.ISSN (e) 1759-7331
(print) 1759-7323
Quantitative Economics
An open-access journal in quantitative economics
Journal of the
Econometric Society
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Quantitative Economics, Volume 11, Issue 1 (January 2020)

A persistence‐based Wold‐type decomposition for stationary time series

Fulvio Ortu, Federico Severino, Andrea Tamoni, Claudio Tebaldi


This paper shows how to decompose weakly stationary time series into the sum, across time scales, of uncorrelated components associated with different degrees of persistence. In particular, we provide an Extended Wold Decomposition based on an isometric scaling operator that makes averages of process innovations. Thanks to the uncorrelatedness of components, our representation of a time series naturally induces a persistence‐based variance decomposition of any weakly stationary process. We provide two applications to show how the tools developed in this paper can shed new light on the determinants of the variability of economic and financial time series.

Wold decomposition temporal aggregation persistence heterogeneity forecasting C18 C22 C50

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