Spectral discontinuity design: Interrupted time series with spectral mixture kernels

Quasi-experimental designs allow researchers to determine the effect of a treatment, even when randomized controlled trials are infeasible. A prominent example is interrupted time series (ITS) design, in which the effect of an intervention is determined by comparing the extrapolation of a model trained on data acquired up to moment of intervention, with the interpolation by a model trained on data up to the intervention. Typical approaches for ITS use (segmented) linear regression, and consequently ignore many of the spectral features of time series data. In this paper, we propose a Bayesian nonparametric approach to ITS, that uses Gaussian process regression and the spectral mixture kernel. This approach can capture more structure of the time series than traditional methods like linear regression or AR(I)MA models, which improves the extrapolation performance, and hence the accuracy of causal inference. We demonstrate our approach in simulations, and use it to determine the causal effect of Kundalini yoga meditation on heart rate oscillations. We show that our approach is able to detect the causal effect of interventions that alter the spectral features of these time series.