Estimation of stochastic models from data and application to el nino data

We analyze data from temperature measurements in the pacific in three steps to obtain a stochastic model. 1) Public data are embedded using the isomap algorithm to obtain an estimate of the dimension of the system and the corresponding embedded time series. 2) These time series are treated by nonparametric regression, a system of three coupled differential equations is obtained. The unexplained deviance can be modeled by a stochastic term, corresponding to observation. As a side result we find a delay of 6 months in one of the variables, consistent with a recently proposed model by Tsiperman, taking into account Rossby waves in the pacific ocean. 3) The so-obtained model is integrated, an ensemble prediction is performed to yield probabilities for el nino occurence.