ARMAX (AutoRegressive Moving Average model with eXogenous inputs)

Information

• ARMAX (AutoRegressive Moving Average model with eXogenous inputs) is a type of statistical model that combines autoregressive (AR) and moving average (MA) models with external variables, also known as exogenous variables.
• The model assumes that the output variable depends on its past values, the past values of the error term, and past values of the exogenous variables.
• ARMAX models are used in time series analysis to predict future values of a variable based on its past values, the past values of the error term, and past values of the exogenous variables.
• The order of the model is determined by the number of autoregressive and moving average terms used.
• ARMAX models can be estimated using maximum likelihood estimation (MLE) or least squares estimation (LSE) methods.
• The model requires that the errors are uncorrelated and have constant variance over time, which can be checked using diagnostic tests.
• ARMAX models are widely used in areas such as finance, economics, engineering, and environmental science for forecasting, monitoring, and decision making.