The primary purpose of this book is to demonstrate that the innovations form of the state space model provides a simple but flexible approach to forecasting time series. However, for reasons that are not completely clear, the innovations form has been largely over-shadowed in the literature by another version of the state space model that has multiple sources of randomness. We refer to this version as the multi-disturbance or multiple source of error (MSOE) model. The two approaches are compared and contrasted in this chapter. When we are comparing the two frameworks directly, both the finite and infinite start-up assumptions are valid; however, when the two are compared via their ARIMA reduced forms, the infinite start-up assumption will be used. The emphasis will be almost exclusively upon linear state space models, because, as we shall see in Sect. 13.4, the MSOE formulation becomes difficult to manage in the nonlinear case.
In Chap. 2, we introduced the local level and local trend models, together with their seasonal extensions. Itwill be seen that these innovations, or single source of error (SSOE), models all have their counterparts within a multiple source of error framework. It is often thought that the MSOE provides a better modeling framework than the SSOE because the multiple sources of error appear to allow greater generality. We will show that any MSOE model has an innovations representation, so that this viewpoint cannot be correct.
A general definition of the state space framework is presented in Sect. 13.1. It is seen to encompass both the innovations and the multiple disturbance forms of the state space model. Several important special cases of the MSOE are also given. A general approach to estimation is given in Sect. 13.2. Reduced forms of the MSOE models are examined in Sect. 13.3. The SSOE and MSOE approaches are then compared in Sect. 13.4.
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© 2008 Springer-Verlag Berlin Heidelberg
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(2008). Conventional State Space Models. In: Forecasting with Exponential Smoothing. Springer Series in Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71918-2_13
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DOI: https://doi.org/10.1007/978-3-540-71918-2_13
Publisher Name: Springer, Berlin, Heidelberg
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