Estimating linear dependence between nonstationary time series using the locally stationary wavelet model

Abstract

Large volumes of neuroscience data comprise multiple, non-stationary electrophysiological or neuroimaging time series recorded from different brain regions. Estimating the dependence between such neural time series accurately is critical, since changes in the dependence structure are presumed to reflect functional interactions between neuronal populations. We propose a new method of wavelet coherence, derived from the new bivariate locally stationary wavelet (LSW) time series model. Since wavelets are localised in both time and scale, this approach leads to a natural, local and multiscale estimate of nonstationary dependence. Our methodology is illustrated by application to a simulated example, and to electrophysiological data relating to interactions between the rat hippocampus and prefrontal cortex during working memory and decision-making. We thereby demonstrate that this novel LSW model can be of use in systems neuroscience applications.

Classification of multiple time signals using localized frequency characteristics applied to industrial process monitoring

“…In these applications, the interest was in allocating an entire time series to one of a number of classes, in contrast to our goal of segmenting a time series as it evolves. Sanderson et al (2010) developed a multivariate LSW process model, which Cho and Fryzlewicz (2015) have used in segmentation of multiple locally stationary time series, while Park et al (2014) have developed estimators for the dependence structure between the multivariate time series. This multivariate LSW model could be used to extend our approach if the structure of the multiple explanatory time series is of interest.…”

Simulating Bivariate Stationary Processes with Scale-Specific Characteristics

“…Similarly, the model of Sanderson et al (2010) is an extension of the locally stationary wavelet time series model of Nason et al (2000) to the bivariate case. It aims at modeling non-stationary time series with a time-varying autocovariance and cross-covariance structure.…”

“…Related methodologies for simulating time series with scale-specifi c characteristics have already appeared in the literature; see, for example, Nason et al (2000) and Sanderson et al (2010). The relation of these methodologies to our approach will be discussed in Section 7.…”

“…In Section 6, Monte Carlo simulation is used to verify that our methodology works well. Section 7 compares our models to the models of Nason et al (2000) and Sanderson et al (2010). Section 8 concludes, pointing out the relevance of our approach to fi nancial time series.…”

The locally stationary dual-tree complex wavelet model

“…Unlike many other such tools, LSW-based methodology affords a statistically wellprincipled means to capture the local covariance and local spectrum. That auto-covariance estimation of non-stationary processes by any other means comes entangled with various fundamental difficulties has enabled LSW models to gain traction across a variety of domains such as forecasting for finance (Fryzlewicz 2005); establishing dependencies in electrophysiological data for neuroscience applications (Sanderson et al 2010); and spectral estimation of environmental time series and ECG traces with missing data (Knight et al 2012).…”