A Spectral Estimation of Discrete Harmonizable Process

In this paper, we develop the non-parametric spectral analysis for non-stationary discrete-time stochastic processes. This development will be investigated by using the multi-tapering and averaging technique. In particular, we obtain an estimator for the spectral density function of a harmonizable time series. This estimator is constructed by dividing the available time series into a number of overlapped and non-overlapped segments and then a multi-tapering technique is applied for each segment. Also, we obtain an estimator for the auto-covariance function and another estimator for the spectral distribution function of these processes, based on the spectral density estimator. Statistical properties of these estimators are investigated, including the asymptotic behaviour of the bias and covariance