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Exponential smoothing: Estimation by maximum likelihood
Author(s) -
Broze Laurence,
Mélard Guy
Publication year - 1990
Publication title -
journal of forecasting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.543
H-Index - 59
eISSN - 1099-131X
pISSN - 0277-6693
DOI - 10.1002/for.3980090504
Subject(s) - exponential smoothing , autoregressive model , smoothing , autoregressive integrated moving average , mathematics , moving average , exponential function , maximum likelihood , basis (linear algebra) , estimation , statistics , econometrics , algorithm , time series , mathematical analysis , geometry , management , economics
In this paper several forecasting methods based on exponential smoothing with an underlying seasonal autoregressive‐moving average (SARIMA) model are considered. The relations between the smoothing constants and the coefficients of the autoregressive and moving average polynomials are used. On that basis, a maximum likelihood procedure for parameter estimation is described. The approach rules out the need for initial smoothed values. Prediction intervals are also obtained as a by‐product of the approach and a fast algorithm for implementing the method is outlined.