arch.univariate.ARCH¶

class arch.univariate.ARCH(p: int = 1)[source]¶

ARCH process.

Parameters:¶

p: int = 1¶

Order of the symmetric innovation. Must be positive.

Raises:¶

• TypeError – If p is not an integer.

• ValueError – If p is smaller than 1.

Notes

The variance dynamics of the model estimated

\[\sigma_t^{2}=\omega+\sum_{i=1}^{p}\alpha_{i}\epsilon_{t-i}^{2}\]

Examples

ARCH(1) process

>>> from arch.univariate import ARCH

ARCH(5) process

>>> arch = ARCH(p=5)

Methods

backcast(resids)	Construct values for backcasting to start the recursion.
backcast_transform(backcast)	Transform user-provided backcast values.
bounds(resids)	Return 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()	Return the names of the model parameters.
simulate(parameters, nobs, rng[, burn, ...])	Simulate data from the model.
starting_values(resids)	Return 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.