ARIMA

Autoregression and integrated moving average model with optimization for best parameters and model order:

y(t) = P₁ y(t - 1) + P₂ y(t - 2) + … + P_n y(t - n) + Q₀ + a(t) - Q₁ a(t - 1) - … - Q_m a(t - m)

where:

y - time series at times t, t - 1, t - 2, ... , t - n

a - white noise with variance at times t, t - 1, t - 2, ... , t - m

n - order of autoregression

m - order of moving average

Q₀ - overall constant