The Engle  test for the presence of ARCH effects was also performed for the residuals of equation (6) for lags 1 through 8 (eight ARCH models
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.
are used to describe a changing, possibly volatile variance.
The Model of Generalized Autoregressive Conditional Heteroskedasticity (GARCH) is developed by  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.
(2005) suggested a Bayesian approach for ARCH models
with auxiliary variables (PITT; WALKER, 2005).
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).