WAVELET ESTIMATION OF THE COVARIANCE OF ALMOST PERIODICALLY CORRELATED PROCESSES AND STUDY OF ASYMPTOTIC PROPERTIES IN A CONTEXT OF WEAK DEPENDENCE

Abstract

We construct a multiresolution estimator and study its asymptotic properties. The estimation of the coefficients of the covariance decomposition of an almost periodically correlated process on a wavelet basis is dealt with. It is found that the covariance relates to random variables satisfying a weak dependence structure of quasi-association type. In this context, we first recall a method for constructing a wavelet base, with the decomposition of the covariance function in this base and obtain a set of coefficients to be estimated. We then construct an estimator of the coefficients obtained, under specific sampling conditions (jitter or delay). Following are the three main results obtained in the paper: • The first result concerns the almost sure convergence of the multiresolution estimator built from the model of the spectral covariance estimator. • The second result establishes consistency under the quasi-association hypothesis, a convergence rate is provided. • The third result establishes the asymptotic normality of the estimator.