On Runs Tests for Directional Data and Their Local and Asymptotic Optimality Properties

In the present paper, we tackle the problem of detecting serial correlation in directional data.We introduce 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 optimality properties against local alternatives with serial dependence.We evaluate 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.