Abstract
The paper illustrates a procedure to calculate prediction intervals in case of heteroscedasticity using Holt-Winters methods. The procedure has been applied to the Italian daily electricity prices (PUN) of the year 2014; then the prediction intervals have compared to those provided by an ARIMA-GARCH model. The intervals obtained with HW methods have been very similar to the others, but easier to calculate. Moreover, the HW procedure is more flexible in dealing with periodic volatility as proved in the case study.
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Notes
- 1.
Instead, the multiplicative HW is not optimal for any linear process. In case of multiplicative composition of the structural components, it is worthwhile to apply the additive HW to the log-serie.
- 2.
Here the multiplicative HW should be preferred to the additive one because it avoids negative values for volatility forecasts.
- 3.
- 4.
The optimal values are reported without inferential information (standard errors, p-values, etc.) because the coefficients are not interpreted here as process parameters.
- 5.
The daily effects on PUN have become quite constant since 2013, but it was not in the previous years [2].
- 6.
We have chosen an EGARCH model to avoid the risk of negative variance because that risk is high including seasonal regressors in classic GARCH model.
References
Bollerslev, T.: A conditionally heteroskedastic time series model for speculative prices and rates of return. Rev. Econ. Stat. 69(3), 542–547 (1987)
Chirico, P.: Which seasonality in Italian daily electricity prices? A study with state space models. In: Alleva, A., Giommi, G. (eds.) Topics in Theoretical and Applied Statistics, pp. 275–284. Springer (2016)
Engle, R.F., Bollerslev, T.: Modelling the persistence of conditional variances. Economet. Rev. 5(1), 1–50 (1986)
Koopman, S.J., Ooms, M., Carnero, M.A.: Periodic seasonal Reg-ARFIMA-GARCH models for daily electricity spot prices. J. Am. Stat. Assoc. 102(477), 16–27 (2007)
Lucchetti, R.J., Balietti, S.: The gig package. Package Guide of Gretl (2016)
MacGregor, J.F., Harris, T.J.: The exponentially weighted moving variance. J. Qual. Technol. 25(2), 106–118 (1993)
Taylor, S.J.: Modeling stochastic volatility: a review and comparative study. Math. Financ. 4(2), 183–204 (1994)
Yar, M., Chatfield, C.: Prediction interval for the holt-winters forecasting procedure. Int. J. Forecast. (North-Holland) 6, 127–137 (1990)
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Chirico, P. (2018). Prediction Intervals for Heteroscedastic Series by Holt-Winters Methods. In: Perna, C., Pratesi, M., Ruiz-Gazen, A. (eds) Studies in Theoretical and Applied Statistics. SIS 2016. Springer Proceedings in Mathematics & Statistics, vol 227. Springer, Cham. https://doi.org/10.1007/978-3-319-73906-9_16
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DOI: https://doi.org/10.1007/978-3-319-73906-9_16
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