The Spectral Density Estimation of Stationary Time Series with Missing Data

The spectral estimation of unevenly sampled data has been widely investigated in astronomical and medical areas. However the investigations are usually carried out in the context of periodicity detection and deterministic signal. Here we consider estimating the spectral density of stationary time series with missing data. An asymptotically unbiased estimation approach is proposed. The simulations are used to compare it to the classical periodogram, the Lomb periodogram (widely used for irregularly sampled data) and the SVD based periodogram. The results show that the new method substantially reduced the bias and slightly increased the variance. Overall the new approach significantly reduced the mean squared percentage error. As an example, the approach is applied to rainfall data in Irelan.