Monitoring Nonstationary Processes Using Stationary Subspace Analysis and Fractional Integration Order Estimation

This article introduces a framework to monitor complex dynamic and mildly nonstationary processes that are driven by a set of latent factors that can have different integration orders. The framework (i) relies on a novel deflation-based stationary subspace analysis that extracts latent source variables from recorded data sets in an iterative manner and (ii) utilizes the exact local Whittle estimator to calculate the fractional integration orders of the extracted source variables. The framework is embedded within a multivariate time-series structure to model the dynamic characteristics of the latent factors and to remove serial correlation in order to construct univariate monitoring statistics. A numerical and an industrial case study show that this framework is capable of modeling dynamic and mildly nonstationary variable inter-relationships that can have different integration orders.