Title: Using singular spectrum analysis for inference on seasonal time series with seasonal unit roots
Authors: Dimitrios D. Thomakos; Hossein Hassani
Addresses: Department of Economics, University of Peloponnese, Tripoli, 221 00, Greece ' Research Institute of Energy Management and Planning, No. 13, Ghods St., Enghelab Ave., Tehran, Iran
Abstract: The problem of optimal linear filtering, smoothing and trend extraction for m-period differences of processes with a unit root is studied. Such processes arise naturally in economics and finance, in the form of rates of change (price inflation, economic growth, financial returns) and finding an appropriate smoother is thus of immediate practical interest. The filter and resulting smoother are based on the methodology of singular spectrum analysis (SSA). An explicit representation for the asymptotic decomposition of the covariance matrix is obtained. The structure of the impulse and frequency response functions indicates that the optimal filter has a 'permanent' and a 'transitory component', with the corresponding smoother being the sum of two such components. Moreover, a particular form for the extrapolation coefficients that can be used in out-of-sample prediction is proposed. In addition, an explicit representation for the filtering weights in the context of SSA for an arbitrary covariance matrix is derived. This result allows one to examine the specific effects of smoothing in any situation. The theoretical results are illustrated using different datasets, namely US inflation and real GDP growth.
Keywords: core inflation; business cycles; differences; Euro; linear filtering; SSA; singular spectrum analysis; smoothing; trend extraction and prediction; unit root.
International Journal of Computational Economics and Econometrics, 2020 Vol.10 No.2, pp.149 - 182
Accepted: 22 Jan 2018
Published online: 21 May 2020 *