Stochastic processes
Autocorrelation (stationary process)
Animate multiple realizations of an AR(1) process and watch how an ensemble autocorrelation at a fixed reference time evolves. Compare raw and normalized estimates with the theoretical curve and explore infinite-data/unbiased mode.
Keeps the process stationary (|a| < 1). Larger |a| makes correlations last longer.
More realizations tighten the ensemble ACF estimate without freezing the page. Infinite uses an unbiased long sequence.
Portion of each realization shown in red between t₁ and t₂.
How far to extend the autocorrelation curves.
Higher values sweep the window faster across the process.
When enabled, playback pauses if the ACF maximum shifts away from τ = 0.
Sample functions
Sliding window across three realizations
Autocorrelation
Sample vs. theoretical Rxx(τ)
Normalized autocorrelation