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Forecast Intervals in ARCH Exponential Smoothing

Author

Listed:
  • BROZE, Laurence

    (CORE, Université catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium)

  • MELARD, Guy

    (CEME, Institut de Statistique and Ecole de Commerce Solvay, Universite de Bruxelles)

  • SCAILLET, Olivier

    (CREST)

Abstract

Exponential smoothing (ES) with ARCH (autoregressive conditionally heteroscedastic) and GARCH (generalized ARCH) errors are introduced. This is done for a large class of ES methods, those for which the forecasts are obtained using a set of additive updating formulas, and also those for which an ARIMA form had been previously established. The class includes HOLT and WINTERS methods but also methods involving a damped trend. The transition from homoscedastic ES to ES-GARCH methods is based on the updating formulas by relaxing the assumption that the errors constitute a white noise process. It is assumed instead that the error process is a martingale difference, with the usual GARCH representation for the conditional variance. The device for deriving the results is the underlying ARIMA-GARCH representation of the ES-GARCH methods. The problems which are discussed are the following: (a) the estimation of the smoothing constants; (b) the computation of the forecast intervals. Examples demonstrating the new approach are given. They are related to finance and marketing.

Suggested Citation

  • BROZE, Laurence & MELARD, Guy & SCAILLET, Olivier, 1994. "Forecast Intervals in ARCH Exponential Smoothing," LIDAM Discussion Papers CORE 1994081, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:1994081
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    Citations

    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. Confidence Intervals for Exponential Smoothing Forecasts
      by Clive Jones in Business Forecasting on 2013-04-20 02:02:53

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