For stationary AR(1) segments of length 2, 3 and 4, the variance of the number of sign changes is computed exactly; the independent interval approximation matches exactly for n=2,3 but deviates slightly for n=4, especially for negative correlation.
Another Look at AR(1)
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Given a stationary first-order autoregressive process X_t (with lag-one correlation rho satisfying |rho|<1), we examine the Central Limit Theorem for (1/n)*ln |X_1...X_n| and compute variances to high precision. Given a nonstationary process X_t (with |rho|>1), we examine instead (1/n)*ln|X_n| and study the distribution of ln|X_n|-n*ln|rho|.
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Number of Sign Changes: Segment of AR(1)
For stationary AR(1) segments of length 2, 3 and 4, the variance of the number of sign changes is computed exactly; the independent interval approximation matches exactly for n=2,3 but deviates slightly for n=4, especially for negative correlation.