arch.univariate.APARCH¶

class arch.univariate.APARCH(p: int = 1, o: int = 1, q: int = 1, delta: float | None = None, common_asym: bool = False)[source]¶

Asymmetric Power ARCH (APARCH) volatility process

Parameters:¶

p: int = 1¶

Order of the symmetric innovation. Must satisfy p>=o.

o: int = 1¶

Order of the asymmetric innovation. Must satisfy o<=p.

q: int = 1¶

Order of the lagged (transformed) conditional variance

delta: float | None = None¶

Value to use for a fixed delta in the APARCH model. If not provided, the value of delta is jointly estimated with other model parameters. User provided delta is restricted to lie in (0.05, 4.0).

common_asym: bool = False¶

Restrict all asymmetry terms to share the same asymmetry parameter. If False (default), then there are no restrictions on the o asymmetry parameters.

Examples

>>> from arch.univariate import APARCH

Symmetric Power ARCH(1,1)

>>> aparch = APARCH(p=1, q=1)

Standard APARCH process

>>> aparch = APARCH(p=1, o=1, q=1)

Fixed power parameters

>>> aparch = APARCH(p=1, o=1, q=1, delta=1.3)

Notes

In this class of processes, the variance dynamics are

\[\sigma_{t}^{\delta}=\omega +\sum_{i=1}^{p}\alpha_{i} \left(\left|\epsilon_{t-i}\right| -\gamma_{i}I_{[o\geq i]}\epsilon_{t-i}\right)^{\delta} +\sum_{k=1}^{q}\beta_{k}\sigma_{t-k}^{\delta}\]

If common_asym is True, then all of \(\gamma_i\) are restricted to have a common value.

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

common_asym	The value of delta in the model.
delta	The value of delta in the model.
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