Financial Econometrics (ASB
Use the data money.dta:
a VAR(1) and a VAR(2) for the four variables, including two dummy
Which is preferred on AIC?
Test for autocorrelation (LM tes
ts) after estimating t
he VAR(2) and after for VAR
. What do
these test suggest
Estimate the cointegrating rank for a second order VAR, including a constant but not
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
concerning the cointegrating rank change?
Now use the
file cons_income.dta is a STATA data file with data on r
and real personal consumption, rc. The third variable is `time’.
he data are quarterly from
1947q1 to 2009q2.
Take the natural logarithms of rpdi and rc,
and then first differ
ence these variables to get the approximate growth rates, So for
income: gen Lrpdi
gen DLrpdi = d.Lrpdi
and similarly for consumption
Analyse the statistical properties of the logs of the series and the diffe
rences of the
series: plot the data and look at ACF and PACF. What features do you
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
Plot the time series for Ls and interpret your results.
Estimate alternative univariate models for the differences (
Dlrdi, Dlrc) using
observations up to
1999q3, leaving the remaini
ng observations for out
forecasting. Start with AR
then you can try different mixed ARMA
The file assignment.dta is a STATA data file containing compu
ter generated data on four
series, x,y,z and w and a series newt whi
ch is a quarterly time
trend running from
1999:Q4). Assume that the series x,y,z and w are already in logs.
Investigate the order of integration of the series x,y,z and w, paying particular
attention to the form
of test regressi
on that you use
Produce dynamic forecasts of x,y,z and w using an estimated VECM model for all 4
series using in
sample forecasting for
d 1990Q1 to 1999Q4. Now compare
step ahead forecast performance of a univariate AR(2) model for ?x with
of the same variable using an estimated VE
CM model for all 4 series using
forecasting for the period 1990Q1 to 1999Q4.
What are the gains (if any) to
VECM compared to the simple time
model for the series? Are these
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