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 sam ple mean and the sample covariance matrix of mixed spectra time series cont aining a sum of sinusoids and a moving average (MA) process. Two central li mit (CL) theorems are proved. As an application of this result, the asympto tic normal distribution of any sinusoidal frequencies estimator of such tim e series based on second-order statistics is deduced.