Can a least-squares fit be feasible for modelling

When modelling a time series from discrete-time data, a continuous-time parametrization is desirable in some situations. It can have good numerical properties and low computational burden, in particular for fast or nonuniform sampling. In a direct estimation approach, the derivatives are approximate...

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Bibliographic Details
Published inProceedings of 1995 34th IEEE Conference on Decision and Control Vol. 2; pp. 1795 - 1800 vol.2
Main Authors Soderstrom, T., Fan, H., Bigi, S., Carlsson, B.
Format Conference Proceeding
LanguageEnglish
Published IEEE Control Systems Society 1995
Subjects
Autoregressive processes
Control system synthesis
Data engineering
Instruments
Linear regression
Nonuniform sampling
Parameter estimation
Sampling methods
Stochastic systems
Time measurement
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ISBN0780326857
9780780326859
ISSN0191-2216
DOI10.1109/CDC.1995.480402

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Summary:When modelling a time series from discrete-time data, a continuous-time parametrization is desirable in some situations. It can have good numerical properties and low computational burden, in particular for fast or nonuniform sampling. In a direct estimation approach, the derivatives are approximated by appropriate differences, leading to a linear regression model. It is shown that standard approximations like Euler backward or Euler forward cannot be used. The precise conditions on the derivative approximation are derived and analysed. It is shown that if the highest order derivative is selected with care, a least-squares estimate will be accurate. The theoretical analysis is complemented by some numerical examples.
ISBN:0780326857
9780780326859
ISSN:0191-2216
DOI:10.1109/CDC.1995.480402