At the start of an R session for this course, remember to type  library(fpp3) in the R Studio Console.  This will then load (most of) the R packages you will need, including some data sets.

Details:

• Total value: 10 marks.

• Submission is due on Friday of Week 5 (17 March), 4pm.

• A submission link is on the Moodle site under the heading Assessments Hub.

• Submit your answer document in PDF format. Your file name should follow this naming convention:

PS1_your first name_zID_your last name_ECON2209.pdf

For example: PS1_John_z1234567_Smith_ECON2209.pdf

• You get one opportunity to submit your file. Make sure that you submit the file that you intend to submit.

• Your submitted answers should include the R code that you used and any tables and figures produced.  Note that in the bottom right quadrant of RStudio, under the Plots tab there is an export button. This  can be used to export figures for inserting into your answer document; e.g. select “Copy to Clipboard” and paste into a Word document. (Other methods are also possible.) You do not need to use Word.  You could use e.g. R Markdown, in which case the figures would be automatically included in your

PDF file.

For all assessments in this course, the marking criteria are as follows.

Marking Criteria:

(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:

library(readabs)

gdp  <-  read_abs_series("A2302459A")  %>%

select(date,  value)  %>%

mutate(Quarter  =  yearquarter(date))  %>%

as_tsibble(

index  =  Quarter

)  %>%

select(-date)  %>%

rename (real_GDP=value)

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.

Some Preliminaries:

• 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.

Tasks:

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.