What does one mean by ARCH effect? I am a little bit confused... I understand the mathematical terms and so on. But I cant explain the ARCH effect in words. Can someone explain the ARCH effect for me in words?
(ARCH effect for time series.)
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$\begingroup$ Are you talking about ARCH models for time series? I don't know any other statistical term for ARCH. $\endgroup$– Michael R. ChernickJan 8, 2017 at 20:48
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$\begingroup$ Please spell out your acronyms. What do you mean by "ARCH", are you referring to time series methods for modeling variance over time, or are you thinking of the horseshoe / arch effect in methods like Principal Components Analysis (cf, here)? $\endgroup$– gung - Reinstate MonicaJan 8, 2017 at 20:50
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$\begingroup$ Sorry, i did not know there where different ARCH effects... I mean ARCH effect as in time serie. $\endgroup$– LeahJan 8, 2017 at 20:52
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1$\begingroup$ Please register &/or merge your accounts (you can find information on how to do this in the My Account section of our help center), then you will be able to edit & comment on your own question. $\endgroup$– gung - Reinstate MonicaJan 8, 2017 at 20:56
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$\begingroup$ Why do you call it an effect? If it is for time series it is a model that ia an autoregressive type but with error terms whose variance varies with time. Maybe the ARCH effect has to do with the heteroskadastic variances. $\endgroup$– Michael R. ChernickJan 8, 2017 at 21:19
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2 Answers
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If the squared residuals/errors of your time series model exhibit autocorrelation, then ARCH effects are present.
A quick google search offers a clear definition:
A time series exhibiting conditional heteroscedasticity—or autocorrelation in the squared series—is said to have autoregressive conditional heteroscedastic (ARCH) effects. Engle's ARCH test is a Lagrange multiplier test to assess the significance of ARCH effects
Source: https://www.mathworks.com/help/econ/engles-arch-test.html?requestedDomain=www.mathworks.com
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I think that by ARCH effect they mean the correlation between volatility of a time series, measured by conditional variance, and its values or innovations in the past. The letter AR stands for auto regressive, C for conditional (i.e conditional variance), and H for heteroskedasticity. So if non-constant conditional variance of x(t) has some correlation with itself/or innovation in the past, then we say there exists ARCH effect.
