Detecting common bubbles in multivariate mixed causal-noncausal models

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titlepage\begin{center} { Detecting common bubbles in multivariate mixed causal-noncausal models } { Gianluca Cubadda\footnote{Tor Vergata University of Rome School of Economics}, Alain Hecq\footnote{Maastricht University School of Business and Economics}\footnote{Corresponding author : Alain Hecq, Maastricht University, Department of Quantitative Economics, School of Business and Economics, P.O.box 616, 6200 MD, Maastricht, The Netherlands. Email: [email removed].} and Elisa Voisin\footnotemark[2] }\\ { Maastricht University} { June, 2022} \end{center} \begin{abstract} This paper proposes methods to investigate whether the bubble patterns observed in individual series are common to various series. We detect the non-linear dynamics using the recent mixed causal and noncausal models. Both a likelihood ratio test and information criteria are investigated, the former having better performances in our Monte Carlo simulations. Implementing our approach on three commodity prices we do not find evidence of commonalities although some series look very similar. \end{abstract} \justifying Keywords: Forward-looking models, bubbles, co-movements \\ JEL. C32

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Conclusion

This paper proposes methods to investigate whether the bubble patterns observed in individual series are common to various series. We detect the non-linear dynamics using the recent mixed causal and noncausal models. The lead component of the model allows to capture, for instance, locally explosive episodes in a parsimonious and strictly stationary setting. We hence employ multivariate mixed causal-noncausal models and apply restrictions to the lead coefficients matrices to test for the presence of commonalities in the forward looking components of the series. We propose a likelihood ratio (LR) test to test for the presence of a common bubble. In a simulation study, we investigate the accuracy of the common bubbles detection using the LR test as well as by model selection using information criteria. Then, implementing our approach on three commodity prices we do not find evidence of commonalities despite the similarities between the series. Our definition of common bubbles requires that all noncausal matrices span the same left null space. A natural extension to our approach would be to relax that hypothesis to investigate non synchronous common bubbles, allowing for some adjustment delays along the lines of cubadda2001non.

Acknowledgments

Elisa Voisin gratefully acknowledges the University of Rome Tor Vergata for organizing a 3-month research visit, during which this paper was partially written.