Autoregressive Modeling with Error Percentage Spread based Triangular Fuzzy Number

Data collected by various methods are often prone to uncertainty of measurement which may affect the information conveyed by the quantitative result. This causes the developed predicted model to be less accurate because of the uncertainty contained in the input data used. Hence, preparing the data by means of handling inherent uncertainties is necessary to avoid the developed prediction model to be less accurate. In this paper, the standard autoregressive model is extended to the case where inherent uncertainty exist in the time series data input is handled by triangular fuzzy number. A systematic strategy to construct a symmetry triangular fuzzy number based on percentage error method to build the autoregressive model is presented. Three different spreads of 1%, 3% and 5% are evaluated under percentage error method. This method is applied to forecast the exchange rate of Association of South East Asian Nation (ASEAN) based on time series data. The enhancement made in data preparation of building fuzzy triangles in this study affirms that the proposed method can produce a better accuracy in predicting as compared to the standard auto regressive model. Importantly, the difficulties to build a triangular fuzzy number to treat the fuzziness which is contained in data is addressed. From the result, we could rank the best percentage error spread which gives higher accuracy among 1%, 3% and 5% model.