ARIMA

ARIMA (AutoRegressive Integrated Moving Average) is a statistical model used for time series forecasting. It combines autoregression (AR), differencing to achieve stationarity (I), and a moving average component (MA) to capture dependencies in data over time. Additionally, it supports seasonal components (S) to model seasonal patterns and exogenous variables (X) to incorporate external factors that influence the forecast.

Order
p is the order (number of time lags) of the auto-regressive (AR) model.
Degree of differencing. ARIMA models that include differencing (i.e. when d is positive) assume that the data becomes stationary after differencing.
q is the order (number of time lags) of the moving-average (MA) model.
Seasonal Order
P is the order of the auto-regressive (AR) part of the seasonal model.
Degree of seasonal differencing. Seasonal ARIMA models that include differencing (i.e. when D is positive) assume that the data becomes stationary after differencing.
Q is the order of the moving-average (MA) part of the seasonal model.
s is the season length of the model.
Trend
Trend cannot have terms of degree smaller than d + D.
Deterministic trend of the model.
Offset from which time trend values should start.
Other
Require the autoregressive parameters to match a stationary process.
Require the moving average parameters to match an invertible process.
Whether or not to concentrate the variance of the error term out of the likelihood.