Purely time series TAR and STR models

In order to estimate the purely time series TAR and STR models, let us open in Eviews the RoutledgeBookData.xlsx file, i.e. the Excel version of the same dataset that I used in estimating the MSPE and MAE values from the Fama equation.

Table 6.2 MSPE and MAE values for the estimation errors of the Fama equation

USD/JPY

USD/AUD

MSPE

6.294303

13.14589

MAE

1.932033

2.855215

After uploading the observations to Eviews, click on the ‘Quick’ menu at the top. A drop-down menu that looks like the one here will open:

Navigate to select the ‘Estimate Equation .. .’option. In the box that opens, change the method to ‘THRESHOLD’ under the estimation settings.

Comparing the predictive powers of models 39 Now you should be facing a screen as follows:

As you see, Eviews gives its users the option to select TAR or a smooth version of it, named STAR, which is no different than our STR model. Look carefully and notice that the period of the sample is reported in the box at the bottom. Eviews allows the manipulation of this sample period. Now, for our example, let us shorten the sample from 1979m08 to 2016m02. This means that we are restricting the observations only to a period stretching from August 1979 to February 2016, i.e. we are taking 90% of the whole dataset. Remember that we have employed 90% of the observations using the hold-out method in the previous section while estimating the Fama equation. We are creating the same training dataset for our TAR and STR models. Now we can estimate these two models one by one. In the Options tab, the tab that you can see at the top of the dialog box in the first screenshot, we set the trimming option to 15%, i.e. we discard the outliers and do the estimation in a self-exciting way. Self-excitement within the regime-switching models jargon refers

Table 6.3 MSPE and MAE values for the estimation errors of the TAR and STR time series models

USD/JPY

USD/AUD

MSPE TAR

6.290992

13.98764

MAE_TAR

1.789345

2.615223

MSPE STR

6.371232

13.341267

MAE_STR

2.191891

3.0321234

to the situation that past value(s) of the dependent variable is (are) used as the regime-switching variable. The regime-switching variable, by the way, is the variable that provokes the transitions between the regimes. In a model of two regimes, for example, one of the regimes would reign when the transition variable takes values below a threshold level and the other regime would kick in when the transition variable begins to take values above the threshold level. If we return to our example, since this is a self-exciting model, past values of the exchange rate changes are assumed to provoke regime-switches. Values from 1-6 are tried in the ‘threshold variable specification’ box. With those settings, I have done the estimation and used the parameter estimates from the initial 90% of the observations (training data) in order to predict the last 10% (testing data). Using the errors, I have calculated the MSPE and MAE values both for USD/JPY and USD/ AUD exchange rates (Table 6.3).

 
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