Dynamic State‐Space Models

. In many cases, multiple time series can be viewed as realizations of the same underlying process and such data usually accumulate in time. The historic time‐series data provide important information for our current prediction. In this paper, we extend the traditional state‐space model to a general dynamic scheme, in which estimation and prediction across time series and within a time series are handled by a unified O(N) sequential procedure. Under this framework, the information from historic data serves as the prior for the current time series and the estimation and prediction of a time series can incorporate the information from other time series as well as its own history. The solution is to construct sequentially a new state‐space model for the next time series conditional on the past time series. Because we achieve the general dynamic estimation and prediction through constructing new conditional state‐space models, existing estimation procedures for state‐space models can be adapted into this framework with minimal modifications. An application to infant growth curves is used as illustration.