Threshold regressions are a type of nonlinear time series model that allow for regime switching.
The coefficients of the model are constant in each regime but can change between regimes.
The switch from one regime to another is triggered by a specific observed data series.
One of the goals of threshold model estimation is to find the value (or values) of the data
series that trigger the regime change.
EViews offers standard Threshold Autoregression (TAR) estimation, as well as the associated
SETAR and STAR models.
As an example we will use data containing annual sunspot counts from 1700 to 1988.
These data were similarly analyzed by, amongst many others, Bruce Hansen in his 1999 paper
“Testing for Linearity”.
We have these data in the series sunspots in our workfile.
Following his example we can take a square root transformation of the data via the EViews
command line.
We can estimate a simple TAR model by clicking on Quick-Estimate Equation, then changing
the estimation method to THRESHOLD.
Following Hansen’s example, we will use up to eleven lags of the dependent variable
as threshold regressors, and a constant as a non-varying regressor.
We will estimate a self-exciting TAR model with 2 lags, by typing in 2 in the Threshold
variable specification.
Clicking OK produces the output results.
The top part of the output shows a summary of the estimation performed, including the
time and date, the number of observations, and the selected threshold value, 7.44 in
this case.
The main part of the output provides the coefficient estimates of the regressors in each regime.
Since we have two regimes in our example, we have two sets of coefficients.
At the bottom we see the non-regime specific coefficient on the constant.
The last section of the output contains the standard regression summary statistics.
In this example we fixed the number of thresholds at 1 (leading to two regimes).
If, instead, we would like EViews to determine the number of regimes, we can bring up the
estimation dialog again and switch to the options tab to change the threshold specification
settings.
We can change the method of threshold determination to Global L thresholds vs none, with a maximum
of 5 breaks.
Clicking OK again produces the results, and we can see that we now have 5 threshold values,
5.27, 8.41, 11.42, 14.06 and 16.64.
These thresholds lead to 6 regimes, and so 6 sets of coefficient values.
Up until now we have set the threshold variable as a two period lag of the dependent variable.
If we aren’t precisely sure on which variable, or how many lags to use for the threshold
variable, we can instruct EViews to test different specifications and chose the best one.
We’ll ask EViews to choose between various lag values by entering them into the Threshold
variable specification box on the Estimate dialog. (4,5,6,7).
We can see that EViews selected a lag of 5 as the most appropriate lag specification,
using a residual-sum-of squares criteria.
We can view RSS values of each of the lag specifications by clicking on View->Model
Selection Summary->Criteria Table.
Here we see that the 5 lag model is clearly superior to the other lag specifications.