|
Unit Root Test
In statistics, a unit root test tests whether a time series variable is non-stationary and possesses a unit root. The null hypothesis is generally defined as the presence of a unit root and the alternative hypothesis is either Stationary process, stationarity, Trend-stationary process, trend stationarity or explosive root depending on the test used. General approach In general, the approach to unit root testing implicitly assumes that the time series to be tested [y_t]_^T can be written as, :y_t = D_t + z_t + \varepsilon_t where, * D_t is the deterministic component (trend, seasonal component, etc.) * z_t is the stochastic component. * \varepsilon_t is the stationary error process. The task of the test is to determine whether the stochastic component contains a unit root or is stationary. Main tests Other popular tests include: * augmented Dickey–Fuller test *: this is valid in large samples. * Phillips–Perron test * KPSS test *: here the null hypothesis is ... [...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] |
KPSS Test
In econometrics, Kwiatkowski–Phillips–Schmidt–Shin (KPSS) tests are used for testing a null hypothesis that an observable time series is stationary around a deterministic trend (i.e. trend-stationary) against the alternative of a unit root. Contrary to most unit root tests, the presence of a unit root is not the null hypothesis but the alternative. Additionally, in the KPSS test, the absence of a unit root is not a proof of stationarity but, by design, of trend-stationarity. This is an important distinction since it is possible for a time series to be non-stationary, have no unit root yet be trend-stationary. In both unit root and trend-stationary processes, the mean can be growing or decreasing over time; however, in the presence of a shock, trend-stationary processes are mean-reverting (i.e. transitory, the time series will converge again towards the growing mean, which was not affected by the shock) while unit-root processes have a permanent impact on the mean (i.e. no c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blackwell Publishers
Wiley-Blackwell is an international scientific, technical, medical, and scholarly publishing business of John Wiley & Sons. It was formed by the merger of John Wiley & Sons Global Scientific, Technical, and Medical business with Blackwell Publishing in 2007.About Wiley-Blackwell John Wiley & Sons, Inc. Wiley-Blackwell is now an imprint that publishes a diverse range of academic and professional fields, including , , , |
Durbin–Watson Statistic
In statistics, the Durbin–Watson statistic is a test statistic used to detect the presence of autocorrelation at lag 1 in the residuals (prediction errors) from a regression analysis. It is named after James Durbin and Geoffrey Watson. The small sample distribution of this ratio was derived by John von Neumann (von Neumann, 1941). Durbin and Watson (1950, 1951) applied this statistic to the residuals from least squares regressions, and developed bounds tests for the null hypothesis that the errors are serially uncorrelated against the alternative that they follow a first order autoregressive process. Note that the distribution of this test statistic does not depend on the estimated regression coefficients and the variance of the errors. A similar assessment can be also carried out with the Breusch–Godfrey test and the Ljung–Box test. Computing and interpreting the Durbin–Watson statistic If ''et'' is the residual given by e_t = \rho e_+ \nu_t , the Durbin-Watson test ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ljung–Box Test
The Ljung–Box test (named for Greta M. Ljung and George E. P. Box) is a type of statistical test of whether any of a group of autocorrelations of a time series are different from zero. Instead of testing randomness at each distinct lag, it tests the "overall" randomness based on a number of lags, and is therefore a portmanteau test. This test is sometimes known as the Ljung–Box Q test, and it is closely connected to the Box–Pierce test (which is named after George E. P. Box and David A. Pierce). In fact, the Ljung–Box test statistic was described explicitly in the paper that led to the use of the Box–Pierce statistic, and from which that statistic takes its name. The Box–Pierce test statistic is a simplified version of the Ljung–Box statistic for which subsequent simulation studies have shown poor performance. The Ljung–Box test is widely applied in econometrics and other applications of time series analysis. A similar assessment can be also carried out with the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Breusch–Godfrey Test
In statistics, the Breusch–Godfrey test is used to assess the validity of some of the modelling assumptions inherent in applying regression-like models to observed data series. In particular, it tests for the presence of serial correlation that has not been included in a proposed model structure and which, if present, would mean that incorrect conclusions would be drawn from other tests or that sub-optimal estimates of model parameters would be obtained. The regression models to which the test can be applied include cases where lagged values of the dependent variables are used as independent variables in the model's representation for later observations. This type of structure is common in econometric models. The test is named after Trevor S. Breusch and Leslie G. Godfrey. Background The Breusch–Godfrey test is a test for autocorrelation in the errors in a regression model. It makes use of the residuals from the model being considered in a regression analysis, and a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Autocorrelation
Autocorrelation, sometimes known as serial correlation in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations of a random variable as a function of the time lag between them. The analysis of autocorrelation is a mathematical tool for finding repeating patterns, such as the presence of a periodic signal obscured by noise, or identifying the missing fundamental frequency in a signal implied by its harmonic frequencies. It is often used in signal processing for analyzing functions or series of values, such as time domain signals. Different fields of study define autocorrelation differently, and not all of these definitions are equivalent. In some fields, the term is used interchangeably with autocovariance. Unit root processes, trend-stationary processes, autoregressive processes, and moving average processes are specific forms of processes with autocorrelation. A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ADF-GLS Test
In statistics and econometrics, the ADF-GLS test (or DF-GLS test) is a test for a unit root in an economic 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. Exa ... sample. It was developed by Elliott, Rothenberg and Stock (ERS) in 1992 as a modification of the augmented Dickey–Fuller test (ADF). A unit root test determines whether a time series variable is non-stationary using an autoregressive model. For series featuring deterministic components in the form of a constant or a linear trend then ERS developed an asymptotically point optimal test to detect a unit root. This testing procedure dominates other existing unit root tests in terms of power. It locally de-trends (de-means) data series to efficiently estimate the deterministic parameters of the series, and use the tran ... [...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 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] |
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] |
Journal Of The American Statistical Association
The ''Journal of the American Statistical Association (JASA)'' is the primary journal published by the American Statistical Association, the main professional body for statisticians in the United States. It is published four times a year in March, June, September and December by Taylor & Francis, Ltd on behalf of the American Statistical Association. As a statistics journal it publishes articles primarily focused on the application of statistics, statistical theory and methods in economic, social, physical, engineering, and health sciences. The journal also includes reviews of academic books which are important to the advancement of the field. It had an impact factor of 2.063 in 2010, tenth highest in the "Statistics and Probability" category of ''Journal Citation Reports''. In a 2003 survey of statisticians, the ''Journal of the American Statistical Association'' was ranked first, among all journals, for "Applications of Statistics" and second (after ''Annals of Statistics'') f ... [...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] |
