A Nonparametric Approach for Testing Long Memory in Stock Returns’ Higher Moments

In this paper, by considering a model-based approach for conditional moment estimation, a nonparametric test was performed to study the long-memory property of higher moments. We considered the daily returns of the stocks included in the S&P500 index in the last ten years (for the period running from the 1st of January 2011 to the 1st of January 2021). We found that mean and skewness were characterized by short memory, while variance and shape had long memory. These results have deep implications in terms of asset allocation, option pricing and market efficiency evaluation.