Isometric operators on Hilbert spaces and Wold decomposition of stationary time series

Severino, Federico

doi:10.1007/s10203-016-0181-5

Decisions Econ Finan

2016

DOI: 10.1007/s10203-016-0181-5

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Isometric operators on Hilbert spaces and Wold decomposition of stationary time series

Federico Severino

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Cited by 3 publications

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“… Interestingly, the same logic underlies the classical Wold decomposition, that can be derived by employing the lag operator as isometry. See Severino (). …”

mentioning

confidence: 99%

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

Ortu¹,

Severino

Tamoni³

et al. 2020

Self Cite

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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.

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“… Interestingly, the same logic underlies the classical Wold decomposition, that can be derived by employing the lag operator as isometry. See Severino (). …”

mentioning

confidence: 99%

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

Ortu¹,

Severino

Tamoni³

et al. 2020

Self Cite

View full text Add to dashboard Cite

show abstract

Multivariate Wold decompositions: a Hilbert A-module approach

Cerreia‐Vioglio

Ortu

Severino

et al. 2023

Decisions Econ Finan

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A Persistence Based Decomposition of Macroeconomic and Financial Time Series

et al. 2011

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Isometric operators on Hilbert spaces and Wold decomposition of stationary time series

Cited by 3 publications

References 4 publications

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

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

Multivariate Wold decompositions: a Hilbert A-module approach

A Persistence Based Decomposition of Macroeconomic and Financial Time Series

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