Cointegration Testing Method for Monitoring Nonstationary Processes

Abstract

This paper introduces cointegration testing method for nonstationary process monitoring, which yields a longrun dynamic equilibrium relationship for nonstationary process systems. The process variables are examined, and then a cointegration model of the tested nonstationary variables is identified. The residual sequence of the cointegration model describes the dynamic equilibrium errors of the nonstationary process system and can be further analyzed for condition monitoring and fault detection purposes. The autocorrelated residual sequence is filtered with AR model first, then compensated to keep the fault signatures from being distorted by the filtering process. An application case study to an industrial distillation unit with a nonstatioanry process shows that a tidy cointegration model can describe the dynamic equilibruim state of the unit and correctly detect abnormal behavior of the process.

Consistent Monitoring of Cointegrating Relationships: The US Housing Market and the Subprime Crisis

“…Inference for this test is based on sub‐sampling, and thus, general forms of error serial correlation and regressor endogeneity can be accommodated while asymptotically controlling size. This wide applicability is a similarity to our approach and is not given for other procedures available in the literature, for example, Chen et al (), Steland and Weidauer () or Wang et al (). This makes the Andrews–Kim test, despite its different focus, a natural candidate for comparison.…”

Approaches to nonlinear cointegration with a view towards applications in SHM

“…Econometricians are often interested in testing for cointegration; if two variables are cointegrated they share common trends and the stationary combination of them that one is able to find will define the long run equilibrium between them [2]. For econometricians attempting to define and understand relationships between economic variables, cointegration is also seen as a solution to the problem of spurious regression [3].…”

Nonlinear Cointegration Approach for Condition Monitoring of Wind Turbines

“…Linear cointegration has been successfully applied to remove unwanted environmental and/or operational variability in various damage detection SHM applications when data are linearly related and operational/environmental common trends are linear, as presented in [17][18][19][20][21][22][23][24].…”

“…The cointegration approach-originally developed in the field of Econometrics in the late 1980s and early 1990s [14][15][16]-has been successfully employed as a reliable tool for dealing with the problem of operational and environmental variability in Process Engineering [17] and Structural Health Monitoring (SHM) [18][19][20][21][22][23][24]. All these applications utilized the linear cointegration concept that is intimately connected with the concept of linear error correction models.…”