arch.univariate.EGARCH¶

class arch.univariate.EGARCH(p=1, o=0, q=1)[source]¶

EGARCH model estimation

Parameters

p (int) -- Order of the symmetric innovation
o (int) -- Order of the asymmetric innovation
q (int) -- Order of the lagged (transformed) conditional variance

num_params¶

The number of parameters in the model

Type: int

Examples

>>> from arch.univariate import EGARCH

Symmetric EGARCH(1,1)

>>> egarch = EGARCH(p=1, q=1)

Standard EGARCH process

>>> egarch = EGARCH(p=1, o=1, q=1)

Exponential ARCH process

>>> earch = EGARCH(p=5)

Notes

In this class of processes, the variance dynamics are

\[\ln\sigma_{t}^{2}=\omega +\sum_{i=1}^{p}\alpha_{i} \left(\left|e_{t-i}\right|-\sqrt{2/\pi}\right) +\sum_{j=1}^{o}\gamma_{j} e_{t-j} +\sum_{k=1}^{q}\beta_{k}\ln\sigma_{t-k}^{2}\]

where \(e_{t}=\epsilon_{t}/\sigma_{t}\).

Methods

`backcast`(resids)	Construct values for backcasting to start the recursion
`backcast_transform`(backcast)	Transformation to apply to user-provided backcast values
`bounds`(resids)	Returns bounds for parameters
`compute_variance`(parameters, resids, sigma2, ...)	Compute the variance for the ARCH model
`constraints`()	Construct parameter constraints arrays for parameter estimation
`forecast`(parameters, resids, backcast, ...)	Forecast volatility from the model
`parameter_names`()	Names of model parameters
`simulate`(parameters, nobs, rng[, burn, ...])	Simulate data from the model
`starting_values`(resids)	Returns starting values for the ARCH model
`variance_bounds`(resids[, power])	Construct loose bounds for conditional variances.

Properties

`name`	The name of the volatilty process
`start`	Index to use to start variance subarray selection
`stop`	Index to use to stop variance subarray selection