| 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. |
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