Talk:Autoregressive conditional heteroskedasticity

message: Alessio Farhadi in the external link (ARCH and GARCH models for forecasting volatility, quantnotes.com) does not seem to follow the more conventional notation that a GARCH(p,q) process has p GARCH terms and q ARCH terms, and not viceversa. These links support the notation I have introduced: , , . The application EViews has the command "arch(p,q)" which uses the convention used by Fahardi (for what I would call a GARCH(q,p)), but even the new versions (>5) have a note "Note the order of the arguments in which the ARCH and GARCH terms are entered, which gives precedence to the ARCH term.", presumably because this is not the standard convention, and it is not even the convention used in their own help file describing GARCH models. (It might even be the case that confounding the order of the terms is a common mistake.)
In my opinion the P Q order is not important given that the formula is specified. However links to similar methods (Locally Stationary Wavelets of Nason for example) should be referenced.  There is also no example application or detailed explaination. This should not only be linked to economics but also to mathematics (via statistics). I can also see no consideration of the assumed distribution, ML estimation for GARCH models is often improved assuming a students t distribution as apposed to a guassian distribution. D M  —Preceding unsigned comment added by 137.222.243.9 (talk) 18:45, August 28, 2007 (UTC) 
How is GARCH pronounced aloud?  Perhaps someone could add it to the page.  —Preceding unsigned comment added by 164.76.125.101 (talk) 14:48, 7 April 2008 (UTC)

message: this the mean reverting model isn't it? i'm gonna add that into the definition. i thought i should state it here because i'm not exactly sure.  —Preceding unsigned comment added by ToyotaPanasonic (talk • contribs) 07:20, 16 June 2008 (UTC)
thread_title:  mean reverting? 

message: The notation applied here for GARCH(p,q) differs from the one used in gretl, where a GARCH(p,q) refers to a model
:: \sigma_t^2 = \alpha_0 + \sum_{i = 1}^p \alpha_i \epsilon_{t-i}^2 + \sum_{j = 1}^q \beta_j \sigma_{t-j}^2\,
: (weak reference: gretl mailing list), and probably also in R (programming language) (reference: garchFit documentation, but it's not clear what model is used; the model appears in garchSim, and it seems that alpha and beta are switched). Albmont (talk) 11:47, 27 November 2008 (UTC)
replies: text: I have just found an interesting source for these models: Parameter Estimation of ARMA Models with GARCH/APARCH Errors - An R and SPlus Software Implementation, by Diethelm Würtz, Yohan Chalabi, and Ladislav Luksan. Albmont (talk) 12:03, 27 November 2008 (UTC)
thread_title:  GARCH(p, q) model specification 

message: I think the page should include a "Notation" paragraph. For exemple, in the R documentation, a (complete) model is referenced like "AR(1)-GARCH(1,1)", meaning that the model of the variable is AR(1) and the model of the volatility is GARCH(1,1). See, for example, the documentation of function garchFit: formula object describing the mean and variance equation of the ARMA-GARCH/APARCH model. A pure GARCH(1,1) model is selected when e.g. formula=~garch(1,1). To specify for example an ARMA(2,1)-APARCH(1,1) use formula = ~arma(2,1)+apaarch(1,1). Albmont (talk) 14:34, 22 May 2009 (UTC)
replies: text: PS: the GARCH paragraph seems to be in error, with p and q reversed. Albmont (talk) 14:34, 22 May 2009 (UTC)
thread_title:  Notation 

message: Yes please, thanks!  132.194.3.162 (talk) 23:42, 1 October 2012 (UTC)
replies: text: I agree with this it tells NOTHING about the alpha value or the process to select the q lags. Nor does it have links to an explanation. Nor does it tell why you should care if there is an ARCH effect or what it is. -Cs california (talk) 11:29, 14 January 2014 (UTC)
thread_title:  "Reads more like a review" 

message: Dr. Bauwens has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:
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Dr. Bauwens has published scholarly research which seems to be relevant to this Wikipedia article:
*Reference 1: Luc, BAUWENS & Arie, PREMINGER & Jeroen, ROMBOUTS, 2007. "Theory and inference for a Markov switching GARCH model," Discussion Papers (ECON - Departement des Sciences Economiques) 2007033, Universite catholique de Louvain, Departement des Sciences Economiques.
*Reference 2: BAUWENS, Luc & GRIGORYEVA, Lyudmila & ORTEGA, Juan-Pablo, 2014. "Estimation and empirical performance of non-scalar dynamic conditional correlation models," CORE Discussion Papers 2014012, Universite catholique de Louvain, Center for Operations Research and Econometrics (CORE).
ExpertIdeasBot (talk) 18:48, 27 June 2016 (UTC)
thread_title:  Dr. Bauwens's comment on this article 

message: Dr. Caporin has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:
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*Reference 1: Massimiliano Caporin & Eduardo Rossi & Paolo Santucci De Magistris, 2014. "Chasing Volatility. A Persistent Multiplicative Error Model With Jumps," "Marco Fanno" Working Papers 0186, Dipartimento di Scienze Economiche "Marco Fanno".
*Reference 2: Caporin, Massimiliano & Jimenez-Martin, Juan-Angel & Gonzalez-Serrano, Lydia, 2013. "Currency hedging strategies, strategic benchmarks and the Global and Euro Sovereign financial crises," MPRA Paper 50940, University Library of Munich, Germany, revised 23 Oct 2013.
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thread_title:  Dr. Caporin's comment on this article 

message: Dr. Otranto has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:
 z_{t} and a time-dependent standard deviation {\displaystyle \sigma _{t}} \sigma _{t}"
Comment: It is more correct to say "time-varying conditional standard deviation"
"A methodology to test for the lag length of ARCH errors using the Lagrange multiplier test was proposed by Engle (1982)". 
Comment: this test is used to verify the presence of ARCH-type heteroskedasticity in the series, not to establish the lag length
"Generally, when testing for heteroscedasticity in econometric models, the best test is the White test. However, when dealing with time series data, this means to test for ARCH and GARCH errors."
Comment: I would erase this statement; the test for heteroskedasticity was commented in the previous section
I think that you can add the following text at the end of the description:
"There are several other extensions of the GARCH model. A review is present in Bollerslev (2010)."
Bollerslev, T. (2010): Glossary to ARCH (GARCH). In
Bollerslev, T., Russell J., Watson M. (Eds.): Volatility and
Time Series Econometrics, Oxford University Press.
Also I would add:
 "Another extension of GARCH models is the modelization of realized volatility, developing  the Multiplicative Error Models (MEM's) (see Engle, 2002, Engle and Gallo, 2006, Gallo and Otranto, 2015)"
Engle, R.F. (2002). New frontiers for ARCH models. Journal of Applied Econometrics
17, 425–446.
Engle, R.F., and Gallo, G.M. (2006). A multiple indicators model for volatility using
intra-daily data. Journal of Econometrics 131, 3–27.
Gallo, G.M. and Otranto, E. (2015). Forecasting realized volatility with changing
average volatility levels. International Journal of Forecasting, 31, 620–634.
 }}
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We believe Dr. Otranto has expertise on the topic of this article, since he has published relevant scholarly research:
*Reference : Edoardo Otranto, 2004. "Classifying the Markets Volatility with ARMA Distance Measures," Econometrics 0402009, EconWPA, revised 05 Mar 2004.
ExpertIdeasBot (talk) 20:08, 24 September 2016 (UTC)
thread_title:  Dr. Otranto's comment on this article 

message: Dr. Terasvirta has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:
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*Reference 1: Paul Catani & Timo Terasvirta & Meiqun Yin, 2014. "A Lagrange Multiplier Test for Testing the Adequacy of the Constant Conditional Correlation GARCH Model," CREATES Research Papers 2014-03, School of Economics and Management, University of Aarhus.
*Reference 2: Annastiina Silvennoinen & Timo Terasvirta, 2012. "Modelling conditional correlations of asset returns: A smooth transition approach," CREATES Research Papers 2012-09, School of Economics and Management, University of Aarhus.
*Reference 3: Silvennoinen, Annastiina & Terasvirta, Timo, 2007. "Modelling Multivariate Autoregressive Conditional Heteroskedasticity with the Double Smooth Transition Conditional Correlation GARCH model," SSE/EFI Working Paper Series in Economics and Finance 0652, Stockholm School of Economics.
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thread_title:  Dr. Terasvirta's comment on this article