  We propose a novel estimator of the autocorrelation function in presence of
missing observations. We establish the consistency, the asymptotic normality,
and we derive deviation bounds for various classes of weakly dependent
stationary time series, including causal or non causal models. In addition, we
introduce a modified version periodogram defined from these autocorrelation
estimators and derive asymptotic distribution of linear functionals of this
estimator.
