Difference between ARMA and ARIMA

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Feature ARMA Model ARIMA Model Definition Models that combine autoregressive (AR) and moving average (MA) components without differencing the data. Models that combine autoregressive (AR), moving average (MA), and differencing components to account for non-stationarity. Components AR(p) + MA(q) AR(p) + MA(q) + Integrated (d) Stationarity Assumes the data is stationary. Does not require the data to be stationary; it handles non-stationarity through differencing. Integration (d) Not applicable; does not include differencing. Includes differencing to make the time series stationary. Suitable for Stationary time series data with no trend or seasonality. Non-stationary time series data with trend and/or seasonality. Trend and Seasonality Does not account for trend or seasonality. Can handle trend and seasonality through differencing. Parameter Estimation Typically estimated using methods like Maximum Likelihood Estimation (MLE) or least squares. Typically estimated using methods like MLE or least squares, with additional consideration for differencing parameter. Application Used when the time series is already stationary or has been made stationary through differencing. Commonly applied to time series with trends, seasonality, or other non-stationary components. Example Forecasting stock prices in a stationary market. Forecasting monthly sales data with trend and seasonality.

Difference between ARMA and ARIMA

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Feature	ARMA Model	ARIMA Model
Definition	Models that combine autoregressive (AR) and moving average (MA) components without differencing the data.	Models that combine autoregressive (AR), moving average (MA), and differencing components to account for non-stationarity.
Components	AR(p) + MA(q)	AR(p) + MA(q) + Integrated (d)
Stationarity	Assumes the data is stationary.	Does not require the data to be stationary; it handles non-stationarity through differencing.
Integration (d)	Not applicable; does not include differencing.	Includes differencing to make the time series stationary.
Suitable for	Stationary time series data with no trend or seasonality.	Non-stationary time series data with trend and/or seasonality.
Trend and Seasonality	Does not account for trend or seasonality.	Can handle trend and seasonality through differencing.
Parameter Estimation	Typically estimated using methods like Maximum Likelihood Estimation (MLE) or least squares.	Typically estimated using methods like MLE or least squares, with additional consideration for differencing parameter.
Application	Used when the time series is already stationary or has been made stationary through differencing.	Commonly applied to time series with trends, seasonality, or other non-stationary components.
Example	Forecasting stock prices in a stationary market.	Forecasting monthly sales data with trend and seasonality.