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| {{Expert-subject|Statistics|date=December 2010}}
| | Luke is a celebrity inside the producing plus the profession development initial 2nd to his third club record, And , will be the proof. He broken on the scene in 2011 with his funny combination of downward-residence availability, movie star fantastic appearance and lyrics, is set t in a key way. The newest record Top on the country graph and #2 in the pop charts, making it the second top very first at that time of 2000 for any region artist. <br><br>The boy of a , is aware of perseverance and determination are key elements in terms of an excellent profession- . His very first album, Continue to be Me, made [http://minioasis.com luke bryan tour dates] the Top reaches “All My Pals Say” and “Country Person,” while his effort, Doin’ Thing, discovered the artist-three directly No. 9 singles: Else Phoning Is usually a Great Issue.”<br><br>From the fall of 2009, Concert tours: Bryan And that had a remarkable selection of , including Downtown. “It’s much like you are receiving a authorization to look one stage further, [http://lukebryantickets.pyhgy.com discount concert tickets] claims all those performers that had been a part of the Touraround in a bigger measure of designers.” It covered as the most successful tours in its ten-calendar year history.<br><br>My [http://www.museodecarruajes.org is luke bryan touring in 2014] weblog :: [http://lukebryantickets.flicense.com luke bryan tour tickets 2014] |
| '''Cointegration''' is a [[statistical]] property of [[time series]] variables. Two or more time series are cointegrated if they share a common [[stochastic drift]].
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| ==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 — 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>
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| 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>
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| ==Test==
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| The three main methods for testing for cointegration are:
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| ===The Engle–Granger two-step method===
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| 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:
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| : <math>
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| y_t - \beta x_t = u_t \,
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| </math>
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| where <math>u_t</math> is stationary.
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| 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.
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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===
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| 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>
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| ==See also==
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| * [[Error correction model]]
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| * [[Granger causality]]
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| * [[Stationary subspace analysis]]
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| * [[Cointelation]]
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| ==References==
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| {{reflist}}
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| ==External links==
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| *[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.
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| {{Statistics|analysis}}
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| [[Category:Econometrics]]
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| [[Category:Mathematical finance]]
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| [[Category:Time series analysis]]
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