Indirect inference for locally stationary ARMA processes with stable innovations

TL;DR

This paper introduces a new class of locally stationary ARMA processes with stable innovations, extending traditional models to handle heavy tails and asymmetry, and proposes an indirect inference method for estimation.

Contribution

It develops the $oldsymbol{ ext{α}}$-stable locally stationary process model and provides theoretical properties and estimation techniques for this novel class.

Findings

The model captures heavy-tailed, asymmetric behaviors consistently over time.

Simulation results demonstrate the effectiveness of the indirect inference method.

Empirical application illustrates practical utility of the proposed model.

Abstract

The class of locally stationary processes assumes that there is a time-varying spectral representation, that is, the existence of finite second moment. We propose the $\alpha$-stable locally stationary process by modifying the innovations into stable distributions and the indirect inference to estimate this type of model. Due to the infinite variance, some of interesting properties such as time-varying auto-correlation cannot be defined. However, since the $\alpha$-stable family of distributions is closed under linear combination which includes the possibility of handling asymmetry and thicker tails, the proposed model has the same tail behavior throughout the time. In this paper, we propose this new model, present theoretical properties of the process and carry out simulations related to the indirect inference in order to estimate the parametric form of the model. Finally, an empirical application is illustrated.