Now use the file cons_income.dta is a STATA data file with data on real personal
disposable income, rpdi, and real personal consumption, rc. The third variable is ‘time’.
The data are quarterly from 1947q1 to 2009q2. Take the natural logarithms of rpdi and rc,
and then first difference these variables to get the approximate growth rates, So for
income: gen Lrpdi = ln(rpdi) gen DLrpdi = d.Lrpdi and similarly for consumption.
1. Analyse the statist s of the logs of the series and the differences of the
logs of the series: plot the data and look at ACF and PACF. What features do you
notice? (15 marks)
2. Test the series Lrc, Lrpdi and Ls (=Lrc – Lrpdi) for being I(1) versus I(0).
What happens if you test Ls on the periods 1947-1980 and 1980-2009 separately?
Plot the time series for Ls and interpret your results.(10 marks)
3. Estimate alternative univariate models for the differences (Dlrdi, Dlrc) using
observations up to 1999q3, leaving the remaining observations for out-of sample
forecasting. Start with AR models, then you can try different mixed ARMA
The file assignment.dta is a STATA data file containing computer generated data on four
time series, x,y,z and w and a series newt which is a quarterly time trend running from
(1950:Q1 to 1999:Q4). Assume that the series x,y,z and w are already in logs.
1. Investigate the order of integration of the series x,y,z and w, paying particular
attention to the form of test regression that you use. (5 marks)
2. Produce dynamic forecasts of x,y,z and w using an estimated VECM model for all 4
series using in-sample forecasting for the period 1990Q1 to 1999Q4. Now comparethe
1-step ahead forecast performance of a univariate AR(2) model for ?x with forecasts
of the same variable using an estimated VECM model for all 4 series using in-sample
forecasting for the period 1990Q1 to 1999Q4. What are the gains (if any) to using the
VECM compared to the simple time-series model for the series? Are these gains what
you’d expect? (10 marks)
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