Asymmetric heavy-tailed vector auto-regressive processes with application to financial data

ABSTRACT

Vector Auto-regressive (VAR) models are commonly used for modelling multivariate time series and the typical distributional form is to assume a multivariate normal. However, the assumption of Gaussian white noise in multivariate time series is often not reasonable in applications where there are extreme and/or skewed observations. In this setting, inference based on using a Gaussian distributional form will provide misleading results. In this paper, we extended the multivariate setting of autoregressive process, by considering the multivariate scale mixture of skew-normal (SMSN) distributions for VAR innovations. The multivariate SMSN family is able to be represented in a hierarchical form which relatively easily facilitates simulation and an EM-type algorithm to estimate the model parameters. The performance of the proposed model is illustrated by using simulated and real datasets.

KEYWORDS:

• VAR processes
• scale mixtures of multivariate skew-normal
• EM-type algorithm
• outliers
• asymmetric distributions
• heavy tailed distributions
• financial data
• multivariate time series

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Mohsen Maleki http://orcid.org/0000-0002-2774-2464