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31 relations: Autoregressive model, Autoregressive–moving-average model, Conditional variance, Econometrica, Econometrics, Errors and residuals, Generalized normal distribution, Innovation (signal processing), Journal of Econometrics, Journal of Economic Perspectives, Lévy process, Least squares, Ljung–Box test, Mathematical finance, Moving-average model, Null hypothesis, Q-statistic, Quadratic variation, Robert F. Engle, Score test, Standard normal deviate, Statistical model, Stochastic differential equation, Stochastic volatility, Time series, Unit root, Variance, Volatility (finance), Volatility clustering, White noise, White test.
Autoregressive model
In statistics 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.
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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 and the second for the moving average.
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Conditional variance
In probability theory and statistics, a conditional variance is the variance of a random variable given the value(s) of one or more other variables.
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Econometrica
Econometrica is a peer-reviewed academic journal of economics, publishing articles in many areas of economics, especially econometrics.
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Econometrics
Econometrics is the application of statistical methods to economic data and is described as the branch of economics that aims to give empirical content to economic relations.
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Errors and residuals
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 "theoretical value".
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Generalized normal distribution
The generalized normal distribution or generalized Gaussian distribution (GGD) is either of two families of parametric continuous probability distributions on the real line.
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Innovation (signal processing)
In time series analysis (or forecasting) — as conducted in statistics, signal processing, and many other fields — the innovation is the difference between the observed value of a variable at time t and the optimal forecast of that value based on information available prior to time t. If the forecasting method is working correctly, successive innovations are uncorrelated with each other, i.e., constitute a white noise time series.
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Journal of Econometrics
The Journal of Econometrics is a scholarly journal in econometrics.
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Journal of Economic Perspectives
The Journal of Economic Perspectives (JEP) is an economic journal published by the American Economic Association.
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Lévy process
In probability theory, a Lévy process, named after the French mathematician Paul Lévy, is a stochastic process with independent, stationary increments: it represents the motion of a point whose successive displacements are random and independent, and statistically identical over different time intervals of the same length.
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Least squares
The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems, i.e., sets of equations in which there are more equations than unknowns.
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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.
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Mathematical finance
Mathematical finance, also known as quantitative finance, is a field of applied mathematics, concerned with mathematical modeling of financial markets.
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Moving-average model
In time series analysis, the moving-average (MA) model is a common approach for modeling univariate time series.
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Null hypothesis
In inferential statistics, the term "null hypothesis" is a general statement or default position that there is no relationship between two measured phenomena, or no association among groups.
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Q-statistic
The Q-statistic is a test statistic output by either the Box-Pierce test or, in a modified version which provides better small sample properties, by the Ljung-Box test.
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Quadratic variation
In mathematics, quadratic variation is used in the analysis of stochastic processes such as Brownian motion and other martingales.
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Robert F. Engle
Robert Fry Engle III (born November 10, 1942) is an American economist and the winner of the 2003 Nobel Memorial Prize in Economic Sciences, sharing the award with Clive Granger, "for methods of analyzing economic time series with time-varying volatility (ARCH)".
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Score test
Rao's score test, also known as the score test or the Lagrange multiplier test (LM test) in econometrics, is a statistical test of a simple null hypothesis that a parameter of interest \theta is equal to some particular value \theta_0.
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Standard normal deviate
A standard normal deviate (or standard normal variable) is a normally distributed random variable with expected value 0 and variance 1.
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Statistical model
A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of some sample data and similar data from a larger population.
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Stochastic differential equation
A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process.
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Stochastic volatility
In statistics, stochastic volatility models are those in which the variance of a stochastic process is itself randomly distributed.
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Time series
A time series is a series of data points indexed (or listed or graphed) in time order.
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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.
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Variance
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean.
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Volatility (finance)
In finance, volatility (symbol σ) is the degree of variation of a trading price series over time as measured by the standard deviation of logarithmic returns.
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Volatility clustering
In finance, volatility clustering refers to the observation, first noted as Mandelbrot (1963), that "large changes tend to be followed by large changes, of either sign, and small changes tend to be followed by small changes." A quantitative manifestation of this fact is that, while returns themselves are uncorrelated, absolute returns |r_| or their squares display a positive, significant and slowly decaying autocorrelation function: corr(|r|, |r |) > 0 for τ ranging from a few minutes to several weeks.
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White noise
In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density.
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White test
In statistics, the White test is a statistical test that establishes whether the variance of the errors in a regression model is constant: that is for homoskedasticity.
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ARCH, ARCH model, ARCH models, Autoregressive Conditional Heteroskedasticity, Autoregressive conditional heteroscedasticity, EGARCH, GARCH, GARCH model, Garch model, Generalized autoregressive conditional heteroscedasticity, Generalized autoregressive conditional heteroskedasticity, IGARCH, Ngarch.
References
[1] https://en.wikipedia.org/wiki/Autoregressive_conditional_heteroskedasticity
