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

## TL;DR

This paper introduces a new estimator for time delay in satellite imagery time series of precipitation and NDVI, which outperforms Pearson's correlation in low signal-to-noise conditions and is validated on ecological data from Mexico.

## Contribution

The paper proposes a sparsity-aware estimator for time delay that reduces variance compared to Pearson's correlation, especially in noisy and real-world ecological datasets.

## Key findings

- Proposed estimator has lower variance than Pearson's in simulations.
- Estimator performs better on ecological satellite data from Mexico.
- Implementation available in the new R package geoTS.

## Abstract

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.