POTENTIAL PROBLEMS IN ESTIMATING BILINEAR TIME-SERIES MODELS

We present evidence of undesirable statistical properties of the bilin ear 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 pronounc ed with increases in the sample size, Consequently, conventional optim ization routines would frequently miss a global optimum with this feat ure. Moreover, although statistical, tests would have strong power aga inst alternatives near the global optimum, they would have almost zero power against the local minimum. This phenomenon also continues to pe rsist in extremely large samples. In addition, we show that the distri butional properties of the parameter estimates and the standard t-stat istic also do not have desirable properties in finite samples.