Use the global mean for both adjacent values
For return observations r₁ through rN with overall mean μ, calculate ρ₁ = Σ from t=2 to N [(rₜ − μ)(rₜ₋₁ − μ)] / Σ from t=1 to N (rₜ − μ)². The AR(1) approximation is Nraw = N × (1 − ρ₁)/(1 + ρ₁). The displayed effective count is clipped to the interval from one through N, while the unclipped approximation remains visible. A constant series has zero denominator and undefined autocorrelation.
A four-observation arithmetic check
For the ordered series 1%, 2%, 3%, and 4%, the mean is 2.5%. Centered adjacent products total 1.25 and centered squared values total 5, so lag-one autocorrelation is 0.25. The effective-count approximation is 4 × 0.75/1.25 = 2.4. Reordering the same values changes adjacent products and can change the result even though the sample mean and ordinary standard deviation remain unchanged.
The approximation has a narrow interpretation
An AR(1)-like stationary dependence pattern is an assumption, not something established by a single correlation estimate. Negative autocorrelation can produce an unclipped count above N; the clipped display is a conservative interface convention, not a universal statistical identity. Higher-lag dependence, changing volatility, and structural breaks are not resolved here. This output does not automatically correct a confidence interval or a backtest p-value. Inspect the actual sequence and use an appropriate dependence-aware method for any later inference.