Convergence Problems with NLS equation with many variables:

[psantoro]

Hello,
I am attempting to model the unemployment rate via the logistic STAR model described in Terasvirta’s 1994 article from the Journal of the American Statistical Association. The first step involves estimating an AR equation with a number of lags sufficient to yield white noise error terms; in this case it was 12. The second step is to estimate via NLS the STAR model. My specification is the following:
d(ue)=c(1)+c(2)*d(ue(-1))+c(3)*d(ue(-2))+c(4)*d(ue(-5))+c(5)*d(ue(-7))+c(6)*d(ue(-8))+c(7)*d(ue(-8))+c(8)*d(ue(-9))+c(9)*d(ue(-10))+c(10)*d(ue(-11))+c(11)*d(ue(-12))+(c(12)*d(ue(-1))+c(13)*d(ue(-2))+c(14)*d(ue(-5))+c(15)*d(ue(-7))+c(16)*d(ue(-8))+c(17)*d(ue(-8))+c(18)*d(ue(-9))+c(19)*d(ue(-10))+c(20)*d(ue(-11))+c(21)*d(ue(-12)))/((1+exp(c(22)*(tv5 – c(23)))))/.276553)

Where tv5 = d(ue(-1))-d(ue(-5)) which serves as the transition variable. The .276553 is the standard deviation of this series, which several authors have advised we divide c(22) (c(22) is often referred to as the smoothness parameter). by if the true value of c(22) is large. I have tried inputting starting values which are very small for each of the coefficients, ranging from .01 to .1, and being sure to select “user supplied” under “coefficient starting values” in the options when estimating an equation. I repeatedly get convergence failure, which as you know means you don’t get t-statistics or standard errors for the coefficients. I also tried estimating only the transition function: (1+exp(c(22)*(tv5 – c(23)))))/.276553), setting small starting values (between 0 and 1) for c(22) and c(23). I have consulted the eviews manual as well as several sources but I still can’t get over this snag. I know convergence problems tend to be more difficult b

Could someone give me some suggestions? I am aware that Logl object is another option. Maximum likelihood is an area in which I haven’t been trained, but to which I fear I may have to resort if this doesn’t work out.

[EViews Gareth]

You might want to upload your workfile.

[psantoro]

Thank you Gareth. Here it is.

[EViews Gareth]

Unmatched parenthesis error, copying the spec you wrote above.

[psantoro]

I was writing it by hand so I may have left out a parenthesis.
Here's the real one.

d(ue) = c(1) + c(2)*d(ue(-1))+c(3)*d(ue(-2))+c(4)*d(ue(-3))+c(5)*d(ue(-4))+c(6)*d(ue(-7))+c(7)*d(ue(-8))+c(8)*d(ue(-9))+c(9)*d(ue(-10))+c(10)*d(ue(-11))+c(11)*d(ue(-12))+(c(12)*d(ue(-1))+c(13)*d(ue(-2))+c(14)*d(ue(-3))+c(15)*d(ue(-4))+c(16)*d(ue(-7))+c(17)*d(ue(-8))+c(18)*d(ue(-9))+c(19)*d(ue(-10))+c(20)*d(ue(-11)))/(1+exp(c(22)*(tv5-c(23))))/.276553

[EViews Gareth]

I didn't get much further than you did - it might be that the model is simply badly specified.

[psantoro]

Thank you for trying. Would you say it's back to the drawing board (that is, estimating a different model), or is a different specification called for (but within the same model/framework)? Just curious to know what your experience might suggest...