Trend computation

A multivariate stochastic process X: \Omega \times\cD \rightarrow \Rset^{\inputDim} of dimension \inputDim where \cD \in \Rset^n may write as the sum of a trend function f_{trend}: \Rset^n \rightarrow \Rset^{\inputDim} and a centered multivariate stochastic process X_{c}: \Omega \times\cD \rightarrow \Rset^{\inputDim} of dimension \inputDim as follows:

(1)\forall \omega \in \Omega, \, \forall \vect{t} \in \cD, \,X(\omega,\vect{t}) = X_{c}(\omega,\vect{t}) + f_{trend}(\vect{t})

The objective here is to identify the trend function f_{trend} from a given field of the process X and then to remove this last one from the initial field. The resulting field is a realization of the centered process X_{c}. The library also allows one to define the function f_{trend} and to remove it from the initial field to get the resulting centered field.