Circulant Singular Spectrum Analysis: A new automated procedure for signal extraction

Abstract: Sometimes, it is of interest to single out the fluctuations associated to a given frequency. We propose a new variant of SSA, Circulant SSA (CiSSA), that allows to extract the signal associated to any frequency specified beforehand. This is a novelty when compared with other procedures that need to identify ex-post the frequencies associated to extracted signals. We prove that CiSSA is asymptotically equivalent to these alternative procedures although with the advantage of avoiding the need of the subsequent frequency identification. We check its good performance and compare it to alternative SSA methods through several simulations for linear and nonlinear time series. We also prove its validity in the nonstationary case. To show how it works with real data, we apply CiSSA to extract the business cycle and deseasonalize the Industrial Production Index of six countries. Economists follow this indicator in order to assess the state of the economy in real time. We find that the estimated cycles match the dated recessions from the OECD showing its reliability for business cycle analysis. Finally, we analyze the strong separability of the estimated components. In particular, we check that the deseasonalized time series do not show any evidence of residual seasonality.