the Augmented Dickey-Fuller unit root test to see if the series is still non-stationary. If you conclude that the series is stationary, move on to the next step.
Question 3: Divide the stationary time series into two periods: the first period goes from January 2, 2003, to December 31, 2004, and the second period goes from January 4, 2005, to December 30, 2005. Use the first period as the in-sample and the second as the hold-out sample. Show the last five data points of the in-sample.
Question 4: Use the Box-Jenkins approach in EViews to find the model(s) that best fit the in-sample from January 2, 2003, to December 31, 2004. Make sure your analysis includes the following components:
a. Identification: Use the correlogram option in EViews to obtain the acf and pacf for the stationary series. Set a lag length of 20 for the correlogram. What are the possible ARIMA models identifiable from the acf and pacf?
b. Estimation: Estimate possible ARMA models in EViews (Note that EViews allows only 23 total ARMA terms when estimating ARMA models.) To keep the amount of work that must be done manageable, do not estimate a model that is larger than ARMA(11,11) and, in fact, you may elect to estimate fewer models than p = q = 11 if you can provide a good rationale for doing so. Show the result of ARMA(5,5). If you were to estimate all the models indicated in the identification stage, how many models in total would you have to estimate?
c. Diagnostic testing: Copy Akaike's Information Criterion (AIC) and Schwarz's Bayesian Information Criterion (SBIC) for each of the estimated models into a table. Which model is the best one according to the AIC? The SBIC?
Question 5: Obtain the regression results in EViews for the best model(s) found in question 4(c) above. (Note: Since there are only two information criteria-AIC and SBIC-there are only two "best" models.).
Question 6: Use these regression results to obtain dynamic forecasts from the model(s) for the hold-out sample. Based on the Root Mean Squared Error (RMSE), MAE, MAPE, Theil's U-statistic, Bias Proportion, Variance Proportion, and Covariance Proportion, which model produces the most accurate dynamic forecasts?
Question 7: Use the regression results you obtained in question 5 to obtain static forecasts from the model(s) for the hold-out sample. Based on the Root Mean Squared Error (RMSE), MAE, MAPE, Theil's U-statistic, Bias Proportion, Variance Proportion, and Covariance Proportion, which model produces the most accurate static forecasts?
Question 8: Based on the results from questions 6 and 7, recommend which model we should use to forecast the price of gold in US dollars. In your recommendation, take into consideration as well the principle of parsimony. What does your recommended model tell us about the changes in gold prices?
Assignment Part 2:
Answer all of the questions below to complete this part. Use only complete sentences for your responses.
Use the Giddy and Dufey (1975) article in the DRR to answer the following two questions:
Question 1: Write a one- to two-page summary (double-spaced, 12-point Times New Roman font, no more than 1000 words) of the Giddy and Dufey article. Omit the section between the asterisks on p. 14 and p. 16. Include in your summary the models, data, and methodology used in the paper, the empirical tests performed, and the conclusions reached by the author.
Question 2: Write a one- to two-page critical review (double-spaced, 12-point Times New Roman font, no more than 1000 words) of the Giddy and Dufey article. Omit the section between the asterisks on p. 14 and p. 16 ("... and the variance of the rate of change of the exchange rate."). Base your review predominantly on concepts from Lessons 7 to 9 and on the readings.
As before, a good starting point might be to see if Giddy and Dufey violate any of the assumptions listed in Chapter 4 of the textbook. You may also wish to review Box 1.4, "Points to consider when reading a published paper," on p. 11 of the textbook. If you require more assistance on writing a critical review of a journal article, some guidelines are available at these URLs (or contact the Student Support Centre for assistance).
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