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
pint

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

oint

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

qint

Order of the lagged (transformed) conditional variance

deltafloat, 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_asymbool, optional

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

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.

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)
Attributes
common_asym

The value of delta in the model.

delta

The value of delta in the model.

name

The name of the volatilty 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

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

variance_bounds(resids[, power])

Construct loose bounds for conditional variances.

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

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 volatilty 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