Visualization of stochastic processes based on ARMA(1,1) model

Autoregression coefficient φ (phi): 0.00
Moving average coefficient θ (theta): 0.00
X(t) = 0.00 × X(t-1) + ε(t) + 0.00 × ε(t-1)
ε(t) ~ N(0, 0.3²)

Step: 0 / 50

The red curve shows the distribution of innovation ε(t). The blue dashed line shows the process of drawing the next point.

Blue arrow: AR part effect (φ)
Green arrow: MA part effect (θ)

Cumulative process: random walk with ARMA(1,1) innovations
Non-cumulative process: pure ARMA(1,1) with mean reversion

φ = θ = 0: white noise (independent innovations)
φ > 0: positive autocorrelation (trend persistence)
φ < 0: negative autocorrelation (oscillations)