A Smoother State Space Multitaper Spectrogram

Abstract

A recent work (Kim et al. 2018) has reported a novel statistical modeling framework, the State-Space Multitaper (SSMT) method, to estimate time-varying spectral representation of non-stationary time series data. It combines the strengths of the multitaper spectral (MT) analysis paradigm with that of state-space (SS) models. In this current work, we explore a variant of the original SSMT framework by imposing a smoothness promoting SS model to generate smoother estimates of power spectral densities for non-stationary data. Specifically, we assume that the continuous processes giving rise to observations in the frequencies of interest follow multiple independent Integrated Wiener Processes (IWP). We use both synthetic data and electroencephalography (EEG) data collected from a human subject under anesthesia to compare the IWP-SSMT with the SSMT method and demonstrate the former's utility in yielding smoother descriptions of underlying processes. The original SSMT and IWP-SSMT can co-exist as a part of a model selection toolkit for nonstationary time series data.