Method Of Using Generalized Order Differentiation And Integration Of Input Variables To Forecast Trends

Background

Stochastic methods have been broadly applied for operational risk management in the industry of forecasting trends. The method can generate predication for any time-dependent quantity (stock market, weather data, solar and wind power production, etc.). However, the conventional models that use divided differences and even integer differentials of input variable, are not effective in the situation that incomplete or limited history data are accessible. It’s desirable to be able to capture the non-local stochastic nature of the input variable and the important history effects, to predict better results for any nonlinear or complex trend.

Description

A researcher at the University of California, Merced introduced a novel concept that extending the restricted definition of variable order operator to any order, and an effective numerical method that using generalized order differentiation and integration of input variables to forecast trends.

The methodology consists of selecting appropriate input variable, applying generalized differintegral operators to these variables, and using different streams of functional behavior as inputs for an artificial neural network (or any other stochastic method) to predict future trends. It has been successfully implemented to enhance the forecasting with real data of solar irradiance.

Applications

The novel UC Merced invention can be used to forecast any nonlinear or complex trend. Applications include (but are not limited to):
•solar and wind forecasting;
•weather forecasting; and
•stock market forecasting.

Advantages

The methodology offers substantially better forecasting models, and allows more accurate prediction of complex trends, particularly when data input is incomplete or limited.

Patent Status

Patent Pending

Inventor

Carlos F.M. Coimbra