Parameters estimation for continuous-time heavy-tailed signals modeled by α-stable autoregressive processes

Abstract

In this paper, we focus on the heavy-tailed stochastic signals generated through continuous-time autoregressive (CAR) models excited by infinite-variance α-stable processes. Our goal is to estimate the parameters of the continuous-time model, such as the autoregressive coefficients and the distribution parameters related to the excitation process for the α-stable CAR process with 0<α<2 based on the state-space representation. Likewise, we investigate the closed form expressions for the parameters of equivalent model in the discrete-time setting via regular samples of the process. We analyze the estimator based on the Monte Carlo simulations and illustrate the estimator consistency to the desired values when sampling frequency and sample size tend to infinity. We also apply the proposed method to the two types of real-world data, financial and ground magnetometer data, to evaluate its performance in real environments.