A justification of conditional confidence intervals

To quantify uncertainty around point estimates of conditional objects such as means or variances, parameter has to be taken into account. Attempts incorporate are typically based on the unrealistic assumption observing two independent processes, where one is used for estimation, and other conditioning upon. Such foundation raises question whether these intervals theoretically justified in a realistic setting. This paper presents an asymptotic justification this type that does not require assumption, but relies sample-split approach instead. By showing our coincide asymptotically with standard intervals, we provide novel, realistic, confidence objects. The analysis carried out rich class time series models. We also present results simulation study evaluate performance approach. indicate practice might more appropriate than intervals.