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()

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

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