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Small collection of numerical experiments
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README.md
contrast_experiments.R
dimensionality_test_experiments.R
example.cpp

README.md

Small introduction:

To launch the code "as it is" (starting from the "Executable part") the requirement is to have futile.logger installed, as throughout the execution some results will be stored in the log file.

contrast_experiments is a collection of experiments devoted to contrast estimation in FitzHugh-Nagumo model (that's how we get the results from the preprint).

dimensionality_test_experiments are more recent, with the main functions being, in particular:

  • construct_test (implementation of statistical tests from paper by Jean Jacod and Mark Podolskij "A test for the rank of the volatility process: the random perturbation approach"). Returns the value of the dimensionality estimator $\hat{R}$ and the value of the test statistics $V$. Input can be either a matrix (for a multidimensional process), or a vector (if the goal is test the observations from one coordinate)
  • hawkes_approximation (implementation of the stochastic diffusion which approximates the Hawkes process, from paper by Eva Löcherbach and Susanne Ditlevsen "Multi-class oscillating systems of interacting neurons)
  • FHN.simulate (simulations of FitzHugh-Nagumo model with higher-order scheme) This script also depends on example.cpp and packages MASS and Rcpp.

example.cpp few matrix algebra functions, implemented in Rcpp/RcppEigen, which are used to speed up the code (which is pretty costly in terms of computation!)

If you have noticed any inaccuracies - you can contact me (up-to-date contact information is available on my website).

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