Estimation of the autocovariance function with missing observations

TL;DR

This paper introduces a new estimator for the autocorrelation function that handles missing data, providing theoretical guarantees and a modified periodogram for weakly dependent stationary time series.

Contribution

It presents a novel autocorrelation estimator robust to missing observations, with proven consistency, asymptotic normality, and deviation bounds for various time series models.

Findings

Estimator is consistent and asymptotically normal.

Derived deviation bounds for weakly dependent series.

Introduced a modified periodogram with known asymptotic distribution.

Abstract

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.