I read in the user guide that the methodology is based on the methodologies of Bai and Perron (1998), and not the fixed regressor bootstrap testing proposed by Hansen (1999), to determine the number of thresholds.
The user guide goes on to say that "We caution you that the approaches based on testing should be viewed as informal in the TAR setting as the lagged endogenous regressors in the model are themselves subject to structural breaks which violates the assumptions for the Sup-F statistics (Hansen, 2000; Hansen, 1999)."
:(
Ok, so...does this mean that estimation results are invalid and not to be used in a formal setting? Can someone break this down in laymans terms? Why would EViews roll out a package based on methodologies that are not statistically valid?
I now understand what the user guide is referring to here. Estimation of the threshold values are consistent under the Bai and Perron methods. However, Hansen(1999) showed that F-statistics in testing for the number of thresholds are non-standard and a bootstrapping method is recommended. For example, Hansen showed that when testing a SETAR model with two regimes against the three regime SETAR, the F-statistic is not Chi-squared distributed, so inference in determining the best fit number of regimes can be misleading.
This leads me to a new question that I'm hoping somebody will help me with.
Hansen is explicit in his use of SETAR models to show that F-statistics are non-standard. However, it is not clear to me if this problem is isolated to SETAR models. The user guide states that
"in the TAR setting the lagged endogenous regressors in the model are themselves subject to structural breaks which violates the assumptions for the Sup-F statistics"
So does this imply that TAR models with exogenous threshold variables do not suffer from non-standard F-stats? Do F-stats follow a chi-squared distribution when the threshold variable is exogenous?
