We establish zero-crossing rate (ZCR) relations between the input and the subbands of a maximally decimated M-channel power complementary analysis filterbank when the input is a stationary Gaussian process. The ZCR at lag l is defined as the number of sign changes between the samples of a sequence and its l-sample shifted version, normalized by the sequence length. We derive the relationship between the ZCR of the Gaussian process at lags that are integer multiples of M and the subband ZCRs. Based on this result, we propose a robust iterative autocorrelation estimator for a signal consisting of a sum of sinusoids of fixed amplitudes and uniformly distributed random phases. Simulation results show that the performance of the proposed estimator is better than the sample autocorrelation over the SNR range of - 6 to 15 dB. Validation on a segment of a trumpet signal showed similar performance gains.