Am 20.07.2011 19:35, schrieb Johann Jaeckel: > Hello. > > It's my first time posting on this list. I hope the issue I am having is > appropriate for this forum. Any help is greatly appreciated. > > I want to estimate a simple model with one independent variable using > MLE with a twist. > > The twist is the following, the effect of the independent variable (X) > is split into a short run (SR) and a long run (LR) coefficient. My model > thus looks like this: > > Y = a + b1*X_LR + e_LR + b2*X_SR + e_SR > > where e_LR and e_SR are i.i.d. disturbances. X_LR is a centered moving > average of the independent variable and X_SR is the deviation of the > actual series from its moving average. > > The length of the moving average should be determined endogenously, i.e. > in such a way that the likelihood function is maximized. > > Now, I am capable of running a basic MLE in Gretl by specifying the > log-likelihood function and the derivatives. However, I am having > troubles with creating the short run and the long run series and in > particular with the endogenous determination of the length of the moving > average. > > I have a hunch that I need to iterate the MLE command itself, but I have > no clue how to implement this in a script. >
Without having thought this through (and thus no guarantees, as always), sounds as if you could use a state-space approach here. (check the Kalman filter documentation) good luck, sven
