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

Author

Listed:
  • Fulvio Ortu
  • Federico Severino
  • Andrea Tamoni
  • Claudio Tebaldi

Abstract

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.

Suggested Citation

  • Fulvio Ortu & Federico Severino & Andrea Tamoni & Claudio Tebaldi, 2020. "A persistence‐based Wold‐type decomposition for stationary time series," Quantitative Economics, Econometric Society, vol. 11(1), pages 203-230, January.
    • Handle: RePEc:wly:quante:v:11:y:2020:i:1:p:203-230
    DOI: 10.3982/QE994
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    Cited by:

    1. Bandi, Federico M. & Chaudhuri, Shomesh E. & Lo, Andrew W. & Tamoni, Andrea, 2021. "Spectral factor models," Journal of Financial Economics, Elsevier, vol. 142(1), pages 214-238.
    2. Bandi, Federico M. & Tamoni, Andrea, 2023. "Business-cycle consumption risk and asset prices," Journal of Econometrics, Elsevier, vol. 237(2).
    3. Jozef Barunik & Lukas Vacha, 2023. "The Dynamic Persistence of Economic Shocks," Papers 2306.01511, arXiv.org.
    4. Baruník, Jozef & Vácha, Lukáš, 2024. "Predicting the volatility of major energy commodity prices: The dynamic persistence model," Energy Economics, Elsevier, vol. 140(C).
    5. Xue Cui & Lu Yang, 2024. "Systemic risk and idiosyncratic networks among global systemically important banks," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 29(1), pages 58-75, January.
    6. Terri van der Zwan & Erik Hennink & Patrick Tuijp, 2021. "Equity Risk Factors for the Long and Short Run: Pricing and Performance at Different Frequencies," Tinbergen Institute Discussion Papers 21-062/III, Tinbergen Institute.

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