4. Final Remarks
We proposed a model for stock price trend forecast based on differential equations that was used as a tool for the investigation of market efficiency. For a realistic situation, it is not expected that any model can accurately predict future prices. In the present case, this is reflected in the variability of the matrices that define the differential equations used to perform the forecasts at every time step. We expect, however, that even with such variation, some predictive power remains. Although predictability in trend forecasting does not always lead to arbitrage opportunity, which depends on factors such as the distributions of returns, the limitations of computational speed and communication, and trading fees, such predictability is at least market inefficiency clue.
