Statistical study of the Inverse First Passage Time Algorithm

We discuss a method that analyzes time series generated by point processes to detect possible non stationarity in the data. We interpret each observation as the first passage time of a stochastic process through a deterministic boundary and we concentrate the effect of different dynamics on the boundary shape. We propose an estimator for the boundary and we compute its confidence intervals. Applying the Inverse First Passage Time Algorithm we then recognize the evolution in the dynamics of the time series by means of a comparison of the boundary shapes. This is performed using a suitable time window fragmentation on the observed data.