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?