Mixed Causal–Noncausal Autoregressions: Bimodality Issues in Estimation and Unit Root Testing

Frédérique Bec, Heino Bohn Nielsen and Sarra Saïdi

Oxford Bulletin of Economics and Statistics, 2020, vol. 82, issue 6, 1413-1428

Abstract: This paper stresses the bimodality of the likelihood function of the Mixed causal–noncausal AutoRegressions (MAR), and it is shown that the bimodality issue becomes more salient as the causal root approaches unity from below. The consequences are important as the roots of the local maxima are typically interchanged, attributing the noncausal component to the causal one and vice‐versa. This severely changes the interpretation of the results, and the properties of unit root tests of the backward root are adversely affected. To circumvent the bimodality issue, this paper proposes an estimation strategy which (i) increases noticeably the probability of attaining the global MLE; and (ii) selects carefully the maximum used for the unit root test against a MAR stationary alternative.

Date: 2020
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https://doi.org/10.1111/obes.12372

Related works:
Working Paper: Mixed Causal-Noncausal Autoregressions: Bimodality Issues in Estimation and Unit Root Testing (2019)
Working Paper: Mixed Causal-Noncausal Autoregressions: Bimodality Issues in Estimation and Unit Root Testing (2019)
Working Paper: Mixed Causal-Noncausal Autoregressions: Bimodality Issues in Estimation and Unit Root Testing * (2019)
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