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- W2891440280 abstract "For $(X_t)$ a two-sided $alpha$-stable moving average, this paper studies the conditional distribution of future paths given a piece of observed trajectory when the process is far from its central values. Under this framework, vectors of the form $boldsymbol{X}_t=(X_{t-m},ldots,X_t,X_{t+1},ldots,X_{t+h})$, $mge0$, $hge1$, are multivariate $alpha$-stable and the dependence between the past and future components is encoded in their spectral measures. A new representation of stable random vectors on unit cylinders -sets ${boldsymbol{s}inmathbb{R}^{m+h+1}: hspace{0.3cm} |boldsymbol{s}|=1}$ for $|cdot|$ an adequate semi-norm- is proposed in order to describe the tail behaviour of vectors $boldsymbol{X}_t$ when only the first $m+1$ components are assumed to be observed and large in norm. Not all stable vectors admit such a representation and $(X_t)$ will have to be > for $boldsymbol{X}_t$ to admit one. The conditional distribution of future paths can then be explicitly derived using the regularly varying tails property of stable vectors and has a natural interpretation in terms of pattern identification. The approach extends to processes resulting from the linear combination of stable moving averages and applied to several examples." @default.
- W2891440280 created "2018-09-27" @default.
- W2891440280 creator A5086737326 @default.
- W2891440280 date "2018-09-10" @default.
- W2891440280 modified "2023-09-27" @default.
- W2891440280 title "Path prediction of aggregated alpha-stable moving averages using semi-norm representations" @default.
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