caa a22 4500 378868489 CHVBK 20180305123403.0 cr unu---uuuuu 161128e20030701xx s 000 0 eng 10.2202/1558-3708.1087 doi (NATIONALLICENCE)gruyter-10.2202/1558-3708.1087 Reconstructing the Kalman Filter for Stationary and Non Stationary Time Series [Elektronische Daten] [Ralph D Snyder, Catherine S Forbes] A Kalman filter for application to stationary or non-stationary time series is proposed. A major feature is a new initialisation method to accommodate non-stationary time series. The filter works on time series with missing values at any point of time including the initialisation phase. It can also be used where a state space model does not satisfy the traditional observability condition, a situation that can arise with seasonal time series.Another feature of the paper is that the Kalman filter is described in terms of the augmented moments of the state vectors, these being an aggregate of means, variances, covariances and other pertinent information. By doing this, the Kalman filter is specified without direct recourse to those relatively complex formulae for calculating associated means and variances found in traditional expositions.A computer implementation of the Kalman filter is also described where the augmented moments are treated as an object; the operations of addition and multiplication are overloaded to work on instances of this object; and a form of statistical conditioning is implemented as an operator. ©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston Snyder Ralph D. Monash University aut Forbes Catherine S. Monash University aut Studies in Nonlinear Dynamics & Econometrics De Gruyter 7/2(2003-07-01) 7:2 2003 7 snde https://doi.org/10.2202/1558-3708.1087 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.2202/1558-3708.1087 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Snyder Ralph D. Monash University aut NATIONALLICENCE 700 1- Forbes Catherine S. Monash University aut NATIONALLICENCE 773 0- Studies in Nonlinear Dynamics & Econometrics De Gruyter 7/2(2003-07-01) 7:2 2003 7 snde CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter