# Non-Linear Non-Stationary Heteroscedasticity Volatility for Tracking of Jump Processes

## TL;DR

This paper introduces a novel non-linear, non-stationary heteroscedasticity model for accurately tracking jump processes with non-Gaussian features, utilizing Kalman filtering and validated through simulations.

## Contribution

The paper proposes a new NNH model for jump process tracking that outperforms traditional methods and is analytically validated.

## Key findings

- NNH model effectively tracks jump processes.
- Proposed method outperforms traditional techniques.
- Simulations confirm the model's superiority.

## Abstract

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.