  In this paper, we introduce a new jump process modeling which involves a
particular kind of non-Gaussian stochastic processes with random jumps at
random time points. The main goal of this study is to provide an accurate
tracking technique based on non-linear non-stationary heteroscedasticity (NNH)
time series. It is, in fact, difficult to track jump processes regarding the
fact that non-Gaussianity is an inherent feature in these processes. The
proposed NNH model is conditionally Gaussian whose conditional variance is
time-varying. Therefore, we use Kalman filter for state tracking. We show
analytically that the proposed NNH model is superior to the traditional
methods. Furthermore, to validate the findings, simulations are performed.
Finally, the comparison between the proposed method and other alternatives
techniques has been made.
