Dan Chen

This paper extends the research and applications of the uncertain Gordon–Schaefer model. We examine two stability criteria for the equation solutions: stability in mean and stability in [ ]-th moment. Then we collect [ ] data points from the International Pacific Halibut Commission and analyze the catch data using the uncertain Gordon–Schaefer equation. Through the uncertain hypothesis test, we demonstrate that the uncertain Gordon–Schaefer equation provides an adequate fit. Finally, we establish why the stochastic Gordon–Schaefer equation fails to characterize the halibut catch data effectively.

A mathematical framework for multi‐factor uncertain fishing is first articulated to model fish population dynamics. Assuming that both the additional mortality rate and natural growth rate fluctuate, we derive a multi‐factor uncertain fishing equation. Then we prove that the fish population size exists and is unique. The explicit expression of the inverse uncertainty distribution is given. Furthermore, we provide three applications of the solution, namely, the first hitting time, the supremum, and the infimum. Finally, the method of moments, a residual‐based approach, is utilized for parameter inference.

This paper aims to employ time series analysis to forecast the per capita output of yarn in China. We note from random time series analysis that the residual data did not pass the normality and homogeneous distribution tests. It means that the disturbance term cannot be assumed as a random variable. The random autoregressive model is not suitable. In this situation, this paper employs an uncertain autoregressive model in which the disturbance term is an uncertain variable. Besides, an uncertain hypothesis test is designed to evaluate whether the uncertain autoregressive model fits the observed values well. From this study, we conclude that the uncertain autoregressive model is a good fit for the per capita output of yarn.

As a basic model, an uncertain regression model with autoregressive time series errors has been investigated. This paper proposes another fundamental model—uncertain regression model with moving average time series errors—by assuming that the errors of regression model have a moving average structure. Then the principle of least squares is used to estimate the unknown parameters in the model. Based on the fitted model, the forecast value and confidence interval of the future data are derived. Finally, an example is presented to verify the feasibility of this approach.

Uncertain regression model is a powerful analytical tool for exploring the relationship between explanatory variables and response variables. It is assumed that the errors of regression equations are independent. However, in many cases, the error terms are highly positively autocorrelated. Assuming that the errors have an autoregressive structure, this paper first proposes an uncertain regression model with autoregressive time series errors. Then, the principle of least squares is used to estimate the unknown parameters in the model. Besides, this new methodology is used to analyze and predict the cumulative number of confirmed COVID-19 cases in China. Finally, this paper gives a comparative analysis of uncertain regression model, difference plus uncertain autoregressive model, and uncertain regression model with autoregressive time series errors. From the comparison, it is concluded that the uncertain regression model with autoregressive time series errors can improve the accuracy of predictions compared with the uncertain regression model.