ARMA

ARMA (Autoregressive Moving Average) is a statistical model used for analyzing and forecasting time series data. It combines two components - autoregressive (AR) model, which uses past values of the variable to predict future values, and the moving average (MA) model, which uses past forecast errors to improve predictions. ARMA models are widely used in fields like economics, finance, and engineering to identify patterns and make accurate forecasts based on time-series data.

Alternative definition

The Autoregressive Moving Average (ARMA) model is a fundamental tool in time series analysis, particularly for modeling and forecasting stationary stochastic processes. It combines two key components: autoregression (AR) and moving average (MA).

Components of ARMA

1. Autoregressive (AR) Component:
   This part of the model regresses the variable on its own past values. The order $p$ indicates how many lagged values are included.
   The AR component can be represented as:$$$$$$$$
2. Moving Average (MA) Component:
   This component models the error term as a linear combination of past error terms. The order $q$ indicates how many lagged forecast errors are included.
   The MA component can be expressed as:$$$$$$$$