A unified approach to asymptotic behaviors for the autoregressive model with fuzzy data

We propose a unified estimator for the autoregressive model with fuzzy input–output variables based on the least squares method. The least squares estimation is investigated in presence of a unified ρ-distance defined on the space of fuzzy numbers. We investigate asymptotic properties of the unified estimator under some simple conditions as well as a generalization, which reduces to the asymptotic properties under those distances when the distances are the special cases of ρ-distance. Some simulation studies are included to compare the asymptotic properties of estimators formed under several distances being the special cases of ρ-distance.