Mixed Causal–Noncausal Autoregressions: Bimodality Issues in Estimation and Unit Root Testing1
研究了混合因果-非因果自回归模型似然函数的双峰性，发现因果根接近1时双峰问题更突出，导致局部极值根互换、结果误读和单位根检验性能下降，并提出一种估计策略来提高找到全局最大似然估计的概率并正确选择用于单位根检验的最大值。
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.