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Normally, "a" would be the intercept, and "b" would be the slope. Is it different in this equation for some reason?
The link to characteristic equation isn't making a lot of sense to me so far. That is an article about characteristics equations of matrices, whose roots are eignvalues. Is that what is intended here? It doesn't look like it. Michael Hardy ( talk) 22:13, 2 August 2008 (UTC)
Agree the links to characteristic equation don't make sense. In one place the link is to the charactaristic equation of a differential equation, and in another to charactaristic polynomial of a matrix. Can an autoregressive process be expressed as a differential equation with identical coefficients, or as a matrix with the same charactaristic polynomial? I think this needs to be clarified. (April 22 2016). — Preceding unsigned comment added by 205.254.147.8 ( talk) 16:49, 22 April 2016 (UTC)
I believe we should split this page into two. The section at the bottom about the Unit Root Hypothesis is well written, interesting, and important for/to economists. The Unit Root, however, is a more general topic that applies to all time-series analysis in all fields. Therefore, I think the Unit Root Hypothesis should be only mentioned as an example with the bulk of its content on a separate page.
This is a big enough change that I am reluctant to do this unless there is evidence of a consensus - and more importantly, since the information is useful for econ people (like me), I would hate to make the change in such a way that it is unavailable while the new page is waiting on approval. — Preceding unsigned comment added by Balaamsgrayass ( talk • contribs) 23:40, 3 December 2017 (UTC)
The audience for this article is severely limited. I suggest an introduction that targets a broader audience with a more limited understanding of statistics. The article is heavy on statistical jargon and does not make the subject more accessible. I would be interested in others thoughts on this. Perhaps accessibility is not a concern. 206.193.225.70 ( talk) 19:01, 26 September 2008 (UTC)
Like the above commentors, I have a background in maths and statistics, but I am having enough trouble with this article that I'm not sure if I've found an error, or simply misunderstood it.
Consider the example, concerning:
The example goes on to show that is a function of t if the characteristic equation has a unit root. However, it is also a function of t for non-unit roots! Proceding just as in the example, but not restricting outselves to m = 1:
Then the variance of is given by:
The first term is zero, since the are not random variates and so have variance 0. The second term expands to:
Which then (generally) simplifies to:
which is clearly just as non-stationary as , if not more so!! - 202.63.39.58 ( talk) 20:45, 25 March 2013 (UTC)
In the Definition section, it almost seems as if the exponents in the polynomial in m are in reverse order. Most of what I could find online deals with AR(1), but in what little I can find for unit roots of AR(p), the characteristic polynomial has the *lowest* power in lag operator (presumably m in this case) bound to the constant coefficient associated with the least lag (a_1 in this case). See, for example, http://www.bauer.uh.edu/rsusmel/phd/ec2-5.pdf. This is, of course, assuming that the operator m is a stand-in for a lag operation. Nowhere is this stated, but if it isn't the case, it sure would be unorthodox and deserving of an explanation. — Preceding unsigned comment added by 131.136.242.1 ( talk) 23:28, 21 April 2015 (UTC)
It seems to be pretty fundamental to time series. I don't know how to bump up the importance.
Dr. Dogru has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:
1. Unit root hypothesis should be taken into account with and withoud draft. Besides that it is okay.
2. You could add this reference to the further readings:
Dogru, B. (2014). Analysis of Long-and Short-run Balance of Money Demand In Turkey Using ARDL and VEC Approaches” The International Journal of Economic and Social Research, Vol. 10, No. 2, 19-32,
We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.
Dr. Dogru has published scholarly research which seems to be relevant to this Wikipedia article:
ExpertIdeas ( talk) 23:46, 23 August 2015 (UTC)
Dr. Platen has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:
The page is well written and allows the reader to get a reasonable overview about the question raised.
We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.
Dr. Platen has published scholarly research which seems to be relevant to this Wikipedia article:
ExpertIdeasBot ( talk) 14:58, 24 June 2016 (UTC)
Dr. Reed has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:
"time serie" should be "time series"
"transitory, the time serie will converge" could be better stated as "over time, the time series will converge"
"while unit-root processes" could be better stated as "while shocks to unit-root processes"
We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.
We believe Dr. Reed has expertise on the topic of this article, since he has published relevant scholarly research:
ExpertIdeasBot ( talk) 20:40, 1 July 2016 (UTC)
Dr. Shi has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:
1. "that can cause problems in statistical inference involving time series models. "
Not if one uses correct model for estimation.
2. "If the other roots of the characteristic equation lie inside the unit circle" The unit root process may have more than two roots. The introduction, in general, is not accurate.
3. "Granger and Newbold called such estimates 'spurious regression' results:" Spurious regression refers to the regression of one I(1) variable on the other I(1) variable when they are not cointegrated. Not the case of regressing y_{t} on y_{t-1} -- the slope of the autoregressive model. The statement is wrong.
4. Estimation Section: when two variables are I(1) and cointegrated, the estimated coefficient is super-consistent. Information along this line is not mentioned.
We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.
We believe Dr. Shi has expertise on the topic of this article, since he has published relevant scholarly research:
This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||||||||||||
|
Daily pageviews of this article
A graph should have been displayed here but
graphs are temporarily disabled. Until they are enabled again, visit the interactive graph at
pageviews.wmcloud.org |
Normally, "a" would be the intercept, and "b" would be the slope. Is it different in this equation for some reason?
The link to characteristic equation isn't making a lot of sense to me so far. That is an article about characteristics equations of matrices, whose roots are eignvalues. Is that what is intended here? It doesn't look like it. Michael Hardy ( talk) 22:13, 2 August 2008 (UTC)
Agree the links to characteristic equation don't make sense. In one place the link is to the charactaristic equation of a differential equation, and in another to charactaristic polynomial of a matrix. Can an autoregressive process be expressed as a differential equation with identical coefficients, or as a matrix with the same charactaristic polynomial? I think this needs to be clarified. (April 22 2016). — Preceding unsigned comment added by 205.254.147.8 ( talk) 16:49, 22 April 2016 (UTC)
I believe we should split this page into two. The section at the bottom about the Unit Root Hypothesis is well written, interesting, and important for/to economists. The Unit Root, however, is a more general topic that applies to all time-series analysis in all fields. Therefore, I think the Unit Root Hypothesis should be only mentioned as an example with the bulk of its content on a separate page.
This is a big enough change that I am reluctant to do this unless there is evidence of a consensus - and more importantly, since the information is useful for econ people (like me), I would hate to make the change in such a way that it is unavailable while the new page is waiting on approval. — Preceding unsigned comment added by Balaamsgrayass ( talk • contribs) 23:40, 3 December 2017 (UTC)
The audience for this article is severely limited. I suggest an introduction that targets a broader audience with a more limited understanding of statistics. The article is heavy on statistical jargon and does not make the subject more accessible. I would be interested in others thoughts on this. Perhaps accessibility is not a concern. 206.193.225.70 ( talk) 19:01, 26 September 2008 (UTC)
Like the above commentors, I have a background in maths and statistics, but I am having enough trouble with this article that I'm not sure if I've found an error, or simply misunderstood it.
Consider the example, concerning:
The example goes on to show that is a function of t if the characteristic equation has a unit root. However, it is also a function of t for non-unit roots! Proceding just as in the example, but not restricting outselves to m = 1:
Then the variance of is given by:
The first term is zero, since the are not random variates and so have variance 0. The second term expands to:
Which then (generally) simplifies to:
which is clearly just as non-stationary as , if not more so!! - 202.63.39.58 ( talk) 20:45, 25 March 2013 (UTC)
In the Definition section, it almost seems as if the exponents in the polynomial in m are in reverse order. Most of what I could find online deals with AR(1), but in what little I can find for unit roots of AR(p), the characteristic polynomial has the *lowest* power in lag operator (presumably m in this case) bound to the constant coefficient associated with the least lag (a_1 in this case). See, for example, http://www.bauer.uh.edu/rsusmel/phd/ec2-5.pdf. This is, of course, assuming that the operator m is a stand-in for a lag operation. Nowhere is this stated, but if it isn't the case, it sure would be unorthodox and deserving of an explanation. — Preceding unsigned comment added by 131.136.242.1 ( talk) 23:28, 21 April 2015 (UTC)
It seems to be pretty fundamental to time series. I don't know how to bump up the importance.
Dr. Dogru has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:
1. Unit root hypothesis should be taken into account with and withoud draft. Besides that it is okay.
2. You could add this reference to the further readings:
Dogru, B. (2014). Analysis of Long-and Short-run Balance of Money Demand In Turkey Using ARDL and VEC Approaches” The International Journal of Economic and Social Research, Vol. 10, No. 2, 19-32,
We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.
Dr. Dogru has published scholarly research which seems to be relevant to this Wikipedia article:
ExpertIdeas ( talk) 23:46, 23 August 2015 (UTC)
Dr. Platen has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:
The page is well written and allows the reader to get a reasonable overview about the question raised.
We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.
Dr. Platen has published scholarly research which seems to be relevant to this Wikipedia article:
ExpertIdeasBot ( talk) 14:58, 24 June 2016 (UTC)
Dr. Reed has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:
"time serie" should be "time series"
"transitory, the time serie will converge" could be better stated as "over time, the time series will converge"
"while unit-root processes" could be better stated as "while shocks to unit-root processes"
We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.
We believe Dr. Reed has expertise on the topic of this article, since he has published relevant scholarly research:
ExpertIdeasBot ( talk) 20:40, 1 July 2016 (UTC)
Dr. Shi has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:
1. "that can cause problems in statistical inference involving time series models. "
Not if one uses correct model for estimation.
2. "If the other roots of the characteristic equation lie inside the unit circle" The unit root process may have more than two roots. The introduction, in general, is not accurate.
3. "Granger and Newbold called such estimates 'spurious regression' results:" Spurious regression refers to the regression of one I(1) variable on the other I(1) variable when they are not cointegrated. Not the case of regressing y_{t} on y_{t-1} -- the slope of the autoregressive model. The statement is wrong.
4. Estimation Section: when two variables are I(1) and cointegrated, the estimated coefficient is super-consistent. Information along this line is not mentioned.
We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.
We believe Dr. Shi has expertise on the topic of this article, since he has published relevant scholarly research: