The Relevance Property For Prediction Intervals
Paul V. Kabaila · Journal of Time Series Analysis · 1999
Suppose that we have time series data which we want to use to find a prediction interval for some future value of the series. It is widely recognized by time series practitioners that, to be practically useful, a prediction interval should possess the property that it relates to what actually happened during the period that the data were collected as opposed to what might have happened during that period but did not actually happen. We call this the ‘relevance property’. Despite its obvious importance, this property has hitherto not been formulated in a mathematically rigorous way. We provide a mathematically rigorous formulation of this property for a broad class of conditionally heteroscedastic processes in the practical context that the parameters of the time series model must be estimated from the data. The importance in applications of this formulation is that it provides us with the most appropriate way of measuring the finite‐sample coverage performance of a time series prediction interval.