Smoothly clipped absolute deviation estimation for uncertain autoregressive model

Abstract

Uncertain time series is chronological sequence overtime where each period is described by an uncertain variable. In this paper, we investigate the smoothly clipped absolute deviation (SCAD) penalized estimation method to determine the unknown parameters in the uncertain autoregressive model, and the autoregressive model order can be simultaneously obtained for a pre-given thresholding parameter λ. Besides, an iterative algorithm based on local quadratic approximations for finding the penalized estimators is provided. Based on the fitted autoregressive model, the forecast value and the future value’s confidence interval are given. Besides, the sum of the squared error approach to select the optimal λ is discussed. Finally, some examples are used to validate the effectiveness of the proposed method by the comparative analysis.