TITLE:
Are Stock Return Dynamics Truly Explosive or Merely Conditionally Leptokurtic? A Case Study on the Impact of Distributional Assumptions in Econometric Modeling
AUTHORS:
Peter A. Ammermann
KEYWORDS:
Multifractal, Leptokurtosis, Conditional Heteroskedasticity, Maximum-Likelihood Estimation, Statistical Adequacy
JOURNAL NAME:
Journal of Data Analysis and Information Processing,
Vol.4 No.1,
February
25,
2016
ABSTRACT: This paper uses the estimation of the Self-Excited Multi Fractal (SEMF) model, which holds theoretical
promise but has seen mixed results in practice, as a case study to explore the impact of distributional
assumptions on the model fitting process. In the case of the SEMF model, this examination
shows that incorporating reasonable distributional assumptions including a non-zero mean
and the leptokurtic Student’s t distribution can have a substantial impact on the estimation results
and can mean the difference between parameter estimates that imply unstable and potentially explosive
volatility dynamics versus ones that describe more reasonable and realistic dynamics for
the returns. While the original SEMF model specification is found to yield unrealistic results for
most of the series of financial returns to which it is applied, the results obtained after incorporating
the Student’s t distribution and a mean component into the model specification suggest that
the SEMF model is a reasonable model, implying realistic return behavior, for most, if not all, of
the series of stock and index returns to which it is applied in this study. In addition, reflecting the
sensitivity of the sample mean to the types of characteristics that the SEMF model is designed to
capture, the results of this study also illustrate the value of incorporating the mean component
directly into the model and fitting it in conjunction with the other model parameters rather than
simply centering the returns beforehand by subtracting the sample mean from them.