Time delay estimation in satellite imagery time series of precipitation and NDVI: Pearson's cross correlation revisited

In order to describe more accurately the time relationships between daily satellite imagery time series of precipitation and NDVI we propose an estimator which takes into account the sparsity naturally observed in precipitation. We conducted a series of simulation studies and show that the proposed estimator's variance is smaller than the canonical's (Pearson-based), in particular, when the signal-to-noise ratio is rather low. Also, the proposed estimator's variance was found smaller than the canonical's one when we applied them to stacks of images (2002-2016) taken on some ecological regions of Mexico. Computations for this paper are based on functions implemented in our new R package geoTS.