Inferring change points and nonlinear trends in multivariate time series: Application to West African monsoon onset timings estimation

International audience Time series in statistical climatology are classically represented by additive models. For example, a seasonal part and a linear trend are often included as components of the sum. Less frequently, hidden elements (e.g., to represent the impact of volcanic forcing on temperatures) can be integrated. Depending on the complexity and the interactions among the different components, the statistical inference challenge can quickly become difficult, especially in a multivariate context where the timings and contributions of hidden signals are unknown. In this article we focus on the statistical problem of decomposing multivariate time series that may contain both nonlinear trends and change points (discontinuities), the change points being assumed to occur simultaneously in time for all variables in the multivariate analysis. The motivation for such a study comes from the statistical analysis of the West African monsoon (WAM) phenomenon for which unknown preonset and onset dates occur each year. The impacts of such onsets can be statistically viewed as yearly change points that affect, almost synchronously, trends in observed time series such as daily Outgoing Longwave Radiation and the Intertropical Discontinuity. Our proposed model corresponds to a multivariate additive model with nonlinear trends and possible yearly discontinuities, modeling the onsets. An inference scheme based on a nonlinear Kalman filtering approach is proposed. It enables to identify the different parts hidden in the original multivariate vector. Our inference strategy is tested on simulated data and applied to the analysis of the WAM phenomenon during the period 1979-2008. Our extracted onset dates are then compared to the ones obtained from past studies.