A Single-Pass Algorithm for Spectrum Estimation With Fast Convergence

We propose a single-pass algorithm for estimating spectral densities of stationary processes. Our algorithm is computationally fast in the sense that, when a new observation arrives, it can provide a real-time update within O(1) computation. The proposed algorithm is probabilistically fast in that, for stationary processes whose auto-covariances decay geometrically, the estimates from the algorithm converge at a rate which is optimal up to a multiplicative logarithmic factor. We also establish asymptotic normality for the recursive estimate. A simulation study is carried out and it confirms the superiority over the classical batched mean estimates.