## Measurement noise and optimal evolution equations of stochastic signals

By: Pedro Lind

From: CFTC

At: Complexo Interdisciplinar, Anfiteatro

[2008-11-19]

This talk is divided in two parts. First, we will present an approach to extract measurement noise in time series, particularly suited for situations where the noise amplitude is of the same order as the signal itself. Starting from the two first conditional moments of a stochastic process with strong measurement noise, we derive explicitly the measurement noise amplitude and the parameters defining the two first Kramers-Moyal coefficients describing the evolution of a general class of stochastic time-series. Our approach is carried out by minimizing a proper non-negative function, which will be discussed in detail. Possible applications in the context of epilepsy data, among other, are briefly discussed. Second, we extend the above nonparametric reconstruction for the evolution of stochastic data to suit multivariate series, i.e. sets with two or more stochastic time series. Applying the methodology to climate indices, typically defined as differences of one proper quantity measured at two different locations of the globe, we show that their stochastic component is very large as compared to the deterministic one.

Such findings naturally raise the hypothesis that the difference between the measured quantities, defining the standard climate indices, might not be a proper choice for enhancing the capability of forecasting their evolution. To improve predictability we proposed a variational procedure to deduce a functional relationship between data measures at two different locations having less stochasticity.