Estimation of non-Gaussian SVAR models: a pseudo-log-likelihood function approach

Abstract

We consider estimation problem in structural vector autoregressive model which disturbance has non-Gaussian distribution. We call this model as non-Gaussian vector autoregressive (NG-SVAR) model. Since the estimation problem of this model is closely related to the independent component analysis (ICA) developed in machine learning and signal processing we apply the theory of ICA to our estimation problem. However, since we do not know the true non-Gaussian distribution in practice, we cannot construct the exact loglikelihood function. In this paper we propose a pseudo maximum loglikelihood estimator instead. It is shown that our estimator is statistical efficient from view point of semiparametric statistics. Furthermore, we show that our estimator has satisfactory performance by Monte Carlo experiment and empirical example in small sample.

KEYWORDS:

• Structural vector autoregressive model
• non-Gaussian distribution
• independent component analysis
• pseudo maximum loglikelihood estimator
• semiparametric statistics
• Monte Carlo experiment

Acknowledgements

This is the revised version of the report entitled ‘Estimation of non-Gaussian structural VAR model – A flexible pseudo-log-likelihood function approach-’ presented at the 4th International Conference on Econometrics and Statistics (EcoSta 2021), 26th June 2021. We are grateful for the comments and discussions from participants at EcoSta 2021 and the annual econometric conference at Singapore Management University in March 2021. We are also grateful to Professor A. Moneta of Institute of Economics, Scuola Superiore Sant’Anna, Pisa, Italy, and Professor J. Fukuchi of Gakushuin University for their valuable discussions and comments.

Disclosure statement

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

Notes

1 The results here are an extension of Maekawa, K. [11] with some corrections.

Additional information

Funding

This work was supported by JSPS KAKENHI Grant Numbers, JP18K01555, JP22K20151 and the Joint Usage and Research Center, Institute of Economic Research, Hitotsubashi University (Grant ID: IERPK2222).