Bootstrap for the second-order analysis of Poisson-sampled almost periodic processes

In this paper we consider a continuous almost periodically correlated process {X(t), t ∈ R} that is observed at the jump moments of a stationary Poisson point process {N (t), t ≥ 0}. The processes {X(t), t ∈ R} and {N (t), t ≥ 0} are assumed to be independent. We define the kernel estimators of the Fourier coefficients of the autocovariance function of X(t) and investigate their asymptotic properties. Moreover, we propose a bootstrap method that provides consistent pointwise and simultaneous confidence intervals for the considered coefficients. Finally, to illustrate our results we provide a simulated data example.