Australian Bureau of Statistics (ABS) Data Availability Assignment - UNSW

Assignment Task

Select the data series that you will analyse

In this project you will use data from the Australian Bureau of Statistics (ABS). Specifically, you will use data on components of the Consumer Price Index: ABS Catalogue 6401.0, Table 9. CPI: Group, Sub-group and Expenditure Class, Index Numbers by Capital City.

The data series you will use will be in the form of a price index. CPI indexes are currently based in financial year 2011-2012. That is, the level of the quarterly values average to 100 for this financial year (i.e. the average of the index values for quarters 2011 Q3 to 2012 Q2 equal 100 for each series).

We can download the Excel spreadsheet from the ABS website, or we can use the R package readabs to read in the data, as follows.

Task

First, plot your data using the following code, without changing anything:

myylab <- substr(myseries$series[1], 1, 6)

myxlab <- "Quarter"

mytitle <- paste0(c("CPI: "),

substr(myseries$series[1],  18,  nchar(myseries$series[1])-2))

myseries  %>%

autoplot(value) +

 theme(title = element_text(size = 10)) +

 labs(y = myylab,

 x = myxlab,

 title = mytitle)

The substr() commands take parts of the series description for use as the y-axis label and the figure title. Note that you can use myylab, myxlab and mytitle where relevant in other figures in this Project.

a. Based on just this plot, discuss characteristics of the series.

b. Decide if a transformation of your data is required. Explain your decision. If a transformation is needed, then use it throughout the rest of this Project.

c. Create a training dataset (denoted as myseries_tr) consisting of observations before 2010. Visually check that the data were split appropriately by plotting the training and test data sets in the same figure.

d. Fit an ETS model to your training data using the default ETS() command. Describe the model chosen and comment on the residuals, using the standard plots (i.e. gg_tsresiduals()) and a Ljung-Box test.

e. Produce forecasts for the test data, and plot these along with the data series from 2000. Include and comment on the prediction intervals.

f. Compare and comment on the accuracy of the model on the training data relative to the accuracy on the test data.

g. In preparation for ARIMA modelling, use the visual inspection of plots to find the appropriate order of differencing needed for stationary data. Then use statistical tests to check your choices.

h. Select an appropriate ARIMA model. Explain your choice. Comment on the residuals, using the standard plots (i.e. gg_tsresiduals()) and a Ljung-Box test.

i. Using the training data set as before, try an STL decomposition followed by ARIMA on the seasonally adjusted data; that is, an STL-ARIMA model. Using the test data set, compare the accuracy of the forecast performance with the ETS model you obtained earlier. Plot forecasts from both models on the same figure, along with the actual data from 2000 onwards. Include and comment on the prediction intervals.

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