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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] |
Probability Theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion). Although it is not possible to perfectly predict random events, much can be said about their behavior. Two major results in probability ... [...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] |
Journal Of Econometrics
The ''Journal of Econometrics'' is a scholarly journal in econometrics. It was first published in 1973. Its current managing editors are Serena Ng and Elie Tamer, Torben Andersen and Xiaohong Chen serve as editors. The journal publishes work dealing with estimation and other methodological aspects of the application of statistical inference to economic data, as well as papers dealing with the application of econometric techniques to economics. The journal also publishes a supplement to the Journal of Econometrics which is called "Annals of Econometrics". Each issue of the Annals includes a collection of papers on a single topic selected by the editor of the issue. See also * ''Econometrics Journal'' References External links Homepage Econometrics, Journal of Econometrics journals Econometrics Econometrics is the application of Statistics, statistical methods to economic data in order to give Empirical evidence, empirical content to economic relationships.M. Hashem P ... [...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 began ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Autoregressive Model
In statistics, econometrics and signal processing, an autoregressive (AR) model is a representation of a type of random process; as such, it is used to describe certain time-varying processes in nature, economics, etc. The autoregressive model specifies that the output variable depends linearly on its own previous values and on a stochastic term (an imperfectly predictable term); thus the model is in the form of a stochastic difference equation (or recurrence relation which should not be confused with differential equation). Together with the moving-average (MA) model, it is a special case and key component of the more general autoregressive–moving-average (ARMA) and autoregressive integrated moving average (ARIMA) models of time series, which have a more complicated stochastic structure; it is also a special case of the vector autoregressive model (VAR), which consists of a system of more than one interlocking stochastic difference equation in more than one evolving random vari ... [...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 consiste ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Econometrica
''Econometrica'' is a peer-reviewed academic journal of economics, publishing articles in many areas of economics, especially econometrics. It is published by Wiley-Blackwell on behalf of the Econometric Society. The current editor-in-chief is Guido Imbens. History ''Econometrica'' was established in 1933. Its first editor was Ragnar Frisch, recipient of the first Nobel Memorial Prize in Economic Sciences in 1969, who served as an editor from 1933 to 1954. Although ''Econometrica'' is currently published entirely in English, the first few issues also contained scientific articles written in French. Indexing and abstracting ''Econometrica'' is abstracted and indexed in: * Scopus * EconLit * Social Science Citation Index According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 5.844, ranking it 22/557 in the category "Economics". Awards issued The Econometric Society aims to attract high-quality applied work in economics for publication in ''Eco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sample Size
Sample size determination is the act of choosing the number of observations or Replication (statistics), replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make statistical inference, inferences about a statistical population, population from a sample. In practice, the sample size used in a study is usually determined based on the cost, time, or convenience of collecting the data, and the need for it to offer sufficient statistical power. In complicated studies there may be several different sample sizes: for example, in a stratified sampling, stratified survey sampling, survey there would be different sizes for each stratum. In a census, data is sought for an entire population, hence the intended sample size is equal to the population. In experimental design, where a study may be divided into different treatment groups, there may be different sample sizes for each group. Sample sizes may be chosen in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Errors And Residuals In Statistics
In statistics and optimization, errors and residuals are two closely related and easily confused measures of the deviation of an observed value of an element of a statistical sample from its "true value" (not necessarily observable). The error of an observation is the deviation of the observed value from the true value of a quantity of interest (for example, a population mean). The residual is the difference between the observed value and the ''estimated'' value of the quantity of interest (for example, a sample mean). The distinction is most important in regression analysis, where the concepts are sometimes called the regression errors and regression residuals and where they lead to the concept of studentized residuals. In econometrics, "errors" are also called disturbances. Introduction Suppose there is a series of observations from a univariate distribution and we want to estimate the mean of that distribution (the so-called location model). In this case, the errors are th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regression Analysis
In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'label' in machine learning parlance) and one or more independent variables (often called 'predictors', 'covariates', 'explanatory variables' or 'features'). The most common form of regression analysis is linear regression, in which one finds the line (or a more complex linear combination) that most closely fits the data according to a specific mathematical criterion. For example, the method of ordinary least squares computes the unique line (or hyperplane) that minimizes the sum of squared differences between the true data and that line (or hyperplane). For specific mathematical reasons (see linear regression), this allows the researcher to estimate the conditional expectation (or population average value) of the dependent variable when the independent variables take on a given ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Autoregressive–moving-average Model
In the statistical analysis of time series, autoregressive–moving-average (ARMA) models provide a parsimonious description of a (weakly) stationary stochastic process in terms of two polynomials, one for the autoregression (AR) and the second for the moving average (MA). The general ARMA model was described in the 1951 thesis of Peter Whittle, ''Hypothesis testing in time series analysis'', and it was popularized in the 1970 book by George E. P. Box and Gwilym Jenkins. Given a time series of data X_t, the ARMA model is a tool for understanding and, perhaps, predicting future values in this series. The AR part involves regressing the variable on its own lagged (i.e., past) values. The MA part involves modeling the error term as a linear combination of error terms occurring contemporaneously and at various times in the past. The model is usually referred to as the ARMA(''p'',''q'') model where ''p'' is the order of the AR part and ''q'' is the order of the MA part (as defined b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Autoregressive Model
In statistics, econometrics and signal processing, an autoregressive (AR) model is a representation of a type of random process; as such, it is used to describe certain time-varying processes in nature, economics, etc. The autoregressive model specifies that the output variable depends linearly on its own previous values and on a stochastic term (an imperfectly predictable term); thus the model is in the form of a stochastic difference equation (or recurrence relation which should not be confused with differential equation). Together with the moving-average (MA) model, it is a special case and key component of the more general autoregressive–moving-average (ARMA) and autoregressive integrated moving average (ARIMA) models of time series, which have a more complicated stochastic structure; it is also a special case of the vector autoregressive model (VAR), which consists of a system of more than one interlocking stochastic difference equation in more than one evolving random vari ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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