Working Papers 2002 – Abstracts
Reconstructing the Kalman Filter for Stationary and Non Stationary Time
Series
Ralph D. Snyder and Catherine S. Forbes
A Kalman filter, suitable for application to a stationary or a non-stationary
time series, is proposed. It works on time series with missing values.
It can be used on seasonal time series where the associated state space
model may not satisfy the traditional observability condition. A new concept
called an 'extended normal random vector' is introduced and used throughout
the paper to simplify the specification of the Kalman filter. It is an
aggregate of means, variances, covariances and other information needed
to define the state of a system at a given point in time. By working with
this aggregate, the algorithm is specified without direct recourse to
those relatively complex formulae for calculating associated means and
variances, normally found in traditional expositions of the Kalman filter.
A computer implementation of the algorithm is also described where the
extended normal random vector is treated as an object; the operations
of addition, subtraction and multiplication are overloaded to work on
instances of this object; and a form of statistical conditioning is implemented
as an operator.
Keywords: Time series analysis, forecasting, Kalman filter, state
space models, object-oriented programming.
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