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{{Expert-subject|Statistics|date=December 2010}}
== here's sight is very open ==
'''Cointegration''' is a [[statistical]] property of [[time series]] variables. Two or more time series are cointegrated if they share a common [[stochastic drift]].


==Introduction==
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If two or more series are individually [[Order of integration|integrated]] (in the time series sense) but some [[linear combination]] of them has a lower [[order of integration]], then the series are said to be cointegrated. A common example is where the individual series are first-order integrated ('''I(1)''') but some ('''cointegrating''') vector of coefficients exists to form a [[Stationary process|stationary]] linear combination of them. For instance, a [[stock market index]] and the price of its associated [[futures contract]] move through time, each roughly following a [[random walk]]. Testing the hypothesis that there is a [[statistically significant]] connection between the futures price and the spot price could now be done by testing for the existence of a cointegrated combination of the two series. (If such a combination has a low order of integration&nbsp;— in particular if it is '''I(0)''', this can signify an equilibrium relationship between the original series, which are said to be '''cointegrated'''.)
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Before the 1980s many economists used [[linear regression]]s on ([[trend estimation|de-trended]]{{Citation needed|date=June 2011}}) non-stationary time series data, which Nobel laureate [[Clive Granger]] and others showed to be a dangerous approach that could produce [[spurious correlation]]<ref>Granger, C. W. J. and Newbold, P. (1974). "Spurious regressions in econometrics". Journal of Econometrics 2 (2): 111–120. doi:10.1016/0304-4076(74)90034-7</ref>, since standard detrending techniques can result in data that are still non-stationary.<ref>{{cite journal |first=Clive |last=Granger |year=1981 |title=Some Properties of Time Series Data and Their Use in Econometric Model Specification |journal=[[Journal of Econometrics]] |volume=16 |issue=1 |pages=121–130 |doi=10.1016/0304-4076(81)90079-8 }}</ref> His 1987 paper with Nobel laureate [[Robert Engle]] formalized the cointegrating vector approach, and coined the term.<ref>{{cite journal |last=Engle |first=Robert F. |last2=Granger |first2=Clive W. J. |year=1987 |title=Co-integration and error correction: Representation, estimation and testing |journal=[[Econometrica]] |volume=55 |issue=2 |pages=251–276 |jstor=1913236 }}</ref>
== Wang Shen repair gently down the portable items ==


The possible presence of cointegration must be taken into account when choosing a technique to test hypotheses concerning the relationship between two variables having [[unit root]]s (i.e. integrated of at least order one).<ref>{{cite journal |last=Granger |first=C. |last2=Newbold |first2=P. |year=1974 |title=Spurious Regressions in Econometrics |journal=[[Journal of Econometrics]] |volume=2 |issue=2 |pages=111–120 |doi=10.1016/0304-4076(74)90034-7 }}</ref>
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The usual procedure for testing hypotheses concerning the relationship between non-stationary variables was to run [[ordinary least squares]] (OLS) regressions on data which had initially been differenced. This method is incorrect if the non-stationary variables are cointegrated.  Cointegration measures may be calculated over sets of time series using fast routines.<ref>{{cite web |url= http://thisisgooglenow.blogspot.com/2013/08/heres-patch-for-scipyspatialdistance.html|title=A Patch for scipy.spatial.distance for cointegration |last1=Yang|first1=Michael|date= August 29, 2013|accessdate=29 August 2013}}</ref>
== are you trying to intimidate me ==


==Test==
Team.<br><br>not only the [http://www.dmwai.com/webalizer/kate-spade-5.html ケイトスペード バッグ 激安] three teams, the team in serious cases, inspectors review the Sun Yi, Wu Guangyu, Xiong Jianfei more than two hours, even with a fool fraud, discharged a lot of evidence that they are students and I sin, to prove that they used to be colleagues, whereby prove something this afternoon, was premeditated once thwarted intimidation.<br><br>'I'm not intimidated, [http://www.dmwai.com/webalizer/kate-spade-13.html kate spade ハンドバッグ] are you trying to intimidate me,' Wu Guangyu question came from the inspectors.<br><br>'thwarted? I did not see ah, drove by.' Sun Yi Shuaqi rogue came.<br><br>'Do not wear lip service, there is evidence that you catch me, no evidence [http://www.dmwai.com/webalizer/kate-spade-10.html バッグ kate spade] I want to sleep.' Xiong Jianfei mouth more firmly, the words are too lazy to say.<br><br>two hours after the fire began inspectors worn heart, police deal with these every day and vicious crime, and temperament also Zhanre the point [http://www.dmwai.com/webalizer/kate-spade-11.html ケイトスペード 財布 通販] where, let them speak, not so easy to estimate, three teams news of the accident, they Okavango just [http://www.dmwai.com/webalizer/kate-spade-7.html ケイトスペード かごバッグ] going to negotiate away Shao people, but unexpectedly Okavango Shao has been with the team of Interpol surrounded the interrogation room, the door, apart from anything else:. 'solitary confinement, write checks, confessed clear, careful I smoke you die.'
The three main methods for testing for cointegration are:
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===The Engle–Granger two-step method===
== for I sin resentment rather heavy ==
If two time series <math>x_t</math> and <math>y_t</math> are cointegrated, a linear combination of them must be stationary.  In other words:


: <math>
Former chief of a small little place, ah, she was a small channel with: 'Lanjie, it is worth it to see a man [http://www.dmwai.com/webalizer/kate-spade-3.html ケイトスペード 財布 新作] I Tuba Lu, of no value?.'<br><br>'hey are right, the whole on a peel.' Xue Fei Tao, for I sin resentment rather heavy, blue in the Beijing dialect, on the [http://www.dmwai.com/webalizer/kate-spade-2.html ケイトスペード 財布 店舗] 'riffraff' means.<br><br>'Oh, sisters ah ...... you get [http://www.dmwai.com/webalizer/kate-spade-6.html kate spade マザーズバッグ] your money line myself, as he was worth it, I do not know, but it should be about it, Need to this extent, do [http://www.dmwai.com/webalizer/kate-spade-15.html ケイトスペード マザーズバッグ] not you ever seen?' Yaoman Lan smile .<br><br>two girl Dole, and also really have not seen, each holding Lanjie, sat waiting for customers at the hotel's lobby, waiting to Lanjie luxury ordered.<br><br>Yingyingyanyan, laughing operculum flower, which had introduced Review endless, I saw beauty jade, beautiful woman who knows what expectations?<br><br>uh ...... I spit.<br><br>uh ...... I continue to spit.<br><br>sewer spit on the street for a long time, I sin long [http://www.dmwai.com/webalizer/kate-spade-0.html ケイトスペード中古バッグ] breath, with great difficulty Huanguo Lai, usually filling neck down, down into the crotch of
y_t - \beta x_t = u_t \,
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</math>
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where <math>u_t</math> is stationary.
== because the dock City Road pocketing team thing ==


If we knew <math>u_t</math>, we could just test it for stationarity with something like a [[Dickey–Fuller test]], [[Phillips-Perron test]] and be done. But because we don't know <math>\beta</math>, we must estimate this first, generally by using [[ordinary least squares]], and then run our stationarity test on the estimated <math>u_t</math> series, often denoted <math>\hat{u}_t</math>. This is the Engle–Granger two-step method.
How is it? 'Xu [http://www.dmwai.com/webalizer/kate-spade-9.html ケイトスペードバッグセール] Pingqiu shook his head, accused of this section, try to fade.<br><br>'That ...... pavement street crime last year, this one is also a bright spot, the provincial capital of more than a dozen [http://www.dmwai.com/webalizer/kate-spade-4.html ケイトスペード ショルダーバッグ] newspapers have reported that hunting chops, good social repercussions. province sets legal channels being interviewed produce feature films.' secretary also reminded of. Shook his head, Xu Pingqiu eyes passing touch of [http://www.dmwai.com/webalizer/kate-spade-3.html ケイトスペード リボン バッグ] dark color, slowly authentic with: 'Crime is still on the main street road policing, is inappropriate, because the dock City Road pocketing team thing, the Captains have changed on the criminal investigation I may be embarrassed to mention. 'it is not, at least in the secretary [http://www.dmwai.com/webalizer/kate-spade-2.html ケイトスペード 財布 新作] does not seem, large and small criminal cases detected [http://www.dmwai.com/webalizer/kate-spade-13.html ケイトスペード 人気バッグ] every year thousands of cases, but far behind the crime rate, which will become a large part of the outstanding issues, fans case was shelved in what police files, even as law enforcement police, can only choose great harm to society, intuitive forms of crime cases to prevent the rejection.<br><br>'I think again ......' Xu Pingqiu uncertain to think, inadvertently picked up the phone, he was thinking just appointed a new commander, sure to burn a few fire, maybe there will be
 
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===The Johansen test===
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The [[Johansen test]] is a test for cointegration that allows for more than one cointegrating relationship, unlike the Engle–Granger method.
 
 
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===Phillips–Ouliaris cointegration test===
 
 
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===Notes===
 
In practice, cointegration is often used for two I(1) series, but it is more generally applicable and can be used for variables integrated of higher order (to detect correlated accelerations or other second-difference effects). '''Multicointegration''' extends the cointegration technique beyond two variables, and occasionally to variables integrated at different orders.
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However, these tests for cointegration assume that the cointegrating vector is constant during the period of study. In reality, it is possible that the long-run relationship between the underlying variables change (shifts in the cointegrating vector can occur). The reason for this might be technological progress, economic crises, changes in the people’s preferences and behaviour accordingly, policy or regime alteration, and organizational or institutional developments. This is especially likely to be the case if the sample period is long. To take this issue into account, tests have been introduced for cointegration with one unknown [[structural break]],<ref>{{cite journal |last=Gregory |first=Allan W. |last2=Hansen |first2=Bruce E. |year=1996 |title=Residual-based tests for cointegration in models with regime shifts |journal=Journal of Econometrics |volume=70 |issue=1 |pages=99–126 |doi=10.1016/0304-4076(69)41685-7 }}</ref> and tests for cointegration with two unknown breaks are also available.<ref>{{cite journal |last=Hatemi-J |first=A. |year=2008 |title=Tests for cointegration with two unknown regime shifts with an application to financial market integration |journal=[[Empirical Economics]] |volume=35 |issue=3 |pages=497–505 |url=http://ideas.repec.org/a/spr/empeco/v35y2008i3p497-505.html }}</ref>
</ul>
 
==See also==
* [[Error correction model]]
* [[Granger causality]]
* [[Stationary subspace analysis]]
* [[Cointelation]]
 
==References==
{{reflist}}
 
==External links==
*[http://www-stat.wharton.upenn.edu/~steele/Courses/434/434Context/Co-integration/Murray93DrunkAndDog.pdf A drunk and her dog: An illustration of cointegration and error correction] by Michael P. Murray, 1994. An intuitive introduction to cointegration.
 
{{Statistics|analysis}}
 
[[Category:Econometrics]]
[[Category:Mathematical finance]]
[[Category:Time series analysis]]

Latest revision as of 23:59, 27 October 2014

here's sight is very open

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'does ケイトスペード 財布 店舗 not, here's sight is very open, unless the owner demands, otherwise they would not clean the engine lid, the general store in which to live are, the owners do not necessarily believe in the mentality of people outside ...... especially the luxury car.' Mouse Road.

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'No, there is a suspicious greatest place.' I sin road.

'Where?' Xiaomeng Qi asked.

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No matter what
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dialect grievances Lengqiao chasing a son, Wang Shen repair gently down the portable items, including earning a lot of money in a nightclub tip, perhaps it is only a ケイトスペード バッグ 通販 marginal decrease in the heart Kuiyi, he knew, pretty sister in sever his last read to, preferring a night as this transaction.

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are you trying to intimidate me

Team.

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for I sin resentment rather heavy

Former chief of a small little place, ah, she was a small channel with: 'Lanjie, it is worth it to see a man ケイトスペード 財布 新作 I Tuba Lu, of no value?.'

'hey are right, the whole on a peel.' Xue Fei Tao, for I sin resentment rather heavy, blue in the Beijing dialect, on the ケイトスペード 財布 店舗 'riffraff' means.

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two girl Dole, and also really have not seen, each holding Lanjie, sat waiting for customers at the hotel's lobby, waiting to Lanjie luxury ordered.

Yingyingyanyan, laughing operculum flower, which had introduced Review endless, I saw beauty jade, beautiful woman who knows what expectations?

uh ...... I spit.

uh ...... I continue to spit.

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because the dock City Road pocketing team thing

How is it? 'Xu ケイトスペードバッグセール Pingqiu shook his head, accused of this section, try to fade.

'That ...... pavement street crime last year, this one is also a bright spot, the provincial capital of more than a dozen ケイトスペード ショルダーバッグ newspapers have reported that hunting chops, good social repercussions. province sets legal channels being interviewed produce feature films.' secretary also reminded of. Shook his head, Xu Pingqiu eyes passing touch of ケイトスペード リボン バッグ dark color, slowly authentic with: 'Crime is still on the main street road policing, is inappropriate, because the dock City Road pocketing team thing, the Captains have changed on the criminal investigation I may be embarrassed to mention. 'it is not, at least in the secretary ケイトスペード 財布 新作 does not seem, large and small criminal cases detected ケイトスペード 人気バッグ every year thousands of cases, but far behind the crime rate, which will become a large part of the outstanding issues, fans case was shelved in what police files, even as law enforcement police, can only choose great harm to society, intuitive forms of crime cases to prevent the rejection.

'I think again ......' Xu Pingqiu uncertain to think, inadvertently picked up the phone, he was thinking just appointed a new commander, sure to burn a few fire, maybe there will be 相关的主题文章：

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