Asymptotic properties of least squares estimation for a new fuzzy autoregressive model

Zhi-Wen Zhao,Cui-Xin Peng

doi:10.1186/1029-242x-2013-56

Abstract

In this paper, we extend the standard autoregressive model to the case where the explanatory and response variables are random fuzzy variables. The fuzzy least-squares estimators (FLSE) of the model parameters are derived and their asymptotic properties are established. A simulation is conducted to evaluate our method, and it is found that the proposed method provides a better performance. AMS Subject Classification:94D05, 62F12.

Highlights

The time series forecasting investigates the relations on the sequential set of past data measured over time to forecast the future values
The deficiencies of traditional forecasting methods are that they cannot deal with forecasting problems in which historical data are linguistic values
In order to overcome the drawback of the traditional forecasting methods, in [ ], Song and Chissom proposed the concepts of fuzzy time series to investigate the forecasting problem in which historical data are linguistic values

Summary

Introduction

The time series forecasting investigates the relations on the sequential set of past data measured over time to forecast the future values. In order to overcome the drawback of the traditional forecasting methods, in [ ], Song and Chissom proposed the concepts of fuzzy time series to investigate the forecasting problem in which historical data are linguistic values. In [ ] and [ ], they proposed two fuzzy time series models to study the forecasting problems of enrollments of the University of Alabama. Some researchers such as [ , ], and [ ] have proposed new fuzzy time series models to improve Song’s model. Randomness resulting from measurement errors and fuzziness resulting from system fuzziness are two different kinds of uncertainty He extended the standard linear regression model to include specific cases where the observations are vague or even linguistic. In Section , we deal with the test of the method through simulation studies

Preliminaries

Asymptotic normality and forecasting

Conclusions