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Models Associated with Extended Exponential Smoothing

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  • Denis Bosq

Abstract

We study an extended form of exponential smoothing which is more flexible than the original one: let (Xt,t∈Z)$(X_{t},\: t\in \mathbb {Z})$ be a real stochastic process, observed until time n, consider the probabilistic predictor of Xn + 1 defined as Xn+1*=α∑j=0∞βjXn-j,(α∈R,β∈R),\[ X_{n+1}^{*}=\alpha \sum _{j=0}^{\infty }\beta ^{j}X_{n-j},\;\;\;(\alpha \in \mathbb {R},\:\beta \in \mathbb {R}), \] 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.

Suggested Citation

  • Denis Bosq, 2015. "Models Associated with Extended Exponential Smoothing," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(3), pages 468-475, February.
  • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:3:p:468-475
    DOI: 10.1080/03610926.2012.748916
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    Cited by:

    1. Wilson Ye Chen & Gareth W. Peters & Richard H. Gerlach & Scott A. Sisson, 2017. "Dynamic Quantile Function Models," Papers 1707.02587, arXiv.org, revised May 2021.

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