Uncertain quantile autoregressive model

Abstract

The propose of uncertain time series is to explore the relationship between response variables and explanatory variables over time based on the imprecise observations. In order to more comprehensively describe the overall picture of the relationship between variables under the time series, a new uncertain quantile autoregressive model is proposed. By studying the uncertain quantile autoregressive model, the estimated method under different quantiles of its unknown parameters is proposed. Based on the fitted uncertain quantile autoregressive model, the residual is analyzed. Furthermore, uncertainty hypothesis testing are used to verify the reasonableness and accuracy of the estimates under different quantiles. Moreover, the point estimate and interval estimate of the predicted value are presented. Finally, the rationality and validity of the model are verified by two examples.