# arch.univariate.MIDASHyperbolic¶

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

MIDAS Hyperbolic ARCH process

Parameters
• m (int) – Length of maximum lag to include in the model

• asym (bool) – Flag indicating whether to include an asymmetric term

num_params

The number of parameters in the model

Type

int

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 $$\sum \phi_i(\theta)=1$$

References

*

Foroni, Claudia, and Massimiliano Marcellino. “A survey of Econometric Methods for Mixed-Frequency Data”. Norges Bank. (2013).

Sheppard, Kevin. “Direct volatility modeling”. Manuscript. (2018).

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 forecast(parameters, resids, backcast, …) Forecast volatility from the model 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