A Persistence-Based Wold-Type Decomposition for Stationary Time Series

84 Pages Posted: 15 Dec 2011 Last revised: 17 Oct 2017

Fulvio Ortu

Bocconi University - Department of Finance

Federico Severino

Bocconi University; University of Lugano

Andrea Tamoni

London School of Economics & Political Science (LSE)

Claudio Tebaldi

Bocconi University - CAREFIN - Centre for Applied Research in Finance; Bocconi University - Department of Finance; Bocconi University - IGIER - Innocenzo Gasparini Institute for Economic Research

Date Written: October 1, 2017

Abstract

This paper shows how to isolate uncorrelated persistent components from macroeconomic and financial time series. This issue stems from the evidence of heterogeneous driving factors that underlie the observable outcome of economic processes. To achieve this goal, we provide an Extended Wold Decomposition based on an isometric scaling operator that makes averages of process innovations. Weakly stationary time series are decomposed into the sum, across time scales, of uncorrelated components associated with different degrees of persistence. Our representation of a time series allows to define multiscale impulse response functions and multiscale variance decomposition. Using these tools, we analyze the exchange rates realized volatility, and we quantify the role of investors with different time horizons, in agreement with the Heterogeneous Market Hypothesis.

Keywords: Wold decomposition, Abstract Wold Theorem, persistence heterogeneity, impulse response functions, forecasting

JEL Classification: E32, E43, E44, G12

Suggested Citation

Ortu, Fulvio and Severino, Federico and Tamoni, Andrea and Tebaldi, Claudio, A Persistence-Based Wold-Type Decomposition for Stationary Time Series (October 1, 2017). Available at SSRN: https://ssrn.com/abstract=1973049 or http://dx.doi.org/10.2139/ssrn.1973049

Fulvio Ortu

Bocconi University - Department of Finance ( email )

Via Roentgen 1
Milano, MI 20136
Italy

Federico Severino

Bocconi University ( email )

Via Sarfatti, 25
Milan, MI 20136
Italy

University of Lugano ( email )

Via Giuseppe Buffi 13
Lugano, Ticino 6900
Switzerland

Andrea Tamoni

London School of Economics & Political Science (LSE) ( email )

Houghton Street
London, WC2A 2AE
United Kingdom
02079557303 (Phone)

Claudio Tebaldi (Contact Author)

Bocconi University - CAREFIN - Centre for Applied Research in Finance ( email )

Via Roentgen 1
Milan, 20136
Italy

Bocconi University - Department of Finance ( email )

Via Roentgen 1
Milano, MI 20136
Italy

Bocconi University - IGIER - Innocenzo Gasparini Institute for Economic Research ( email )

Via Roentgen 1
Milan, 20136
Italy

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