Periodic and seasonal (co-)integration in the state space framework

In this paper (multivariate) periodic and seasonally integrated autoregressive (moving average) processes are investigated by embedding the linear dynamic models for vectors of all observations within a year into the state space framework. In the case of quarterly data this corresponds to models for the vector of quarters (VQ) process. In the general case this may be called a vector of seasons (VS) process. It is demonstrated that this combination of the VS and the state space representation makes the relations between the various series transparent and thus helps in identifying cointegration properties both between as well as within the seasons. The setting is more revealing than the generally used periodic autoregressive (PAR) or seasonally integrated autoregressive moving average (SARIMA) framework.