Asymptotic normality of sample covariance matrix for mixed spectra time series: Application to sinusoidal frequencies estimation

This correspondence addresses the asymptotic normal distribution of the sample mean and the sample covariance matrix of mixed spectra time series containing a sum of sinusoids and a moving average (MA) process. Two central limit (CL) theorems are proved. As an application of this result, the asymptotic normal distribution of any sinusoidal frequencies estimator of such time series based on second-order statistics is deduced.