Methods for estimation of dynamical noise
M.S. Diudin, E.N. Kalaidin · Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation · 2018
The article discusses methods for measuring the random component of time series. Existing random noise processing methods work poorly in the case of dynamic noise even for regular dynamics. We consider the existing methods for measuring dynamic noise and propose to use an algorithm based on the Grassberger and Procaccia method. Analysis of the geometric structure of the reconstruction of the attractor (according to the Takens theorem) allows us to determine the scale at which the deterministic signal begins to exceed the noise. The resulting noise estimate allows us to estimate the accuracy of the prediction of the deterministic component. Random deviation grows in proportion to the root of time, complicating an accurate prediction even with accurate simulation of the deterministic component. Measurement of random noise allows us to estimate the possible horizon of the forecast. Methods based on measuring the correlation integral require a large number of points for analysis and take a lot of time for calculations, but have no alternative in the study of dynamic noise.