Forecast Intervals in ARCH Exponential Smoothing

Laurence Broze (), Guy Melard and Olivier Scaillet
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Guy Melard: CEME, Institut de Statistique and Ecole de Commerce Solvay, Universite de Bruxelles

No 1994081, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

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.

Keywords: exponential smoothing; forecast interval; time series; financial data; marketing data; autoregressive conditionally heteroscedastic errors (search for similar items in EconPapers)
Date: 1994-12-01
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