Why the long-term auto-correlation has not been eliminated by arbitragers: Evidences from NYMEX

The efficient market hypothesis claims that market prices follow the random walk and that any predictable trend will be eliminated by arbitragers in a short period of time. However, the fractal market hypothesis disagrees, asserting that long-term memory can persist in the market. To understand why this conflict exists, we propose a method to explore the long-term market trend using the local Hurst exponent and seek to obtain the extra yield. Performance is evaluated by using both a simulation and the high frequency 5-min data and the daily data. The result indicates that the model performs well with the uni-fractal series in the simulation. However, the model shows limited predictive abilities with the data from the real market due to the multi-fractal characteristics. Although the long-term trends persist in the markets and can be identified with statistical significance, traders cannot beat the market because of the time-varying feature and because the strength of long-term memory is not strong enough to cover the transaction costs. The result reconciles the long-term auto-correlations with EMH in a quantitative manner.