Detecting and estimating intensity of jumps for discretely observed ARMAD(1,1) processes

Delphine Blanke (1) , Denis Bosq (2)

1 LMA - EA2151 Laboratoire de Mathématiques d'Avignon
2 LSTA - Laboratoire de Statistique Théorique et Appliquée

We consider $n$ equidistributed random functions, defined on [0,1], and admitting fixed or random jumps, the context being $D[0,1]$-valued ARMA (1,1) processes. We begin with properties of ARMAD(1,1) processes. Next, different scenarios are considered: fixed instants with a given but unknown probability of jumps (the deterministic case), random instants with ordered intensities (the random case), and random instants with non ordered intensities (the completely random case). By using discrete data and for each scenario, we identify the instants of jumps, whose number is either random or fixed, and then estimate their intensity.

Keywords: Functional linear processes; ARMAD(1; 1) processes; Jumps; Estimation of intensity; Discrete data

Domains: Statistics [math.ST]

Delphine Blanke, Denis Bosq. Detecting and estimating intensity of jumps for discretely observed ARMAD(1,1) processes. Journal of Multivariate Analysis, 2016, 146, pp.119-137. ⟨10.1016/j.jmva.2015.08.014⟩. ⟨hal-01207305⟩