Indirect inference for locally stationary ARMA processes with stable innovations

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 α-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 autocorrelation cannot be defined. However, since the α-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 behaviour 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.

Keywords:

• Locally stationary process
• stable distribution
• indirect inference

2010 Mathematics Subject Classifications:

• 62M10
• 62F86

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The authors are grateful to the support of a Conselho Nacional de Desenvolvimento Científico e Tecnol ogico (CNPq) grant (141607/2017-3) and the University of Costa Rica (SWC), and a Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) grant 2018/04654-9 (PAM).