# A Multitaper, Causal Decomposition for Stochastic, Multivariate Time Series: Application to High-Frequency Calcium Imaging Data

## TL;DR

This paper introduces a multitaper, causal decomposition method for multivariate stochastic time series that considers the full lagged covariance, improving the analysis of neural data and circuit connectivity.

## Contribution

It presents a novel multitaper-based decomposition technique that leverages the full lagged covariance for better causal analysis of multivariate time series.

## Key findings

- Method outperforms standard zero-lag approaches in simulations
- Reveals important dynamical information in neural imaging data
- Enhances understanding of circuit connectivity

## Abstract

Neural data analysis has increasingly incorporated causal information to study circuit connectivity. Dimensional reduction forms the basis of most analyses of large multivariate time series. Here, we present a new, multitaper-based decomposition for stochastic, multivariate time series that acts on the covariance of the time series at all lags, $C(\tau)$, as opposed to standard methods that decompose the time series, $\mathbf{X}(t)$, using only information at zero-lag. In both simulated and neural imaging examples, we demonstrate that methods that neglect the full causal structure may be discarding important dynamical information in a time series.