# Autoregression algorithms

Autoregessive models use past time series values to predict future values. These models assume that a future value in a time series is dependent on its past values, and attempt to capture this relationship in a set of coefficient values.

Vertica supports both autoregression (AR) and vector autoregression (VAR) models:

- AR is a univariate autoregressive time series algorithm that predicts a variable's future values based on its preceding values. The user specifies the number of lagged timesteps taken into account during computation, and the model then predicts future values as a linear combination of the values at each lag.
- VAR is a multivariate autoregressive time series algorithm that captures the relationship between multiple time series variables over time. Unlike AR, which only considers a single variable, VAR models incorporate feedback between different variables in the model, enabling the model to analyze how variables interact across lagged time steps. For example, with two variables—atmospheric pressure and rain accumulation—a VAR model could determine whether a drop in pressure tends to result in rain at a future date.

The AUTOREGRESSOR function automatically executes the algorithm that fits your input data:

- One value column: the function executes autoregression and returns a trained AR model.
- Multiple value columns: the function executes vector autoregression and returns a trained VAR model.