# Autoregressive Conditional Heteroskedasticity

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Related to Autoregressive Conditional Heteroskedasticity: GARCH

## Autoregressive Conditional Heteroskedasticity (ARCH)

A nonlinear stochastic process, where the variance is time-varying, and a function of the past variance. ARCH processes have frequency distributions which have high peaks at the mean and fat-tails, much like fractal distributions. The ARCH model was invented by Robert Engle. The Generalized ARCH (GARCH) model is the most widely used and was pioneered by Tim Bollerslev. See: Fractal Distributions.

## Autoregressive Conditional Heteroskedasticity

A statistical measure of the average error between a best fit line and actual data that uses past data to predict future performance. General Autoaggressive Conditional Heteroskedasticity is the most common way of doing this. See also: Fractal Distribution.
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Standard autoregressive conditional heteroskedasticity tests (not reported here) conducted on the standardized residuals cannot reject the null hypothesis that all heteroskedasticity effects have been removed after fitting with a GARCH(1,1) process.
This approach can be considered a particular case of the generalized autoregressive conditional heteroskedasticity (GARCH) model, and according to Jorion (2001, p.
When we consider the short-run dynamics of the demeaned variables through a vector autoregression (VAR) analysis, we show that the error covariance of this VAR model is significantly conditionally heteroskedastic and go on to specifically account for this phenomenon with a VAR-generalized autoregressive conditional heteroskedasticity (GARCH) model.
Because the homoskedasticity assumption of the traditional market-model approach may be violated, we also utilize generalized autoregressive conditional heteroskedasticity (GARCH) and exponential generalized autoregressive conditional heteroskedasticity (EGARCH) models to ensure robustness.
They documented a positive conditional volatility--volume relationship in models with Gaussian errors and Generalized Autoregressive Conditional Heteroskedasticity (GARCH)-type volatility specifications.
In regard to the latter, LJB is the Lomnicki-Jarque-Bera test of normality; ARCH denotes the statistic of no autoregressive conditional heteroskedasticity with four lags; and BCH is Ocal and Osborn's (2000) test of business cycle heteroskedasticity.
Thus, to help understand certain aspects of petroleum price volatility, we utilized the generalized autoregressive conditional heteroskedasticity (GARCH) model for estimating the conditional variance of returns, which allows the conditional variance to be time-variant.
Following an innovation in the inflation rate, short periods of increased volatility are indicated by the presence of autoregressive conditional heteroskedasticity (ARCH) in the regression residuals.
In this study, we examine the short-run dynamic information transmission between the Chinese A and B share markets using a Bivariate Generalized Autoregressive Conditional Heteroskedasticity (GARCH) framework, which simultaneously models the return transmission and volatility spillover across the two markets.
This study considers several residual diagnostic tests: the Jarque-Bera statistic test for normality, the Ljung-Box Q-statistic test for serial correlation, the Lagrange Multiplier statistic test for autoregressive conditional heteroskedasticity (ARCH), and the White test for heteroskedasticity (with cross terms).
1) The discrete-time approximation of the continuous-time specification is then formulated as a generalized autoregressive conditional heteroskedasticity (GARCH) framework introduced by Bollerslev (1986).

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