In this paper, the existence of unstable regions of two modified linear predictive coding (LPC) models are shown by numeral examples in order to contrast the conventional ones. The instability due to the excess model parameter reduction in the transfer function denominators is the trade-off of SER improvement. In comparison with the traditional LPC modeling, the two studied modelings can at least double the order of their transfer functions, provided that an improvement in the SER is achieved. In order to demonstrate the effects of parameter reductions, the models are simulated by random generated sets of predictor coefficients with p = 5. Experimental results show that there exist some regions where no stable pole can be obtained inside. This pole stability criterion can be used to design the filter for modern communication system.