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Cointegration
Cointegration is a statistical property of a collection of time series variables. First, all of the series must be integrated of order ''d'' (see Order of integration). Next, if a linear combination of this collection is integrated of order less than d, then the collection is said to be co-integrated. Formally, if (''X'',''Y'',''Z'') are each integrated of order ''d'', and there exist coefficients ''a'',''b'',''c'' such that is integrated of order less than d, then ''X'', ''Y'', and ''Z'' are cointegrated. Cointegration has become an important property in contemporary time series analysis. Time series often have trends—either deterministic or stochastic. In an influential paper, Charles Nelson and Charles Plosser (1982) provided statistical evidence that many US macroeconomic time series (like GNP, wages, employment, etc.) have stochastic trends. Introduction If two or more series are individually integrated (in the time series sense) but some linear combination of them ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Johansen Test
In statistics, the Johansen test, named after Søren Johansen, is a procedure for testing cointegration of several, say ''k'', I(1) time series. This test permits more than one cointegrating relationship so is more generally applicable than the Engle–Granger test which is based on the Dickey–Fuller (or the augmented) test for unit roots in the residuals from a single (estimated) cointegrating relationship. There are two types of Johansen test, either with trace or with eigenvalue, and the inferences might be a little bit different. The null hypothesis for the trace test is that the number of cointegration vectors is ''r'' = ''r''* < ''k'', vs. the alternative that ''r'' = ''k''. Testing proceeds sequentially for ''r''* = 1,2, etc. and the first non-rejection of the null is taken as an estimate of ''r''. The null hypothesis for the "maximum eigenvalue" test is as for the trace test but the alternative is ''r'' = ''r' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structural Break
In econometrics and statistics, a structural break is an unexpected change over time in the parameters of regression models, which can lead to huge forecasting errors and unreliability of the model in general. This issue was popularised by David Hendry, who argued that lack of stability of coefficients frequently caused forecast failure, and therefore we must routinely test for structural stability. Structural stability − i.e., the time-invariance of regression coefficients − is a central issue in all applications of linear regression models. Structural break tests A single break in mean with a known breakpoint For linear regression models, the Chow test is often used to test for a single break in mean at a known time period for . This test assesses whether the coefficients in a regression model are the same for periods and . Other forms of structural breaks Other challenges occur where there are: :Case 1: a known number of breaks in mean with unknown br ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clive Granger
Sir Clive William John Granger (; 4 September 1934 – 27 May 2009) was a British econometrician known for his contributions to nonlinear time series analysis. He taught in Britain, at the University of Nottingham and in the United States, at the University of California, San Diego. Granger was awarded the Nobel Memorial Prize in Economic Sciences in 2003 in recognition of the contributions that he and his co-winner, Robert F. Engle, had made to the analysis of time series data. This work fundamentally changed the way in which economists analyse financial and macroeconomic data. Biography Early life Clive Granger was born in 1934 in Swansea, south Wales, United Kingdom, to Edward John Granger and Evelyn Granger. The next year his parents moved to Lincoln. During World War II Granger and his mother moved to Cambridge because Edward joined the Royal Air Force and deployed to North Africa. Here they stayed first with Evelyn's mother, then later Edward's parents, while Clive b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spurious Correlation
In statistics, a spurious relationship or spurious correlation is a mathematical relationship in which two or more events or variables are associated but '' not'' causally related, due to either coincidence or the presence of a certain third, unseen factor (referred to as a "common response variable", "confounding factor", or " lurking variable"). Examples An example of a spurious relationship can be found in the time-series literature, where a spurious regression is a regression that provides misleading statistical evidence of a linear relationship between independent non-stationary variables. In fact, the non-stationarity may be due to the presence of a unit root in both variables. In particular, any two nominal economic variables are likely to be correlated with each other, even when neither has a causal effect on the other, because each equals a real variable times the price level, and the common presence of the price level in the two data series imparts correlation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sam Ouliaris
Sam, SAM or variants may refer to: Places * Sam, Benin * Sam, Boulkiemdé, Burkina Faso * Sam, Bourzanga, Burkina Faso * Sam, Kongoussi, Burkina Faso * Sam, Iran * Sam, Teton County, Idaho, United States, a populated place People and fictional characters * Sam (given name), a list of people and fictional characters with the given name or nickname * Sam (surname), a list of people with the surname ** Cen (surname) (岑), romanized "Sam" in Cantonese ** Shen (surname) (沈), often romanized "Sam" in Cantonese and other languages Religious or legendary figures * Sam (Book of Mormon), elder brother of Nephi * Sām, a Persian mythical folk hero * Sam Ziwa, an uthra (angel or celestial being) in Mandaeism Animals * Sam (army dog) (died 2000) * Sam (horse) (b 1815), British Thoroughbred * Sam (koala) (died 2009), rescued after 2009 bush fires in Victoria, Australia * Sam (orangutan), in the movie ''Dunston Checks In'' * Sam (ugly dog) (1990–2005), voted the world's ugliest dog in 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter C
Peter may refer to: People * List of people named Peter, a list of people and fictional characters with the given name * Peter (given name) ** Saint Peter (died 60s), apostle of Jesus, leader of the early Christian Church * Peter (surname), a surname (including a list of people with the name) Culture * Peter (actor) (born 1952), stage name Shinnosuke Ikehata, Japanese dancer and actor * ''Peter'' (album), a 1993 EP by Canadian band Eric's Trip * ''Peter'' (1934 film), a 1934 film directed by Henry Koster * ''Peter'' (2021 film), Marathi language film * "Peter" (''Fringe'' episode), an episode of the television series ''Fringe'' * ''Peter'' (novel), a 1908 book by Francis Hopkinson Smith * "Peter" (short story), an 1892 short story by Willa Cather Animals * Peter, the Lord's cat, cat at Lord's Cricket Ground in London * Peter (chief mouser), Chief Mouser between 1929 and 1946 * Peter II (cat), Chief Mouser between 1946 and 1947 * Peter III (cat), Chief Mouser between ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phillips–Perron Test
In statistics, the Phillips–Perron test (named after Peter C. B. Phillips and Pierre Perron) is a unit root test. That is, it is used in time series analysis to test the null hypothesis that a time series is integrated of order 1. It builds on the Dickey–Fuller test of the null hypothesis \rho = 1 in \Delta y_= (\rho -1)y_+u_\,, where \Delta is the first difference operator. Like the augmented Dickey–Fuller test, the Phillips–Perron test addresses the issue that the process generating data for y_ might have a higher order of autocorrelation than is admitted in the test equation—making y_ endogenous and thus invalidating the Dickey–Fuller t-test. Whilst the augmented Dickey–Fuller test addresses this issue by introducing lags of \Delta y_ as regressors in the test equation, the Phillips–Perron test makes a non-parametric correction to the t-test statistic. The test is robust with respect to unspecified autocorrelation and heteroscedasticity In statistics, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dickey–Fuller Test
In statistics, the Dickey–Fuller test tests the null hypothesis that a unit root is present in an autoregressive time series model. The alternative hypothesis is different depending on which version of the test is used, but is usually stationarity or trend-stationarity. The test is named after the statisticians David Dickey and Wayne Fuller, who developed it in 1979. Explanation A simple AR(1) model is : y_=\rho y_+u_\, where y_ is the variable of interest, t is the time index, \rho is a coefficient, and u_ is the error term (assumed to be white noise). A unit root is present if \rho = 1. The model would be non-stationary in this case. The regression model can be written as : \Delta y_=(\rho-1)y_+u_=\delta y_+ u_\, where \Delta is the first difference operator and \delta \equiv \rho - 1. This model can be estimated and testing for a unit root is equivalent to testing \delta = 0. Since the test is done over the residual term rather than raw data, it is not possible t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spurious Correlation
In statistics, a spurious relationship or spurious correlation is a mathematical relationship in which two or more events or variables are associated but '' not'' causally related, due to either coincidence or the presence of a certain third, unseen factor (referred to as a "common response variable", "confounding factor", or " lurking variable"). Examples An example of a spurious relationship can be found in the time-series literature, where a spurious regression is a regression that provides misleading statistical evidence of a linear relationship between independent non-stationary variables. In fact, the non-stationarity may be due to the presence of a unit root in both variables. In particular, any two nominal economic variables are likely to be correlated with each other, even when neither has a causal effect on the other, because each equals a real variable times the price level, and the common presence of the price level in the two data series imparts correlation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
R-squared
In statistics, the coefficient of determination, denoted ''R''2 or ''r''2 and pronounced "R squared", is the proportion of the variation in the dependent variable that is predictable from the independent variable(s). It is a statistic used in the context of statistical models whose main purpose is either the prediction of future outcomes or the testing of hypotheses, on the basis of other related information. It provides a measure of how well observed outcomes are replicated by the model, based on the proportion of total variation of outcomes explained by the model. There are several definitions of ''R''2 that are only sometimes equivalent. One class of such cases includes that of simple linear regression where ''r''2 is used instead of ''R''2. When only an intercept is included, then ''r''2 is simply the square of the sample correlation coefficient (i.e., ''r'') between the observed outcomes and the observed predictor values. If additional regressors are included, ''R''2 i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ordinary Least Squares
In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values of the variable being observed) in the input dataset and the output of the (linear) function of the independent variable. Geometrically, this is seen as the sum of the squared distances, parallel to the axis of the dependent variable, between each data point in the set and the corresponding point on the regression surface—the smaller the differences, the better the model fits the data. The resulting estimator can be expressed by a simple formula, especially in the case of a simple linear regression, in which there is a single regressor on the right side of the regression equation. The OLS estimator is con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unit Root
In probability theory and statistics, a unit root is a feature of some stochastic processes (such as random walks) that can cause problems in statistical inference involving time series models. A linear stochastic process has a unit root if 1 is a root of the process's characteristic equation. Such a process is non-stationary but does not always have a trend. If the other roots of the characteristic equation lie inside the unit circle—that is, have a modulus ( absolute value) less than one—then the first difference of the process will be stationary; otherwise, the process will need to be differenced multiple times to become stationary. If there are ''d'' unit roots, the process will have to be differenced ''d'' times in order to make it stationary. Due to this characteristic, unit root processes are also called difference stationary. Unit root processes may sometimes be confused with trend-stationary processes; while they share many properties, they are different in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
