Explosive Threshold VAR

[asmith05]

Hello,

I am somewhat new to estimating threshold VARs but I am having a strange problem. Any insight or suggestion is appreciated. I have a simple 4 variable VAR (ordered: log difference of real GDP, log difference CPI, fed funds rate, credit market variable) all data is monthly from 1980:01 to 2011:01. I am estimating a threshold VAR with the threshold variable being the credit market variable. I am having no problem estimating the threshold break. However when I estimate the sample above the threshold the impulse responses are explosive. When I estimate the sample below the threshold the impulse responses are well behaved. When I estimate over the entire sample (a traditional VAR) the impulse responses are well behaved.

I can not figure out why the VAR is becoming non-stationary over this sub-sample. The way the threshold is being identified the sub-sample above the break includes 80 of the 360 observations. Below the break the sub-sample is obviously the remaining 280 observations. I don't see how this is related to sample size though.

Any suggestions?

Thanks,

Lee

[TomDoan]

That's possible with a self-exciting TVAR. In fact, if you look at the Terasvirta lynx data, both branches are explosive; the lower one is explosive up, the upper one is explosive down. As long as the explosive branch is driving the process towards the threshold value, the overall process can be stable.

[asmith05]

Tom,

Thanks for your quick reply. If I understand you correctly the overall model may be stationary without each individual branch remaining stationary (which certainly seems to be true in my case). If this is the case, then is it still valid to analyze both branches individually (i.e. look at each individual branches impulse responses) or should the analysis be carried out using GIRF's only?

Thanks for your assistance!

Lee

[TomDoan]

Tom,

Thanks for your quick reply. If I understand you correctly the overall model may be stationary without each individual branch remaining stationary (which certainly seems to be true in my case). If this is the case, then is it still valid to analyze both branches individually (i.e. look at each individual branches impulse responses) or should the analysis be carried out using GIRF's only?

Thanks for your assistance!

Lee

All three are of interest.