Hey there,

currently im working with CRP trying to reconstruct the phase space of financial time series but Im obtaining weird results, ill try to make me clear.

In order to obtain a delay embedding coordinates representation from financial time series, we are using Mutual Information (MI) and False Nearest Neighbors (FNN) as proposed by [Takens, 1981]; the implementation is based on CRP classes working in MATLAB 2009b environment. As far as we understand, Mutual Information and False Nearest Neighbors are deterministic methods, in this sense, as long as the same data and the same parameters are used MI and FNN they must provide the exact same results, right? This conception makes CRP's FNN results difficult to understand. So here comes our questions:

1. First, why would the MAX DIMENSION parameter would affect the Embedding dimension obtained? FNN states as false nearest neighbor any vector which would not satisfy two criteria: The euclidian distance between two vectors with two difference sizes would not be greater than a R_tol Threshold, and the degree of dispersion between a vector and all vectors standard deviation would not be greater than a R_accept threshold. We dont understand why when we change in the MAX DIMENSION parameter we dont obtained the same embedding dimension (keep in mind that we always increase this parameter from ranges of 20-50)

2. Even when using the same exact parameters (DATA, MAX DIMENSION, TIME DELAY, NEIGHBOURHOOD CRITERION, NEIGHBOURHOOD SIZE, 'EUCLIDIAN DISTANCE'), running several times the programm we obtain several results for the correct embedding dimension.

We would appreciate any information about this issue.

Thanks in advance

Guillermo Santamaria