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The data required for the Assessment are provided on the module web page. Your answer should be no more than 2000 words (excluding bibliography, notes, tables, figures and equations).
Use the data money.dta:
1. Estimate a VAR(1) and a VAR(2) for the four variables, including two dummy variables (dumy, dumo). Which is preferred on AIC? (15 marks)
2. Test for autocorrelation (LM tests) after estimating the VAR(2) and after for VAR
(1). What do these test suggest ? (10 marks)
3. Estimate the cointegrating rank for a second order VAR, including a constant but not a trend. What do you .nd the cointegrating rank to be? Repeat with a restricted trend (this allows for a trend in the cointegrating relationships). How do the results concerning the cointegrating rank change?(15 marks)
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 specifications.(20 marks)
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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