State Space Models for Non-Stationary Intermittently Coupled Systems: An Application to the North Atlantic Oscillation

Philip G Sansom,Daniel B Williamson,David B Stephenson

doi:10.1111/rssc.12354

Abstract

SummaryWe develop Bayesian state space methods for modelling changes to the mean level or temporal correlation structure of an observed time series due to intermittent coupling with an unobserved process. Novel intervention methods are proposed to model the effect of repeated coupling as a single dynamic process. Latent time varying auto-regressive components are developed to model changes in the temporal correlation structure. Efficient filtering and smoothing methods are derived for the resulting class of models. We propose methods for quantifying the component of variance attributable to an unobserved process, the effect during individual coupling events and the potential for skilful forecasts. The methodology proposed is applied to the study of winter time variability in the dominant pattern of climate variation in the northern hemisphere: the North Atlantic oscillation. Around 70% of the interannual variance in the winter (December–January–February) mean level is attributable to an unobserved process. Skilful forecasts for the winter (December–January–February) mean are possible from the beginning of December.

Highlights

Coupled systems can be found in many areas of both the natural and social sciences
Latent Time-varying autoregressive (TVAR) components are proposed to capture any inherent non-stationarity in the temporal dependence structure
A linearised approximation is proposed that allows efficient forwardfiltering and backward-sampling for models containing latent TVAR components, without requiring complicated and computationally expensive sequential Monte Carlo methods

Summary

Introduction

Coupled systems can be found in many areas of both the natural and social sciences. We define an intermittently coupled system as one which can be modelled by two or more component processes which only interact at certain times. Physical reasoning or prior knowledge may support the existence of such components, and provide information about their behaviour and their effect on the component of interest We refer to these secondary processes as intermittently coupled components, and the times at which the processes interact as coupling events. By incorporating this information through careful statistical modelling we can separate the effect of intermittently coupled components from the underlying behaviour of the observed system

Methods

Results

Conclusion