Ubiquitous multimodality in mixed causal-noncausal processes

Igor Kindop

MPRA Paper from University Library of Munich, Germany

Abstract: According to the literature, the bimodality of estimates in mixed causal–non-causal autoregressive processes is due to unlucky starting values and happens only ocassionally. This paper shows that a unique and convergent solution is not always the case for models of this class. Instead, the likelihood function is not convex leading to the multimodality of estimated parameters. It can be attributed to the magnitude and sign of the autoregressive coefficients. Simultaneously, the number of local modes grows with the number of autoregressive parameters in the model. This multimodality depends on the parameters of the process and the chosen error distribution. We have to apply grid search methods to extract candidate solutions. The independence of residuals is a necessary hypothesis for the proper identification of the processes. A simple AIC criterion helps to select an independent model. Finally, I sketch a roadmap on estimating mixed causal-noncausal autoregressive models and illustrate the approach with Brent spot oil price returns.

Keywords: non-causal model; non-convex likelihood; non-Gaussian; nonfundamentalness; multimodality. (search for similar items in EconPapers)
JEL-codes: C13 C22 C51 C52 C53 E37 (search for similar items in EconPapers)
Date: 2021-07-09, Revised 2021-09-04
New Economics Papers: this item is included in nep-ecm, nep-ets, nep-isf, nep-mac and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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