Auto Regressive Conditional Heteroskedasticity (ARCH) is an econometric model employed to find dependency of current error variance on the squares of model errors for previous observations.
If autoregressive members are used to describe error variance, this model is described as Generalized Auto Regressive Conditional Heteroskedasticity (GARCH).
Parameters of GARCH(p, q) model are estimated:
Where:
T. Number of observations.
yt. Endogenous variable.
xt. Exogenous variable.
b0. Mean.
b. Vector of regression coefficients.
εt. Residuals.
ht. Conditional residual variance.
p. Autoregression order.
q. Moving average order.
To calculate conditional variance ht, the user can use one of the following equations:
Standard:
Type 1:
Type 2:
Where γ - skewness parameter.
Available models are:
Without regressors and without constant:
Without regressors and with constant:
With regressors and without constant:
With regressors and with constant:
See also:
ISmGARCH | Library of Methods and Models