arch.univariate.HARCH¶

class arch.univariate.HARCH(lags: int | Sequence[int] = 1)[source]¶

Heterogeneous ARCH process

Parameters:¶

lags: int | Sequence[int] = 1¶

List of lags to include in the model, or if scalar, includes all lags up the value

Examples

>>> from arch.univariate import HARCH

Lag-1 HARCH, which is identical to an ARCH(1)

>>> harch = HARCH()

More useful and realistic lag lengths

>>> harch = HARCH(lags=[1, 5, 22])

Notes

In a Heterogeneous ARCH process, variance dynamics are

\[\sigma_{t}^{2}=\omega + \sum_{i=1}^{m}\alpha_{l_{i}} \left(l_{i}^{-1}\sum_{j=1}^{l_{i}}\epsilon_{t-j}^{2}\right)\]

In the common case where lags=[1,5,22], the model is

\[\sigma_{t}^{2}=\omega+\alpha_{1}\epsilon_{t-1}^{2} +\alpha_{5} \left(\frac{1}{5}\sum_{j=1}^{5}\epsilon_{t-j}^{2}\right) +\alpha_{22} \left(\frac{1}{22}\sum_{j=1}^{22}\epsilon_{t-j}^{2}\right)\]

A HARCH process is a special case of an ARCH process where parameters in the more general ARCH process have been restricted.

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()	Construct parameter constraints arrays for parameter estimation
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