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

- We propose a method to predict market trend using Hurst exponent.
- The reconciliation of EMH and long-term trends is discussed.
- The time-varying characteristics and transaction cost in financial markets are discussed.

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.