On stationary subspace analysis

Abstract

Multivariate times series occur in many application areas and are challenging to model. They are used in very various areas such as signal processing, pattern recognition, econometric and mathematical finance, weather forecasting or electroencephalography. A common approach is therefore to assume that the observed time series can be decomposed into latent components with different exploitable properties. Popular models for time series modelling are for example moving average or autoregressive models. In some of these models especially non-stationary components are of interest. In the following we will consider in more detail the so called Stationary Subspace Analysis approach (SSA). This work considers two questions. On the one hand, how to separate non-stationary components from stationary components within a multivariate time series? On the other hand how to identify the right number of non-stationary components within a multivariate time series? In order to answer these questions we fill first introduce some definitions and properties needed to develop the differents methods that once can implement to perform SSA. Once we have explained these methods we will demonstrate them in a simulation study.