Powers Correlation Analysis of Returns with a Non-stationary Zero-Process

The higher order dynamics of individual stocks is investigated. We show that classical powers correlation analysis can lead to a spurious assessment of the volatility persistence or long memory volatility effects, if the zero return probability is non-constant over time. In other words, classical tools are not able to distinguish between long-run volatility effects, such as IGARCH, and the case where the zero returns are not evenly distributed over time. As a remedy, new diagnostic tools are proposed that are robust to changes in the zero return probability. Since a time-varying zero return probability could potentially be accompanied by a non-constant unconditional variance, we also develop powers correlation analysis that is robust in such a case. In addition, the diagnostic tools we propose offer a rigorous analysis of the short-run volatility effects, while the use of the classical powers correlations lead to doubtful conclusions. Monte Carlo experiments, and the study of the absolute value correlation of daily returns taken from the Chilean financial market and the 1-min returns of Facebook stocks, suggest that the volatility effects are only short-run in many cases.

Automated summary

This study investigates the higher order dynamics of individual stocks and finds that classical powers correlation analysis may lead to erroneous assessment of volatility persistence when the zero return probability varies over time. To address this issue, new diagnostic tools are proposed that are robust to changes in the zero return probability. Additionally, robust powers correlation analysis is developed to account for time-varying zero return probability and non-constant unconditional variance. The study also demonstrates that the use of classical powers correlations may lead to doubtful conclusions, while the proposed diagnostic tools offer a rigorous analysis of short-run volatility effects.