Convergence of the Zero-Crossing Rate of Autoregressive Processes and Its Link to Unit Roots

摘要

The asymptotic zero-crossing rate (ZCR) of the general first and second order autoregressive processes is investigated. When the associated characteristic polynomial has a unit root exp(i theta), 0 theta < or = pi, the ZCR converges in mean square to theta/pi, and the rate of convergence is very fast regardless of the noise level. It is conjectured that in higher order autoregressive processes multiple unit roots can be determined by the ZCR of the filtered processes. An indication to this effect is given. (jhd)