In this presentation, we tackle the problem of detecting serial correlation in the
context of directional data. Motivated by a real data example involving sunspots
locations, we define a concept of runs properly adapted to the directional context.
We then show that tests based on the latter runs enjoy some local and asymptotic
property against local alternatives with serial dependence. We compute the finite
sample performances of our tests using Monte Carlo simulations and show their
usefulness on a real data illustration that involves the analysis of sunspots locations
for various solar cycles. According to the time, we will evoke the goodness of fit problem for the longitude of the location of sunspots (then circular data) using trigonometrics moments.