Multivariate STAR Model

by TomDoan » Tue Jun 17, 2014 1:21 pm

Attached is an example of a bivariate STAR model. The base model is a VAR on the GDP growth rate and an interest rate spread. The threshold variables are different lags of the growth rate: lag one in GDP equation and lag two in the spread equation. In this case, all four branches (two regimes x two equations) use the standard two lag VAR explanatory variables, though that isn't required.

As I've told a number of people who have asked about this, it's a straightforward extension of the STAR model to a multivariate setting. In fact, this uses the univariate regressions (done withNLLS) to get guess values for the multivariate regression (done with NLSYSTEM). The main reason there's a relatively thin literature with actual data is that it can be hard to get it to work properly. In this case, for instance, the spread equation fits better with a "sharp" rather than "smooth" transition, which means that the optimal value for the gamma (the scale in the logistic) is infinity and the center point can't be estimated well using non-linear least squares since the sum of squares isn't differentiable.

app19-9-2.rpfProgram file(1.71 KiB) Downloaded 74 times
g7_japan.datData file(2.93 KiB) Downloaded 53 times