On the goodness-of-fits of the generalized lambda distribution on high-frequency stock index returns

Peterson Owusu Junior, Nagaratnam Jeyasreedharan and Imhotep Paul Alagidede

Cogent Economics & Finance, 2022, vol. 10, issue 1, 2095764

Abstract: In this paper, we investigate the goodness-of-fit of the flexible four-parameter generalized Lambda Distribution (GLD) for high-frequency 5-min returns sampled from the DJI30 Index. Applying Moment Matching (MM) and Maximum Likelihood Estimation (MLE) techniques, we highlight the significance of the higher-order parameters of the GLD distribution to depict the asymmetric and fat-tailed behaviour observed in high-frequency returns data. We also show and explain why the MLE consistently outperforms the MM; especially in the presence of “outliers”. Finally, we use lambda-space scatterplots to introduce, clarify and discuss additional stylized facts of high-frequency index returns not found in the extant high-frequency literature.

Date: 2022
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DOI: 10.1080/23322039.2022.2095764

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