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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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Leah
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  • Are you talking about ARCH models for time series? I don't know any other statistical term for ARCH. – Michael R. Chernick Jan 08 '17 at 20:48
  • 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](http://ordination.okstate.edu/eigen.htm))? – gung - Reinstate Monica Jan 08 '17 at 20:50
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    Please register &/or merge your accounts (you can find information on how to do this in the **My Account** section of our [help]), then you will be able to edit & comment on your own question. – gung - Reinstate Monica Jan 08 '17 at 20:56
  • Sorry, i did not know there where different ARCH effects... I mean ARCH effect as in time serie. – Leah Jan 08 '17 at 20:52
  • 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. – Michael R. Chernick Jan 08 '17 at 21:19
  • Can you clarify what it is about the ARCH model that you want help understanding? – gung - Reinstate Monica Jan 08 '17 at 21:35
  • @MichaelChernick, the applied econometrics literature is full of the term "ARCH effect". Why it has come to existence in its precise form is a good question, but why the user here calls it this way is clear – it is a pretty standard expression. – Richard Hardy Jan 15 '17 at 19:43
  • @RichardHardy So why don't you tell us what it is? Very few of us are econometricians. There is nothing wrong with me asking the question. – Michael R. Chernick Jan 15 '17 at 19:47
  • @MichaelChernick, I did not intend to imply there is anything wrong. I did not intend to pick on you :) I just answered the question you had for the user. Now, another user has already given an answer on what ARCH effects are. I think it is good enough. In the meantime, the OP is long gone... – Richard Hardy Jan 15 '17 at 19:48

2 Answers2

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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

Richard Hardy
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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.

Minh Nguyen
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