(a)  Identify a relevant time series for the total number of new vehicles sold in Australia (for at least the last 10 years) which may be useful in generating the forecasts required by the insurance company. Justify your choice of time series.

(Data should be available on relevant Australian government websites such as the Reserve Bank (RBA) or Australian Bureau of Statistics (ABS). It may also be available on relevant governmental department websites or through relevant trade organisations and/or commercial data/research agencies)

(i)                Provide a line chart of the relevant time series for approximately the last 10 years.

(ii)              Comment in general on the characteristics of the time series line chart. What systematic components are evident in the time series?

(iii)            Outline the economic and environmental factors or circumstances which are likely to have influenced the characteristics or components of the time series identified in (ii)? Will these factors or circumstances apply to the relevant forecasting period?

(b)   Apply an appropriate method to smoothe (remove randomness) from the time series chosen in (a) to help further identify the relevant systematic components.  

(i)                From the results of the above smoothing, provide a time series line chart comparing the original time series with the generated smoothed values.

(ii)             Does the line chart generated in (b (i)) suggest any re-evaluation or modification (if at all) to your answer to (a.(ii))? Explain.

(iii)           Using the results of the smoothing method you applied, provide numerical estimates for the underlying systematic components (for example, if a trend is observed provide a relevant trend equation and/or if seasonality is observed provide estimates of the seasonal relatives or indexes).

(c)   Provide at least one appropriate time series model for the time series you selected in (a) and provide relevant monthly forecasts for total new vehicle sales in Australia for April -18 to Mar-19. Justify your choice of model.