forecast horizon lengthens beyond 7 or 8 periods, the forecasts from the nonlinear models become more similar to those from a linear model. Tables 2 and 3 display the results corresponding to the power simulation exercises. Before proceeding, it is important at this point to describe the differences and similarities between those two types of models. An model can be well approximated by an ESTAR LSTAR model if most of the data generated by the model lie above the value of the threshold parameter As such, only the increasing portion of the transition function matters and this can be well c. mapped by a monotonically increasing function of type. Conversely, an model LSTAR LSTAR may be well approximated by an model provided that the move from one regime to the ESTAR other is not quick. Therefore, the simulations below describe a wide variety of competing testing frameworks to help when one does not know how many terms to include in the Taylor a priori series approximation. Table 2 reveals several findings concerning the power of the test when the true are DGPs processes. As increases from 5 to 20, the transition function changes from an LSTAR approximately linear to a threshold with two states regime. Accordingly, the power increases in for both processes. Also, Panels of Figure 3 show that the power of the test also LSTAR a f – increases with the sample size for both processes. Comparing directly the two it seems DGPs, that the process displays slightly higher power at all horizons for both samples. Finally, LSTAR2 for both it is evident that the power decreases with the forecasting horizon. This follows as DGPs forecasts from nonlinear models should be very close to those from linear models as the forecast horizon gets large. Table 3 shows the results from the power simulation exercises where the is an DGP process. Panels of Figure 4 plot the results in Table 3. Note that for the ESTAR a c ESTAR1, –
forecast horizon lengthens beyond 7 or 8 periods, the forecasts from the nonlinear models become more similar to those from a linear model. Tables 2 and 3 display the results corresponding to the power simulation exercises. Before proceeding, it is important at this point to describe the differences and similarities between those two types of models. An ESTAR model can be well approximated by an LSTAR model if most of the data generated by the model lie above the value of the threshold parameter c. As such, only the increasing portion of the transition function matters and this can be well mapped by a monotonically increasing function of LSTAR type. Conversely, an LSTAR model may be well approximated by an ESTAR model provided that the move from one regime to the other is not quick. Therefore, the simulations below describe a wide variety of competing testing frameworks to help when one does not know a priori how many terms to include in the Taylor series approximation. Table 2 reveals several findings concerning the power of the test when the true DGPs are LSTAR processes. As increases from 5 to 20, the transition function changes from an approximately linear to a threshold with two states regime. Accordingly, the power increases in for both LSTAR processes. Also, Panels a – f of Figure 3 show that the power of the test also increases with the sample size for both processes. Comparing directly the two DGPs, it seems that the LSTAR2 process displays slightly higher power at all horizons for both samples. Finally, for both DGPs it is evident that the power decreases with the forecasting horizon. This follows as forecasts from nonlinear models should be very close to those from linear models as the forecast horizon gets large. Table 3 shows the results from the power simulation exercises where the DGP is an ESTAR process. Panels a – c of Figure 4 plot the results in Table 3. Note that for ESTAR1, the
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