# Autoregressive Conditional Heteroskedasticity

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## 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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References in periodicals archive ?
The Engle [13] test for the presence of ARCH effects was also performed for the residuals of equation (6) for lags 1 through 8 (eight ARCH models estimated).
Estimating and forecasting ARCH models using G@RCH 5.
For a comprehensive introduction to ARCH models and applications in finance see Gourieroux (1997).
We have estimated ARCH models on the residuals of the VAR models and presented the results in Tables 2A and 2B.
Using a group of ARCH models under different assumption, Wong (2016) explores the impact of bilateral exchange rate volatility on both total real and sectoral real exports to Singapore, China, Japan, the USA and Korea.
ARCH models are used to describe a changing, possibly volatile variance.
The Model of Generalized Autoregressive Conditional Heteroskedasticity (GARCH) is developed by [13] which is the development of the ARCH model. This model is built to avoid too high order in ARCH models that are based on the principle of parsimony or choose a simple model, so it will ensure the variance is always positive.
Of nine series tested (because the CDI and the SABOR were not estimated in the GARCH models), seven exhibited better results when estimated by EGARCH models, and the other two--TICHILE and BAIBOR--were estimated by ARCH models, demonstrating the skewness inmost of the studied series.
The developed ARCH models were aimed at capturing the high volatility in the log returns of financial time series data.
Chib, "Stochastic volatility: likelihood inference and comparison with ARCH models," The Review of Economic Studies, vol.
Bera and Higgins (1993) provide a comprehensive summary on the developments in ARCH models. Some of the other survey papers which show the evolution of ARCH models include Engle and Bollerslev (1986); Bollerslev, Chou and Kroner (1992); and Bollerslev, Engle and Nelson (1994).

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