Conditional Minimum Volume Predictive Regions for Stochastic Processes
针对非线性时间序列的区间/区域预测，提出一种最小体积预测器，在保证名义覆盖概率下具有最小勒贝格测度，并建立了其一致性和渐近正态性。
Abstract Motivated by interval/region prediction in nonlinear time series, we propose a minimum volume (MV) predictor for a strictly stationary process. The MV predictor varies with respect to the current position in the State space and has the minimum Lebesgue measure among all regions with the nominal coverage probability. We have established consistency, convergence rates, and asymptotic normality for both coverage probability and Lebesgue measure of the estimated MV predictor under the assumption that the observations are from a strong mixing process. Applications with both real and simulated datasets illustrate the proposed methods.