Time Series Exercise 1 - Stationary Data

Due: Wed. Nov. 7, 2007

This exercise is on stationary methods only. Use brneal.dta which is
Harold Clarke's British approval data for the Thatcher-Major
period. The data are described in his Electoral Studies piece which is
on the web. The DV is either CONS (conservative party support) or
pmsat (support for the pm). All data are as described in their
article (on the web site), but some variables are missing.

Here are the stationary models I can think of. You will work with more
than one IV, but for interpretation discuss only one iv of interest. I
have given them names, but these are non-standard and may not appear
in texts.  ERRORS ARE IID UNLESS NOTED, ADD CONSTANTS

OLS y_t=bx_t
AR1 y_t=bx_t, errors ar1 (\epsilon_t = \rho \epsilon_{t-1}+\nu_t)
Finite DL y_t = b1 x_t + b2 x_{t-1}
LDV y_t = b x_t + \phi y_{t-1)
ADL y_t = b1 x_t + b2 x_{t-2}  + \phi y_{t-1) 
EC \Delta y_t = \Delta x_t - \phi(y_{t-1_ - \gamma x_{t-1})

1. Estimate each model.

2. Which models are nested inside bigger models? For those that are
   nested, test the smaller against the bigger model. (If you cannot
   do the actual tests, look at the coefs and see whether you think
   the constraint (the smaller model) makes sense).

3. For each model, plot an impulse response function for one x - that
   is, generate enough data points so that the model is in steady
   state, then shock x by one unit for one time period and plot the
   behavior of y.

3a. Use your words to describe each of the plots.

4. Do the same thing but for a unit response function, that is shock x
   by one unit and keep it at the new level until a new equilibrium is
   reached.

5.  Use your words to describe each of the plots.

6. Take your estimate of the Cochrane-Orcutt AR1 error model
   (specification 2). Make sure you can repeat the first iteration by
   hand, that is, do OLS, compute rho, transform and reestimate. How
   close are the results to the fully iterated Cochrane-Orcutt?