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Vector Autoregression
Vector autoregression (VAR) is a statistical model used to capture the relationship between multiple quantities as they change over time. VAR is a type of stochastic process model. VAR models generalize the single-variable (univariate) autoregressive model by allowing for multivariate time series. VAR models are often used in economics and the natural sciences. Like the autoregressive model, each variable has an equation modelling its evolution over time. This equation includes the variable's lagged (past) values, the lagged values of the other variables in the model, and an error term. VAR models do not require as much knowledge about the forces influencing a variable as do structural models with simultaneous equations. The only prior knowledge required is a list of variables which can be hypothesized to affect each other over time. Specification Definition A VAR model describes the evolution of a set of ''k'' variables, called ''endogenous variables'', over time. Each perio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Process
In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes have applications in many disciplines such as biology, chemistry, ecology, neuroscience, physics, image processing, signal processing, control theory, information theory, computer science, cryptography and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance. Applications and the study of phenomena have in turn inspired the proposal of new stochastic processes. Examples of such stochastic processes include the Wiener process or Brownian motion process, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Correlation
In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are ''linearly'' related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve. Correlations are useful because they can indicate a predictive relationship that can be exploited in practice. For example, an electrical utility may produce less power on a mild day based on the correlation between electricity demand and weather. In this example, there is a causal relationship, because extreme weather causes people to use more electricity for heating or cooling. However ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Main Diagonal
In linear algebra, the main diagonal (sometimes principal diagonal, primary diagonal, leading diagonal, major diagonal, or good diagonal) of a matrix A is the list of entries a_ where i = j. All off-diagonal elements are zero in a diagonal matrix. The following four matrices have their main diagonals indicated by red ones: :\begin \color & 0 & 0\\ 0 & \color & 0\\ 0 & 0 & \color\end \qquad \begin \color & 0 & 0 & 0 \\ 0 & \color & 0 & 0 \\ 0 & 0 & \color & 0 \end \qquad \begin \color & 0 & 0 \\ 0 & \color & 0 \\ 0 & 0 & \color \\ 0 & 0 & 0 \end \qquad \begin \color & 0 & 0 & 0 \\ 0 & \color & 0 & 0 \\ 0 & 0 &\color & 0 \\ 0 & 0 & 0 & \color \end \qquad Antidiagonal The antidiagonal (sometimes counter diagonal, secondary diagonal, trailing diagonal, minor diagonal, off diagonal, or bad diagonal) of an order N square matrix B is the collection of entries b_ such that i + j = N+1 for all 1 \leq i, j \leq N. That is, it runs from the top right corner to the bottom left corner. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Error
An error (from the Latin ''error'', meaning "wandering") is an action which is inaccurate or incorrect. In some usages, an error is synonymous with a mistake. The etymology derives from the Latin term 'errare', meaning 'to stray'. In statistics, "error" refers to the difference between the value which has been computed and the correct value. An error could result in failure or in a deviation from the intended performance or behavior. Human behavior One reference differentiates between "error" and "mistake" as follows: In human behavior the norms or expectations for behavior or its consequences can be derived from the intention of the actor or from the expectations of other individuals or from a social grouping or from social norms. (See deviance.) Gaffes and faux pas can be labels for certain instances of this kind of error. More serious departures from social norms carry labels such as misbehavior and labels from the legal system, such as misdemeanor and crime. Departures ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Identity Matrix
In linear algebra, the identity matrix of size n is the n\times n square matrix with ones on the main diagonal and zeros elsewhere. Terminology and notation The identity matrix is often denoted by I_n, or simply by I if the size is immaterial or can be trivially determined by the context. I_1 = \begin 1 \end ,\ I_2 = \begin 1 & 0 \\ 0 & 1 \end ,\ I_3 = \begin 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end ,\ \dots ,\ I_n = \begin 1 & 0 & 0 & \cdots & 0 \\ 0 & 1 & 0 & \cdots & 0 \\ 0 & 0 & 1 & \cdots & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & 0 & \cdots & 1 \end. The term unit matrix has also been widely used, but the term ''identity matrix'' is now standard. The term ''unit matrix'' is ambiguous, because it is also used for a matrix of ones and for any unit of the ring of all n\times n matrices. In some fields, such as group theory or quantum mechanics, the identity matrix is sometimes denoted by a boldface one, \mathbf, or called "id" (short for identity). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General Matrix Notation Of A VAR(p)
A general officer is an officer of high rank in the armies, and in some nations' air forces, space forces, and marines or naval infantry. In some usages the term "general officer" refers to a rank above colonel."general, adj. and n.". OED Online. March 2021. Oxford University Press. https://www.oed.com/view/Entry/77489?rskey=dCKrg4&result=1 (accessed May 11, 2021) The term ''general'' is used in two ways: as the generic title for all grades of general officer and as a specific rank. It originates in the 16th century, as a shortening of ''captain general'', which rank was taken from Middle French ''capitaine général''. The adjective ''general'' had been affixed to officer designations since the late medieval period to indicate relative superiority or an extended jurisdiction. Today, the title of ''general'' is known in some countries as a four-star rank. However, different countries use different systems of stars or other insignia for senior ranks. It has a NATO rank sc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix Difference Equation
A matrix difference equation is a difference equation in which the value of a vector (or sometimes, a matrix) of variables at one point in time is related to its own value at one or more previous points in time, using matrices. The order of the equation is the maximum time gap between any two indicated values of the variable vector. For example, :\mathbf_t = \mathbf\mathbf_ + \mathbf\mathbf_ is an example of a second-order matrix difference equation, in which is an vector of variables and and are matrices. This equation is homogeneous because there is no vector constant term added to the end of the equation. The same equation might also be written as :\mathbf_ = \mathbf\mathbf_ + \mathbf\mathbf_ or as :\mathbf_n = \mathbf\mathbf_ + \mathbf\mathbf_ The most commonly encountered matrix difference equations are first-order. Nonhomogeneous first-order case and the steady state An example of a nonhomogeneous first-order matrix difference equation is :\mathbf_t = \mathb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic
Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselves, these two terms are often used synonymously. Furthermore, in probability theory, the formal concept of a ''stochastic process'' is also referred to as a ''random process''. Stochasticity is used in many different fields, including the natural sciences such as biology, chemistry, ecology, neuroscience, and physics, as well as technology and engineering fields such as image processing, signal processing, information theory, computer science, cryptography, and telecommunications. It is also used in finance, due to seemingly random changes in financial markets as well as in medicine, linguistics, music, media, colour theory, botany, manufacturing, and geomorphology. Etymology The word ''stochastic'' in English was originally used as a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Error Correction Model
An error correction model (ECM) belongs to a category of multiple time series models most commonly used for data where the underlying variables have a long-run common stochastic trend, also known as cointegration. ECMs are a theoretically-driven approach useful for estimating both short-term and long-term effects of one time series on another. The term error-correction relates to the fact that last-period's deviation from a long-run equilibrium, the ''error'', influences its short-run dynamics. Thus ECMs directly estimate the speed at which a dependent variable returns to equilibrium after a change in other variables. History Yule (1926) and Granger and Newbold (1974) were the first to draw attention to the problem of spurious correlation and find solutions on how to address it in time series analysis. Given two completely unrelated but integrated (non-stationary) time series, the regression analysis of one on the other will tend to produce an apparently statistically significant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 has ... [...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] |
Applied Economics (journal)
''Applied Economics'' is a peer-reviewed academic journal published by Routledge with focus on the application of economic analyses. It is currently published by Routledge and circulates 60 issues per year. It was established in 1969 by the founding Editor Maurice H. Peston. The current editor-in-chief is Mark P. Taylor. Its companion journal is ''Applied Economics Letters ''Applied Economics Letters'' is a peer-reviewed academic journal covering applied economics. It was established in 1994 and is published 21 times per year by Routledge. It is a companion journal to ''Applied Economics''. The editor-in-chief is Mar ...''. It incorporated ''Applied Financial Economics'' from 2015. External links * Economics journals English-language journals Publications established in 1969 Routledge academic journals Journals more frequent than weekly {{econ-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
