76 Pages Posted: 15 Dec 2011 Last revised: 10 Apr 2017
Date Written: February 13, 2017
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: Suggested Citation
Ortu, Fulvio and Severino, Federico and Tamoni, Andrea and Tebaldi, Claudio, A Persistence-Based Wold-Type Decomposition for Stationary Time Series (February 13, 2017). Available at SSRN: https://ssrn.com/abstract=1973049 or http://dx.doi.org/10.2139/ssrn.1973049
By Mary Finn