Uncertain max-autoregressive model with imprecise observations

Uncertain time series analysis has been developed for studying the imprecise observations. In this paper, we propose a nonlinear model called uncertain max-autoregressive (UMAR) model. The unknown parameters in model are estimated by the least squares estimation. Then the residual analysis is presented. In many cases, there are some outliers in the time series due to short-term change in the underlying process. The UMAR model offers an alternative for detecting outliers in the imprecise observations. Based on the previous theoretical results, the UMAR model is used to forecast the future. Finally, an example suggests that the new proposed time series model works well compared to the uncertain autoregressive (UAR) model.

Cross-Validation for the Uncertain Chapman-Richards Growth Model with Imprecise Observations

Regression analysis estimates the relationships among variables which has been widely used in growth curves, and cross-validation as a model selection method assesses the generalization ability of regression models. Classical methods assume that the observation values of variables are precise numbers while in many cases data are imprecisely collected. So this paper explores the Chapman-Richards growth model which is one of the widely used growth models with imprecise observations under the framework of uncertainty theory. The least squares estimates of unknown parameters in this model are given. Moreover, cross-validation with imprecise observations is proposed. Furthermore, estimates of the expected value and variance of the uncertain error using residuals are given. In addition, ways to predict the value of response variable with new observed values of predictor variables are discussed. Finally, a numerical example illustrates our approach.