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

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