# Autoregressive conditional heteroskedasticity

## Time series model / From Wikipedia, the free encyclopedia

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In econometrics, the **autoregressive conditional heteroskedasticity** (**ARCH**) model is a statistical model for time series data that describes the variance of the current error term or innovation as a function of the actual sizes of the previous time periods' error terms;[1] often the variance is related to the squares of the previous innovations. The ARCH model is appropriate when the error variance in a time series follows an autoregressive (AR) model; if an autoregressive moving average (ARMA) model is assumed for the error variance, the model is a **generalized autoregressive conditional heteroskedasticity** (**GARCH**) model.[2]

ARCH models are commonly employed in modeling financial time series that exhibit time-varying volatility and volatility clustering, i.e. periods of swings interspersed with periods of relative calm. ARCH-type models are sometimes considered to be in the family of stochastic volatility models, although this is strictly incorrect since at time *t* the volatility is completely pre-determined (deterministic) given previous values.[3]

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