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.