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

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 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 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