Statistical Approach to Implied Market Inefficiency Estimation

This study aims to estimate the information efficiency of financial markets based on the Hurst exponent, with a focus on the S&P 500 index. The approach involves using statistical models to estimate the implied Hurst exponent through the historical series of the VIX (a proxy for implied volatility) with a 30-day time lag. In this way, the traditional backward-type Hurst estimation is reconciled with that derived from the VIX, which represents a forward-looking measure (a proxy for 30-day volatility). The test sample also includes the COVID pandemic period. The results reveal a good fit from ensemble stacking models, with the random forest standing out as the most effective approach in estimating the implied Hurst index.