Local Functional Coefficient Autoregressive Model for Multistep Prediction of Chaotic Time Series

Algorithm 1

Searching algorithm for optimal parameter set.

Input: The relevant data, such as: chaotic time series, the initial parameters

Output: Results, such as: the optimal parameters

 Scale chaotic time series between ;

For  %  

 For  %  

   The autocorrelation function method, The Cao method.

 End

End %  Obtain the embedding dimension and the time delay

 Choose training set and select primary functions, Phase space reconstruction based on ,

Compute the Euclidean distances between phase points in the reconstructed phase space.

For

%  ,  ,  

 Compute .

End

 Select the optimal parameter set: