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

50 Pages Posted: 15 Dec 2011 Last revised: 31 Jul 2019

See all articles by Fulvio Ortu

Fulvio Ortu

Bocconi University - Department of Finance

Federico Severino

University of Lugano - Institute of Finance

Andrea Tamoni

Rutgers, The State University of New Jersey - Rutgers Business School at Newark & New Brunswick

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: January 19, 2019

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.

Keywords: Wold decomposition, temporal aggregation, persistence heterogeneity, forecasting

JEL Classification: C18, C22, C50

Suggested Citation

Ortu, Fulvio and Severino, Federico and Tamoni, Andrea and Tebaldi, Claudio, A Persistence-Based Wold-Type Decomposition for Stationary Time Series (January 19, 2019). 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

University of Lugano - Institute of Finance ( email )

Via Buffi 13
CH-6900 Lugano
Switzerland

HOME PAGE: http://federicoseverino.org

Andrea Tamoni

Rutgers, The State University of New Jersey - Rutgers Business School at Newark & New Brunswick ( email )

1 Washington Park
Newark, NJ 07102
United States

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

Register to save articles to
your library

Register

Paper statistics

Downloads
295
Abstract Views
1,412
rank
103,456
PlumX Metrics