Problem Set 3
Robert Kohn
UNSW School of Business University of New South Wales ECON 2021
March 18, 2021
Please hand in the solution to this problem set by 5 pm on March 25th.
Q1. Are the following statements true or false? Explain your answer.
a. Good forecast methods should have normally distributed residu- als.
b. A model with small residuals will give good forecasts.
c. The best measure of forecast accuracy is MAPE.
d. Always choose the model with the best forecast accuracy as mea- sured on the training set.
e. Always choose the model with the best forecast accuracy as mea- sured on the test set.
Q2. Consider the number of pigs slaughtered in New South Wales (data set aus livestock). Produce some plots of the data in order to become familiar with it. Create a training set of 486 observations, withholding a test set of 72 observations (6 years). Consider the forecasting methods: naive, naive seasonal and drift
a. Which method do you think does best on the test data set in terms of prediction?
b. Which method do you think does best on the test data set in terms of prediction intervals?
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c. Check the standardised residuals of your preferred method. Do they resemble white noise?
d. Are the standardised residuals of your preferred method approxi-
mately normally distributed? Do a normal quantile plot to check
for normality; see https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/qqnorm
d. Are the standardised residuals of your preferred method approxi- mately independent of the fitted values?
Q3. Consider the Bricks data from aus production (Australian quarterly clay brick production 1956–2005) for this question. Use the data from 1956-2000 (4th quarter) to train each model.
a. Use an STL decomposition to calculate the trend-cycle and sea- sonal indices. (Experiment with having fixed or changing season- ality.)
b. Compute and plot the seasonally adjusted data.
c. UseaNa ̈ıvemethodtoproduceforecastsoftheseasonallyadjusted data.
d. Use decomposition model() to reseasonalise the results, giving fore- casts for the original data.
e. Do the residuals look uncorrelated?
f. Repeat with a robust STL decomposition. Does it make much difference?
g. Compare forecasts from decomposition model() with those from SNAIVE(), using a test set comprising the last 4 years of data. Which is better?
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