ARMAX is a statistical model used in the analysis of time series and in the prediction of dynamic variables. ARMAX is an acronym for "AutoRegressive Moving Average model with eXogenous inputs".
The ARMAX model combines autoregressive (AR) and moving average (MA) models with exogenous variables (X) to model the relationship between a variable of interest and other explanatory variables. The ARMAX model is useful when future values of the variable of interest may depend on past values of the same variable, as well as on past values of other related variables.
In practice, the ARMAX model can be fitted to the data by identifying the AR, MA and X parameters that best describe the time series. The fitted model can then be used to make future predictions or to analyze the relationship between the variable of interest and exogenous variables.
The ARMAX model was originally proposed in the paper "Transfer Function Modeling and Digital Simulation for Non-Gaussian Processes" written by George E. P. Box and Gwilym M. Jenkins in 1976. This paper is considered to be one of the seminal works in time series model theory and has been widely cited in the statistics and econometrics literature. Since then, several extensions and variations of the ARMAX model have been proposed to address different problems in time series analysis.
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