The e1.xls file contains seasonally adjusted quarterly observations from the first quarter of 1960 to the third quarter of 2011 on the volume index (2005=100) of GDP of Australia (rgdpaus). Take the logarithms of this variable and call it lnrgdpaus. In the subsequent tasks always use this log transformed variable.
a) Plot the level and first difference of lnrgdpaus and briefly comment on the graphs.
b) Obtain the sample correlograms of the level and first difference of lnrgdpaus for 20 lags. What do they suggest to you?
c) Perform various unit root tests on lnrgdpaus by executing the unitroot.prg program. Use a maximum lag of 12 quarters and the SC model selection criterion. What do you conclude?
d) Execute the EViews add-in program called Automatic ARIMA selection on lnrgdpaus to determine the best ARIMA model. Use only a constant term as extra independent variable, maximum four AR and MA terms, no SAR (seasonal AR) and SMA (seasonal MA) terms, only first difference and the SC model selection criterion.
e) Decompose the lnrgdpaus series into the permanent (i.e. trend) and transitory (i.e. cycle) components. First perform the Beveridge-Nelson decomposition based on your preferred ARIMA specification from part (d) above by executing the EViews add-in program of the same name. Then, apply the Hodrick-Prescott filter and save both the trend (smoothed series) and the cycle. In both cases plot the estimated permanent and transitory components. Compare the two graphs to each other.
f) Suppose that you previously concluded that lnrgdpaus is trend-stationary and estimate the deterministic trend component of the alleged data generating process by regressing lnrgdpaus on a constant and the time variable. If lnrgdpaus is indeed trend-stationary then the deviations from the estimated trend (i.e. the residuals from your regression) constitute a third alternative estimate of the transitory component. Compare the three estimated transitory components to each other by displaying them on a single time-series plot. What do you notice?
Attachment:- e1.xls