We analyze the stochastic function C n (i)≡ y (i)− y n (i), where y (i) is a long-range correlated time series of length N max and y n (i)≡(1/n)∑ k= 0 n− 1 y (i− k) is the moving average with window n. We argue that C n (i) generates a stationary sequence of self-affine clusters C with length l, lifetime τ, and area s. The length and the area are related to the lifetime by the relationships l∼ τ ψ l and s∼ τ ψ s, where ψ l= 1 and ψ s= 1+ H. We also find that l, τ, and s are power law distributed with exponents depending on H: P (l)∼ l− α, P (τ)∼ τ− β, and P (s)∼ s− γ, with α= β= 2− H and γ= 2/(1+ H). These predictions are tested by extensive simulations on series generated by the midpoint displacement algorithm of assigned Hurst exponent H (ranging from 0.05 to 0.95) of length up to N max= 2 21 and n up to 2 13.