Abstract
This paper proposes threshold models to analyze and forecast interval-valued time series. A relatively simple algorithm is proposed to obtain least square estimates of the threshold and slope parameters. The construction of forecasts based on the proposed model and methods for the analysis of their forecast performance are also introduced and discussed, as well as forecasting procedures based on the combination of different models. To illustrate the usefulness of the proposed methods, an empirical application on a weekly sample of S&P500 index returns is provided. The results obtained are encouraging and compare very favorably to available procedures.
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Notes
Note that it is not clear if the results obtained in the following sections will hold for the lower-upper bound representation of ITS, and we do not pursue this extension in this paper. However, this presents an interesting line of research for further investigation.
Following the suggestion of one referee, to compare predictive accuracy we have also conducted Diebold–Mariano tests (see Appendix) and the results obtained corroborate these conclusions.
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Acknowledgments
We are grateful to the participants of the ISF 2010 conference in San Diego and the SDA Workshop 2012 in Madrid for useful comments and suggestions. We would also like to thank Guest Editor Dr. Javier Arroyo, Coordinating Editor Professor Maurizio Vichi and three anonymous referees for helpful and constructive comments on an earlier version of this paper.
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Appendix: Diebold–Mariano predictive accuracy tests
Appendix: Diebold–Mariano predictive accuracy tests
Table 4 provides Diebold and Mariano (1995) test results for the comparison of different forecast methods. The results in this table are for center and radius forecasts and are based on loss differentials which are defined as the difference of squared forecast errors.
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Rodrigues, P.M.M., Salish, N. Modeling and forecasting interval time series with threshold models. Adv Data Anal Classif 9, 41–57 (2015). https://doi.org/10.1007/s11634-014-0170-x
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DOI: https://doi.org/10.1007/s11634-014-0170-x