The impedance plethysmography (IP) has long been used to monitor respiration. The IP signal is also suitable for portable monitoring of respiration due to its simplicity. However, this signal is very susceptible to motion artifact (MA). As a result, MA reduction is an indispensable part of portable acquisition of the IP signal. Often, the amplitude of the MA is much larger than the amplitude of the respiratory component in the IP signal. This study proposes a novel filtering method to remove the high-amplitude MA's from the IP signal. The proposed method combines the idea of ε-tube loss function and an autoregressive exogenous model to estimate the MA while leaving the periodic respiratory component of the IP signal intact. Also, a regularization method is used to find the best filter coefficients that maximize the regularity of the output signal. The results indicate that the proposed method can effectively remove the MA, outperforming the popular MA reduction methods. Several different performance measures are used for the comparison and the differences are found to be statistically significant.