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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 Nonparametric statistics is the branch of statistics that is not based solely on parametrized families of probability distributions (commo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling as ... [...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 1947 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre Perron
Pierre Perron (born March 14, 1959) is a Canadian econometrician at Boston University. Perron is known for the Phillips–Perron test of a 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 ... in time series regression, which was the result of his Ph.D. studies under Peter C. B. Phillips. References External links * Website at Boston University {{DEFAULTSORT:Perron, Pierre 1959 births Living people Canadian statisticians Yale University alumni Boston University faculty Fellows of the Econometric Society ... [...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 many asp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biometrika
''Biometrika'' is a peer-reviewed scientific journal published by Oxford University Press for thBiometrika Trust The editor-in-chief is Paul Fearnhead (Lancaster University). The principal focus of this journal is theoretical statistics. It was established in 1901 and originally appeared quarterly. It changed to three issues per year in 1977 but returned to quarterly publication in 1992. History ''Biometrika'' was established in 1901 by Francis Galton, Karl Pearson, and Raphael Weldon to promote the study of biometrics. The history of ''Biometrika'' is covered by Cox (2001). The name of the journal was chosen by Pearson, but Francis Edgeworth insisted that it be spelt with a "k" and not a "c". Since the 1930s, it has been a journal for statistical theory and methodology. Galton's role in the journal was essentially that of a patron and the journal was run by Pearson and Weldon and after Weldon's death in 1906 by Pearson alone until he died in 1936. In the early days, the American ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Series
In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average. A time series is very frequently plotted via a run chart (which is a temporal line chart). Time series are used in statistics, signal processing, pattern recognition, econometrics, mathematical finance, weather forecasting, earthquake prediction, electroencephalography, control engineering, astronomy, communications engineering, and largely in any domain of applied science and engineering which involves temporal measurements. Time series ''analysis'' comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data. Time series ''forecasting' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Null Hypothesis
In scientific research, the null hypothesis (often denoted ''H''0) is the claim that no difference or relationship exists between two sets of data or variables being analyzed. The null hypothesis is that any experimentally observed difference is due to chance alone, and an underlying causative relationship does not exist, hence the term "null". In addition to the null hypothesis, an alternative hypothesis is also developed, which claims that a relationship does exist between two variables. Basic definitions The ''null hypothesis'' and the ''alternative hypothesis'' are types of conjectures used in statistical tests, which are formal methods of reaching conclusions or making decisions on the basis of data. The hypotheses are conjectures about a statistical model of the population, which are based on a sample of the population. The tests are core elements of statistical inference, heavily used in the interpretation of scientific experimental data, to separate scientific claims fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Order Of Integration
In statistics, the order of integration, denoted ''I''(''d''), of a time series is a summary statistic, which reports the minimum number of differences required to obtain a covariance-stationary series. Integration of order ''d'' A time series is integrated of order ''d'' if :(1-L)^d X_t \ is a stationary process, where L is the lag operator and 1-L is the first difference, i.e. : (1-L) X_t = X_t - X_ = \Delta X. In other words, a process is integrated to order ''d'' if taking repeated differences ''d'' times yields a stationary process. In particular, if a series is integrated of order 0, then (1-L)^0 X_t = X_t is stationary. Constructing an integrated series An ''I''(''d'') process can be constructed by summing an ''I''(''d'' − 1) process: *Suppose X_t is ''I''(''d'' − 1) *Now construct a series Z_t = \sum_^t X_k *Show that ''Z'' is ''I''(''d'') by observing its first-differences are ''I''(''d'' − 1): :: \Delta ... [...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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First Difference
In mathematics, a recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms. Often, only k previous terms of the sequence appear in the equation, for a parameter k that is independent of n; this number k is called the ''order'' of the relation. If the values of the first k numbers in the sequence have been given, the rest of the sequence can be calculated by repeatedly applying the equation. In ''linear recurrences'', the th term is equated to a linear function of the k previous terms. A famous example is the recurrence for the Fibonacci numbers, F_n=F_+F_ where the order k is two and the linear function merely adds the two previous terms. This example is a linear recurrence with constant coefficients, because the coefficients of the linear function (1 and 1) are constants that do not depend on n. For these recurrences, one can express the general term of the sequence as a closed-form expression ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operator (mathematics)
In mathematics, an operator is generally a mapping or function that acts on elements of a space to produce elements of another space (possibly and sometimes required to be the same space). There is no general definition of an ''operator'', but the term is often used in place of ''function'' when the domain is a set of functions or other structured objects. Also, the domain of an operator is often difficult to be explicitly characterized (for example in the case of an integral operator), and may be extended to related objects (an operator that acts on functions may act also on differential equations whose solutions are functions that satisfy the equation). See Operator (physics) for other examples. The most basic operators are linear maps, which act on vector spaces. Linear operators refer to linear maps whose domain and range are the same space, for example \R^n to \R^n. Such operators often preserve properties, such as continuity. For example, differentiation and indef ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Augmented Dickey–Fuller Test
In statistics, an augmented Dickey–Fuller test (ADF) tests the null hypothesis that a unit root is present in a time series sample. The alternative hypothesis is different depending on which version of the test is used, but is usually stationarity or trend-stationarity. It is an augmented version of the Dickey–Fuller test for a larger and more complicated set of time series models. The augmented Dickey–Fuller (ADF) statistic, used in the test, is a negative number. The more negative it is, the stronger the rejection of the hypothesis that there is a unit root at some level of confidence. Testing procedure The testing procedure for the ADF test is the same as for the Dickey–Fuller test but it is applied to the model :\Delta y_t = \alpha + \beta t + \gamma y_ + \delta_1 \Delta y_ + \cdots + \delta_ \Delta y_ + \varepsilon_t, where \alpha is a constant, \beta the coefficient on a time trend and p the lag order of the autoregressive process. Imposing the constraints \alp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
