# Autoregressive

Autoregressive is a stochastic process that can be described by a weighted sum of its previous values and a white noise error. An autoregressive process operates under the premise that past values have an effect on current values.

# Autoregressive

**Autoregressive** is a stochastic process that can be described by a weighted sum of its previous values and a white noise error. An autoregressive process operates under the premise that past values have an effect on current values.

## Autoregressive Calculation

A process considered AR(1) is the first order process, meaning that the current value is based on the immediately preceding value. An AR(2) process has the current value based on the previous two values. An AR(1) process can be described mathematically as follows:

An AR(2) would have the form (below) and so on. In theory a process might be represented by an AR(infinity).

## Autoregressive Intrepretation

Autoregressive Conditional Heteroskedasticity (ARCH) models assume that the variance of the current error term is related to the size of the previous periods' error terms, giving rise to volatility clustering. This phenomenon is widely observable in financial markets, where periods of low volatility are followed by periods of high volatility and vice versa.

Autoregressive Moving Average Model (ARMA) is a tool for understanding and, perhaps, predicting future values of autocorrelated time series data series. consists of two parts, an autoregressive (AR) part and a moving average (MA) part.