Autoregression Depth

Davy Paindaveine (1, 2) , Germain van Bever (3)

1 ULB - Université libre de Bruxelles
2 UT Capitole - Université Toulouse Capitole
3 UNamur - Université de Namur [Namur]

We introduce a concept of autoregression depth that provides a robust ordering of autoregression parameter values according to their adequacy with respect to the underlying process. We dérivé a uniform strong consistency resuit for the corresponding sample autoregressive depth. which allows us to prove that the sample deepest parameter value is strongly consistent for its population version. Our depth concept finds applications in both point estimation and hypothesis testing: regarding point estimation, the deepest parameter value provides a robust estimator of the parameter of autoregressive processes, which we show to be strongly consistent by complementing the aforementioned consistency results with a Fisher-consistency resuit. Regarding hypothesis testing, the depth of the zéro parameter value yields a natural test statistic to test for randomness. We investigate the AR(1) case in some details. Our results are illustrated with Monte Carlo exercises.

Domaines: Statistiques [math.ST]

Davy Paindaveine, Germain van Bever. Autoregression Depth. Annales de l'ISUP, 2019, 63 (2-3), pp.57-70. ⟨hal-03604249⟩