Talk:Vector autoregression

An urgent problem that needs to be addressed

I think someone has deleted the annex for the concise matrix notation under the Estimation section last month. It reads "Starting from the concise matrix notation (for details see this annex): XXX" I believe there used to be link to a separate wikipedia page under that annex that describes carefully how to write the VAR(p) in a concise matrix form to do estimation. That page, though not perfectly written, is EXTREMELY helpful. My friends in academia and industry frequently consult that page for research and learning purposes. Therefore that page, in this humble opinion, should be brought back.

The thing is that I believe there is ambiguity and a poor example in the "Concise Matrix Notation" section. The example there is absolutely NOT a concise matrix notation. It is merely an example of VAR with two variables written in a matrix. For concise matrix notation on the other hand, Y and Z should both be matrices that incorporate the entire time series of the variables.

I tried to undo the previous changes and bring back the link to " General matrix notation of a VAR(p)". However I think the original wiki page was deleted unfortunately. Could someone kindly recover it, or perhaps rewrite it to fit into this page?

Thank you so much! Wbtdave (talk) 05:57, 13 October 2021 (UTC).

Related Topics

I think Vector ARMA (VARMA) and cointegration models should be mentioned as generalizations of VAR models

Structured versus Structural

A requested article is SVAR, or Structured Vector Autoregression. Is this the same as Structural VAR? It's unclear. Thanks. — RJH (talk) 22:19, 19 December 2006 (UTC)

Same thing (although the usual form is structural, as in structural model). You could make a redirect for the moment AdamSmithee 09:24, 20 December 2006 (UTC)

I've authored a method for computing Structural VAR coefficient matrices using Cholesky decomposition here: http://arxiv.org/abs/1309.6290, and corresponding MATLAB code in http://www.mathworks.it/matlabcentral/fileexchange/44106-large-inverse-cholesky. Please include this information if you think it adds value Aravindh Krishnamoorthy (talk) 15:15, 10 January 2014 (UTC)

estimation

with method of moments, Yule Walker equations??? Jackzhp (talk) 03:26, 30 May 2011 (UTC)

recently, paul krugman had a blog post on how people need to be more simple this article is a good example; if you really understand VAR, you could do a much better job of explaining it in much simpler terms. — Preceding unsigned comment added by 50.195.10.169 (talk) 02:07, 19 February 2014 (UTC)

Dr. Matthes's comment on this article

Dr. Matthes has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

I think this entry is decent, but could be improved along several dimensions. First, some statements are sloppy ("All variables in a VAR are treated symmetrically in a structural sense" - I am not sure what structural means here). Second, there actually is an entire literature on "Structural VARs" that this entry is completely missing. It deals with the question "How do we impose economic theory to identify the structural VAR representation?".

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Dr. Matthes has published scholarly research which seems to be relevant to this Wikipedia article:

• Reference : Amir-Ahmadi, Pooyan & Matthes, Christian & Wang, Mu-Chun, 2014. "Drifts, Volatilities, and Impulse Responses Over the Last Century," Working Paper 14-10, Federal Reserve Bank of Richmond.

ExpertIdeasBot (talk) 15:57, 19 May 2016 (UTC)

Dr. Smith's comment on this article

Dr. Smith has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

There is an expositional issue with articles on technical topics: who is the intended audience? Is it someone who knows no statistics or an expert research worker in that field. I think this article works quite well at the level of those most likely to use it: students doing a course which covers VARs or coming across VARs in research articles. It also has references to the main texts, Enders, Lutkepohl and Hamilton and useful cross-referencing, e.g. to Bayesian VARs. This is in the "see also" rather than in the relevant places in the text. For instance under forecasting it could say say something like VARs can quickly use up degrees of freedom, with 7 variables and four lags, one is estimating 28 coefficients, plus intercept, in each equation. This can cause forecasting performance to deteriorate so Bayesian VARs are often used. There are some minor technical issues. For instance it says "all variables have to be of the same order of integration", which is not necessarily the case if there is cointegration, one could have some I(0) and some I(0) combinations of I(1) variables. But this starts to get into more controversial judgements about appropriate modelling strategies. At the top it could also warn people not to confuse VAR with VaR, value at risk..

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Dr. Smith has published scholarly research which seems to be relevant to this Wikipedia article:

• Reference 1: Dees, Stephane & Pesaran, Hashem & Smith, Vanessa & Smith, Ron P., 2010. "Supply, demand and monetary policy shocks in a multi-country New Keynesian Model," Working Paper Series 1239, European Central Bank.

• Reference 2: Dees, Stephane & Pesaran, Hashem & Smith, Vanessa & Smith, Ron P., 2010. "Supply, demand and monetary policy shocks in a multi-country New Keynesian Model," Working Paper Series 1239, European Central Bank.

ExpertIdeasBot (talk) 13:37, 11 June 2016 (UTC)

Dr. Lutkepohl's comment on this article

Dr. Lutkepohl has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

I wonder for which audience this text is written. For a general audience it is fine to give some general information about the VAR model. However, the purpose of many of the formulas is not clear to me in particular if no proper definitions of the symbols are given. For these items, im my view it would be much better to refer to the related textbook literature. Also the choice of references is partly unclear to me. For example, the article under note [1] is on testing for autocorrelation. Is that really an article someone should read who wants to learn about the VAR model? Also some of the other references are on special issues rather than general reading on VAR models ([2], [3], [5]).

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Dr. Lutkepohl has published scholarly research which seems to be relevant to this Wikipedia article:

• Reference 1: Helmut Lutkepohl & Anna Staszewska-Bystrova & Peter Winker, 2013. "Comparison of Methods for Constructing Joint Confidence Bands for Impulse Response Functions," MAGKS Papers on Economics 201325, Philipps-Universitat Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).

• Reference 2: Helmut Lutkepohl & Anton Velinov, 2014. "Structural Vector Autoregressions: Checking Identifying Long-Run Restrictions via Heteroskedasticity," Discussion Papers of DIW Berlin 1356, DIW Berlin, German Institute for Economic Research.

ExpertIdeasBot (talk) 09:20, 16 June 2016 (UTC)

Dr. Shi's comment on this article

Dr. Shi has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

1. Estimation of the covariance matrix

Lütkepohl, Helmut. New introduction to multiple time series analysis. Springer Science & Business Media, 2005.

2. "Writing VAR(p) as VAR(1)" The VAR(1) model is referred to as its companion form. The [A1 A2; I 0] matrix is the companion matrix.

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We believe Dr. Shi has expertise on the topic of this article, since he has published relevant scholarly research:

• Reference : Shu-Ping Shi & Peter C.B. Phillips & Jun Yu, 2011. "Speci fication Sensitivities in Right-Tailed Unit Root Testing for Financial Bubbles," Working Papers 08-2011, Singapore Management University, School of Economics.

ExpertIdeasBot (talk) 16:06, 12 July 2016 (UTC)

Dr. Dees's comment on this article

Dr. Dees has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

In the part on Structural VARs, information should be given to the various methods to identify structural shocks, inter alia Cholesky decomposition or sign restrictions.

Section 4 is too short. More details should be given in particular to impulse responses, detailing Orthogonal Impulse Responses, Generalised Impulse Responses.

References to the Global VAR could be given

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

We believe Dr. Dees has expertise on the topic of this article, since he has published relevant scholarly research:

• Reference 1: Dees, Stephane & Pesaran, Hashem & Smith, Vanessa & Smith, Ron P., 2010. "Supply, demand and monetary policy shocks in a multi-country New Keynesian Model," Working Paper Series 1239, European Central Bank.

• Reference 2: Dees, Stephane & Saint-Guilhem, Arthur, 2009. "The role of the United States in the global economy and its evolution over time," Working Paper Series 1034, European Central Bank.

ExpertIdeasBot (talk) 19:01, 26 July 2016 (UTC)

Impulse response

The very brief section Vector autoregression#Interpretation of estimated model links to impulse response, but that article doesn't explain how to get the impulse response numerically from an estimated model. So I think that this article should do that. Loraof (talk) 18:33, 1 August 2016 (UTC)

I've done it. Loraof (talk) 19:35, 3 August 2016 (UTC)

Dr. Vonnak's comment on this article

Dr. Vonnak has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

This half-sentence seems to be orphan:

„use VAR in time series data when data not stationary on first difference.(by chashman)”

Instead this: „Note that y2,t can have a contemporaneous effect on y1,t if B0;1,2 is not zero. This is different from the case when B0 is the identity matrix (all off-diagonal elements are zero — the case in the initial definition), when y2,t can impact directly y1,t+1 and subsequent future values, but not y1,t. Because of the parameter identification problem, ordinary least squares estimation of the structural VAR would yield inconsistent parameter estimates. This problem can be overcome by rewriting the VAR in reduced form.”, I would suggest this more precise wording: „Note that y2,t can have a contemporaneous effect on y1,t if B0;1,2 is not zero. This is different from the case when B0 is the identity matrix (all off-diagonal elements are zero — the case in the initial definition), when y2,t can impact directly y1,t+1 and subsequent future values, but not y1,t. Note also that y2,t can be correlated with the disturbance term. Because of this endogeneity problem, ordinary least squares estimation of the structural VAR would yield inconsistent parameter estimates. This problem can be overcome by rewriting the VAR in reduced form.”

At the end of the reduced form, I would put this paragraph: „Although a structural model has unique reduced form, a VAR can be a representation of many structural models. In order to recover the true underlying model from a VAR, additional identifying restrictions are needed.”

What is very much missing from this article is to write at least a paragraph about when is a VAR stable (related to the eigenvalues of the coefficient matrix, mentioned at the very end).

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

We believe Dr. Vonnak has expertise on the topic of this article, since he has published relevant scholarly research:

• Reference : Balazs Vonnak, 2010. "Risk premium shocks, monetary policy and exchange rate pass-through in the Czech Republic, Hungary and Poland," MNB Working Papers 2010/1, Magyar Nemzeti Bank (the central bank of Hungary).

ExpertIdeasBot (talk) 11:32, 22 December 2016 (UTC)