Unit Root Tests With Wavelets

Abstract

This paper develops a wavelet (spectral) approach to testing the presence of a unit root in a stochastic process. The wavelet approach is appealing, since it is based directly on the different behavior of the spectra of a unit root process and that of a short memory stationary process. By decomposing the variance (energy) of the underlying process into the variance of its low frequency components and that of its high frequency components via the discrete wavelet transformation (DWT), we design unit root tests against near unit root alternatives. Since DWT is an energy preserving transformation and able to disbalance energy across high and low frequency components of a series, it is possible to isolate the most persistent component of a series in a small number of scaling coefficients. We demonstrate the size and power properties of our tests through Monte Carlo simulations.

Modeling coexisting business scenarios with time-series panel data: A dynamics-based segmentation approach

“…Development of better diagnostic tests would improve the reliability of our dynamic segmentation approach. Current research on unit-root tests using wavelets shows promise in increasing power, especially when analyzing near unit-root alternatives (e.g., Fan & Gençay, 2010). Although wavelets have been previously used in marketing to study time-series properties in the frequency domain (Lemmens, Croux, & Dekimpe, 2007), their use in unit-root testing is less developed and is a promising area for future research.…”

Wavelet Coherence as a Research Tool for Stability of the Banking System (The Example of Ukraine)

“…Then wavelet analysis methodology has been widely used in the disclosure of dynamics of time series that define various economic data [20] [21].…”

Spectral approach to parameter-free unit root testing

“…Our objective in this section is to devise a test with parameter-free asymptotic distribution, the tuning parameters of which do not require data based selection. Compared to spectral-type testing procedures by Choi and Phillips (1993) or Fan and Gençay (2010), this is a very different type of test with a different limit distribution. It does not require estimation of the spectral density, uses a preselected finite number of Fourier frequencies and is easy to compute.…”