Abstract
Improved implementations of previously suggested methods for constructing bootstrap prediction intervals for the self-exciting threshold autoregressive model are presented. The simulation results are compared with those reported by Li (2011). It is found that better estimates of actual coverage rates are obtained using the improved version of the methods.
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Notes
The impact may be not so large here, as the sample averages of the residuals from regressions without the constant are close to zero. E.g., for the cases reported in the three panels of Fig. 1, the means of residual sample averages calculated over 1,000 Monte Carlo replications are \(-\)0.029, \(-\)0.031, and \(-\)0.031, respectively. The corresponding standard deviations are equal to 0.085, 0.087, and 0.092.
The stationarity correction seems relevant as it was required relatively often for specific DGPs. For example, for the cases studied in Fig. 4, the means and the standard deviations (in parentheses) of the frequency of application of the bias correction was equal to 6.3 % (9.7 %) for \(\beta _{11}=0.2\), 19.25 % (13.15 %) for \(\beta _{11}=0.8\), and 13.75 % (13.9 %) for \(\beta _{11}=1.0.\)
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Acknowledgments
Support from the MNiSW/DAAD PPP Grant (56268818) and the National Science Center, Poland (NCN) through MAESTRO 4: DEC–2013/08/A/HS4/00612 are gratefully acknowledged.
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Staszewska-Bystrova, A., Winker, P. Improved bootstrap prediction intervals for SETAR models. Stat Papers 57, 89–98 (2016). https://doi.org/10.1007/s00362-014-0643-1
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DOI: https://doi.org/10.1007/s00362-014-0643-1