Selecting between student and normal mixture distributions

ABSTRACT

It is widely recognized that financial data distributions have heavier tails than normal distributions. These tails can be modeled as Student distributions and normal mixture distributions. However, selecting between these distributions has not been previously studied. To this end, this study proposes an information-criterion approach. The efficacy of the proposed method for selecting the number of mixture components is examined via simulation studies that compare the conventional hypothesis test. Empirical results using Japanese stock returns data are also provided.

KEYWORDS:

• Information criterion
• normal mixture distribution
• Student distribution
• hypothesis test

JEL CLASSIFICATION:

• C15
• C12
• C19

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ Kon (1984) applied an ad hoc rule that if the log-likelihood ratio is positive, the mixture of normal distributions model is ‘more likely’ than the Student model to have generated the stock return data.