Online Program

A Persistence-Based Decomposition of Time Series: A Tale of Two Spectra (309612)

Keywords: Haar transform, Extended Wold Decomposition, persistent components, nonparametric estimation, stationary time series

We investigate two econometric approaches to model covariance stationary time series that rely on their decomposition in scale-specific components using a Haar-wavelet transform. These components correspond to different levels of aggregation or frequencies of the data. On the one hand, the multiresolution decomposition (MRD) of a time series applies the transform to a time process. On the other hand, the extended Wold decomposition (EWD) proposed by Ortu et al. (2020) applies the transform to the infinite moving-average parameters and innovations of the Wold representation, which leads to orthogonal components. While this property is theoretically appealing, the empirical estimation of the components in the second approach requires the knowledge of the infinite parameter vector. We investigate the restrictions that lead to equivalent classes of scale-specific data-generating processes or the relations between them and propose MRA-based nonparametric estimators for the EWD framework. The estimation methodology is illustrated in two real data studies on the realized volatility and the interactions between macroeconomic variables with persistent components at selected scales.