Models Associated with Extended Exponential Smoothing

Author： Bosq Denis  

Publisher： Taylor & Francis Ltd

E-ISSN： 1532-415X|44|3|468-475

ISSN： 0361-0926

Source： Communications in Statistics: Theory and Methods, Vol.44, Iss.3, 2015-02, pp. : 468-475

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

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Abstract

We study an extended form of exponential smoothing which is more flexible than the original one: let be a real stochastic process, observed until time n, consider the probabilistic predictor of Xn + 1 defined as where the series is supposed to be convergent in mean square. We look for stochastic models such that X*n + 1 is the best linear predictor of Xn + 1, given Xt, t n. We obtain various ARIMA models depending on (α, β). In this context we study estimation of (α, β) and give some indications concerning hypotheses testing. Finally, extension to functional stochastic processes is considered.

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