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.
(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).