arch.univariate.MIDASHyperbolic¶

class arch.univariate.MIDASHyperbolic(m: int = 22, asym: bool = False)[source]¶

MIDAS Hyperbolic ARCH process

Parameters:¶

m: int = 22¶: Length of maximum lag to include in the model
asym: bool = False¶: Flag indicating whether to include an asymmetric term

Examples

>>> from arch.univariate import MIDASHyperbolic

22-lag MIDAS Hyperbolic process

>>> harch = MIDASHyperbolic()

Longer 66-period lag

>>> harch = MIDASHyperbolic(m=66)

Asymmetric MIDAS Hyperbolic process

>>> harch = MIDASHyperbolic(asym=True)

Notes

In a MIDAS Hyperbolic process, the variance evolves according to

\[\sigma_{t}^{2}=\omega+ \sum_{i=1}^{m}\left(\alpha+\gamma I\left[\epsilon_{t-j}<0\right]\right) \phi_{i}(\theta)\epsilon_{t-i}^{2}\]

where

\[\phi_{i}(\theta) \propto \Gamma(i+\theta)/(\Gamma(i+1)\Gamma(\theta))\]

where \(\Gamma\) is the gamma function. \(\{\phi_i(\theta)\}\) is normalized so that \(\sum \phi_i(\theta)=1\). See [1] and [2] for further details.

References

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`()	Constraints
`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
`update`(index, parameters, resids, sigma2, ...)	Compute the variance for a single observation
`variance_bounds`(resids[, power])	Construct loose bounds for conditional variances.

Properties

`name`	The name of the volatility process
`num_params`	The number of parameters in the model
`start`	Index to use to start variance subarray selection
`stop`	Index to use to stop variance subarray selection
`updateable`	Flag indicating that the volatility process supports update
`volatility_updater`	Get the volatility updater associated with the volatility process