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.