(a) Suitability of methods.
(b) Interpretation of the results, arguments used and conclusions drawn.
(c) Presentation: Appropriate style of graphs, tables, reporting and clarity of writing.
Forecasting official statistics is very common in business and government. In this Problem Set you will use data from the Australian Bureau of Statistics (ABS). Specifically, some data from latest release of the National Accounts.
Problem [10 marks]:
One of the most watched statistics for business and government is real Gross Domestic Product (GDP).
We can use the package readabs to read Australian real GDP directly from ABS website and create a tsibble,as follows:
gdp <- read_abs_series(“A2302459A”) %>%
select(date, value) %>%
mutate(Quarter = yearquarter(date)) %>%
index = Quarter
A2302459A is the series ID for “Gross domestic product: Chain volume measures”, or “real GDP”, that can be looked up from the relevant ABS data spreadsheet.
- The data are in the form of a quantity index (“chain volume measure”), with the values expressed in 2020-21 fiscal-year dollars. For tidier plots, transform the series from millions to billions of dollars.
- Restrict your data set to start from 1990 Q1. Use this data set of the rest of this problem. Do not use a transformation.
a.Make a time plot of your data and describe the main features of the series using this one plot.
b.Create a training set that withholds the last five years of available data. Forecast the five-year test set using each of the following methods:
i) a naive model;
ii) an ETS model automatically selected by R (report the model selected);
iii) Holt’s linear trend method;
iv) an STL decomposition applied to the data followed by an ETS model applied to the seasonally adjusted data.
c.Plot the point forecasts for all the models on one figure along with the actual data, starting from 2012 (to make it easier to see the forecasts). Discuss the relative performance of the different methods.
d.Compare the accuracy of your forecasts against the actual values in the test set of data by comparing the RMSE of the methods (using accuracy()). Based on the RMSE, which method is best? Explain.
e.Using plots, check and comment on the residuals of the preferred method chosen by the RMSE.
f.Conduct a Ljung-Box test with 8 lags. What do you conclude? Now do the Ljung-Box test with 16 lags. What do you conclude? Discuss.
Marking for this Problem:
(a) Suitability of methods. 3 marks: Methods are chosen for you, so the emphasis is on appropriate mplementation
- 0 marks: Inappropriate methods used or methods inappropriately implemented.
- 1 mark: An attempt has been made to answer the question using methods that are appropriate and appropriately implemented.
- 2 marks: Answers generally follow the provided solutions.
- 3 marks: All methods are appropriate and appropriately implemented.
(b) Interpretation of the results, arguments used and conclusions drawn. 5 marks
- 0 marks: Little or no discussion of results.
- 1 mark: Little attempt to discuss the results, or a poor understanding of the results found.
- 2 marks: An attempt has been made to understand and explain all the results.
- 3 marks: Systematic and sensible discussion of all results.
- 4 marks: Discussion of the results seem correct and insightful.
- 5 marks: Insightful discussion beyond what might reasonably be expected, possibly drawing on external references and other research.
(c) Presentation: Appropriate style of graphs, tables, reporting and clarity of writing. 2 marks
- 0 marks: Difficult to follow what has been done. Small font making graphs and tables hard to read.
Lack of clear writing.
- 1 mark: Presentation of results falls short of the standard in the provided solutions for tutorial exercises.
- 2 marks: Presentation of results consistent with the standard in the provided solutions for tutorial exercises.
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