2008, Vol.11, No.2, pp.241-249
In the nonlinear prediction of scalar time series, the common
practice is to reconstruct the state space using time-delay
embedding and apply a local model on neighborhoods of the
reconstructed space. The method of false nearest neighbors is
often used to estimate the embedding dimension. The optimal
embedding dimension can also be estimated by some prediction error
minimization criterion. We investigate the proper state space
reconstruction for multivariate time series and modify the two
abovementioned criteria to search for optimal embedding in the set
of the variables and their delays. We pinpoint the problems that
can arise in each case and compare the state space reconstructions
(suggested by each of the two methods) on the predictive ability
of the local model that uses each of them. Results obtained from
Monte Carlo simulations on known chaotic maps revealed the
non-uniqueness of optimum reconstruction in the multivariate case
and showed that prediction criteria perform better when the task
is prediction.
Key words:
nonlinear analysis, multivariate analysis, time series, local prediction,
state space reconstruction
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