Conditional Minimum Volume Predictive Regions for Stochastic Processes

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.

Key Words:

• Conditional distribution
• Level set
• Minimum volume predictor
• Nadaraya-Watson estimator
• Nonlinear time series
• Predictor
• Strong mixing