ACF/PACF Correlogram: Identifying ARIMA Order

This simulator builds a stationary ARMA(1,1) process from adjustable AR (φ) and MA (θ) coefficients, then integrates it d times to produce an observed series that can be trend-drifting and non-stationary — the same "I" step that gives ARIMA its name. A 3D correlogram renders the autocorrelation (ACF) and partial autocorrelation (PACF) as two rows of bars across 20 lags, alongside the raw time series itself, so you can watch the ACF's decay shape change in real time as you switch between the raw series and its differenced counterpart. A split-sample heuristic compares the mean and variance of the first and second half of the series to flag drift, and the live ACF(1)/PACF(1) readouts show exactly the numbers an analyst would use to pick an ARIMA order.