# arch.univariate.APARCH¶

class arch.univariate.APARCH(p=1, o=1, q=1, delta=None, common_asym=False)[source]

Asymmetric Power ARCH (APARCH) volatility process

Parameters
p : int

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

o : int

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

q : int

Order of the lagged (transformed) conditional variance

delta : float, optional

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, optional

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 Construct parameter constraints arrays for parameter estimation 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

 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