Correlated stochastic processes analysis with RQA

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lucianoz
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Affiliation (Univ., Inst., Dept.): Centro de Investigaciones Opticas (CIOp)
Location: La PLata, Buenos Aires, Argentina

Correlated stochastic processes analysis with RQA

Post by lucianoz »

Dear all,
I am analyzing long-range correlated stochastic processes with RP and RQA. More specifically, I am trying to correlate the Hurst exponent associated to fBm numerical simulations with RQA quantifiers like determinism, L_{max} or entropy. My question is about the selection of the parameters (embedding dimension, embedding delay and the size of neighborhood) required for the RQA estimations. Due to the presence of correlations the optimal values for these parameters change. For example, by employing FNN, the optimal value for the embedding dimension is equal to 8 when the Hurst exponent is close to 0.1 and it decreases to 4 when the Hurst exponent is near 0.9. Then, which is the best strategy to perform the analysis? The parameters should be fixed independently of the Hurst exponent or they should be chosen following the optimal for each Hurst value? My intention is to compare the behavior of the RQA quantifiers as a function of the Hurst exponent. The first approach was to fix parameters in order to make the comparison easier. However, in this way, the election of the parameters for a better estimation is optimal only for one of the Hurst exponent considered.
Do you know related papers?

Thanks in advance for your attention.

All the best,

Luciano Zunino
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Norbert
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Affiliation (Univ., Inst., Dept.): Potsdam Institute for Climate Impact Research, Germany
Location: Potsdam, Germany
Location: Potsdam Institute for Climate Impact Research, Germany

Re: Correlated stochastic processes analysis with RQA

Post by Norbert »

Hi Luciano,

indeed not easy to solve. I suggest to keep the embedding constant. Theoretically, we should then use the largest embedding dimension we would expect for the entire system. But usually a smaller embedding is also working. Have you had a look in the book of Kantz & Schreiber (Nonlinear Time Series Analysis)? There are also some papers by Doyne Famer on embedding issues (e.g. Phys D 1982).

Best
Norbert
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