POTENTIAL PROBLEMS IN ESTIMATING BILINEAR TIME-SERIES MODELS

We present evidence of undesirable statistical properties of the bilinear model. We show that in certain regions of the parameter space the expected likelihood function exhibits bimodality. The true optimum is often characterized by a long, narrow spike that becomes more pronounced with increases in the sample size, Consequently, conventional optimization routines would frequently miss a global optimum with this feature. Moreover, although statistical, tests would have strong power against alternatives near the global optimum, they would have almost zero power against the local minimum. This phenomenon also continues to persist in extremely large samples. In addition, we show that the distributional properties of the parameter estimates and the standard t-statistic also do not have desirable properties in finite samples.