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. Must be positive.

asym: bool = False¶

Flag indicating whether to include an asymmetric term.

Raises:¶

• TypeError – If m is not an integer or asym is not a bool.

• ValueError – If m is smaller than 1.

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

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)

Methods

backcast(resids)	Construct values for backcasting to start the recursion.
backcast_transform(backcast)	Transform user-provided backcast values.
bounds(resids)	Return 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()	Return the names of the model parameters.
simulate(parameters, nobs, rng[, burn, ...])	Simulate data from the model.
starting_values(resids)	Return 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.