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Autoregressive conditional heteroskedasticity
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<p> In <a href="/facts/Econometrics/7U52gzHt">econometrics</a>, the autoregressive conditional heteroskedasticity (ARCH) model is a <a href="/facts/Statistical_model/jKkT5ftm">statistical model</a> for <a href="/facts/Time_series/fSXPR817">time series</a> data that describes the <a href="/facts/Variance/ULBJKXD1">variance</a> of the current <a href="/facts/Errors_and_residuals_in_statistics/Ef0LgAS4">error term</a> or <a href="/facts/Innovation_(signal_processing)/gyC0RrBG">innovation</a> as a function of the actual sizes of the previous time periods' error terms; 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 <a href="/facts/Autoregressive/LpboAQ0W">autoregressive</a> (AR) model; if an <a href="/facts/Autoregressive_moving_average_model/sALPoUzm">autoregressive moving average</a> (ARMA) model is assumed for the error variance, the model is a generalized autoregressive conditional heteroskedasticity (GARCH) model. </p><p>ARCH models are commonly employed in modeling <a href="/facts/Mathematical_finance/P9otEltQ">financial</a> <a href="/facts/Time_series/fSXPR817">time series</a> that exhibit time-varying <a href="/facts/Volatility_(finance)/mCdus1MW">volatility</a> and <a href="/facts/Volatility_clustering/HhAIFmcX">volatility clustering</a>, i.e. periods of swings interspersed with periods of relative calm (this is, when the time series exhibits heteroskedasticity). ARCH-type models are sometimes considered to be in the family of <a href="/facts/Stochastic_volatility/d5zBCcUP">stochastic volatility</a> models, although this is strictly incorrect since at time <i>t</i> the volatility is completely predetermined (deterministic) given previous values. </p>