Estimation of spectral density for seasonal time series models

For estimating spectral densities of stationary seasonal time series processes, a new kernel is proposed. The proposed kernel is of the shape which is in harmony with oscillating patterns of the autocorrelation functions of typical seasonal time series process. Basic properties such as consistency and nonnegativity of the spectral density estimator are discussed. A Monte-Carlo simulation is conducted for multiplicative monthly autoregressive process and moving average process, which reveal that the proposed kernel provides more efficient spectral density estimator than the classical kernels of Bartlett, Parzen, and Tukey-Hanning.