Indirect inference for locally stationary ARMA processes with stable innovations

Author(s)

Chou-Chen, Shu Wei ; Morettin, Pedro A.

• Document type: Journal article
• Source: JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION; v. 90, n. 17, p. 29-pg., 2020-07-28.

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 autocorrelation 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 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. (AU)

• FAPESP's process: 18/04654-9 - Time series, wavelets and high dimensional data
• Grantee: Pedro Alberto Morettin
• Support Opportunities: Research Projects - Thematic Grants