Forecasting Thai Traditional Drugs Values Using Grey System Theory with Fractional Order Buffer Operator and Periodic Correction Models

Abstract

The quantitative prediction of Thai traditional drugs for human production values is important to the
national policy on traditional herbal development. The production values from Bureau of Drug Control,
Food and Drug of Thailand (Thai FDA) during 1987 to 2013 showed the upward trend nonstationary time
series. The grey system theory with fractional order buffer operator GM(1,1) model or p/q WGM(1,1)
has the feature to deal with this type of time series and the traditional GM(1,1) also the subset of
p/q WGM(1,1) . The p / q buffer operator is weighted the past data before input to the GM(1,1) model,
the p / q with minimum mean absolute percentage error (MAPE) is selected as the prediction model. The
production values during 1987 to 2013 are used as input, the results from the conventional varying p / q
computations show the minimum MAPE at p / q =0, then the 0WGM(1,1) model or the traditional
GM(1,1) model is the forecasting model. The algorithm to find the optimal p / q with minimum MAPE
should be developed for p/q WGM(1,1) . For the upward trend time series of Thai traditional drugs for
human production values, the expanded from of GM(1,1) with the Fourier series periodic correction model
(GM(1,1)E&PC) exhibits lower MAPE than the minimum MAPE from p/qWGM(1,1) .