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  • 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 paperTesting

  • 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. Well

  • 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.

Threshold regressions are a type of nonlinear time series model that allow for regime switching.

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