arch.univariate.RiskMetrics2006¶

class arch.univariate.RiskMetrics2006(tau0: float = 1560, tau1: float = 4, kmax: int = 14, rho: float = 1.4142135623730951)[source]¶

RiskMetrics 2006 Variance process.

Parameters:¶

tau0: float = 1560¶

Length of long cycle. Default is 1560. Must be finite and larger than tau1.

tau1: float = 4¶

Length of short cycle. Default is 4. Must be finite and positive.

kmax: int = 14¶

Number of components. Default is 14. Must be positive, and tau1 * rho ** (kmax - 1) cannot be larger than tau0.

rho: float = 1.4142135623730951¶

Relative scale of adjacent cycles. Default is sqrt(2). Must be finite and larger than 1.

Raises:¶

• TypeError – If tau0, tau1 or rho is not a real number or kmax is not an integer.

• ValueError – If tau0, tau1 or rho is NaN or inf, tau1 is not positive, tau0 is not larger than tau1, kmax is smaller than 1, rho is not larger than 1, or tau1 * rho ** (kmax - 1) is larger than tau0.

Notes

The variance dynamics of the model are given as a weighted average of kmax EWMA variance processes where the smoothing parameters and weights are determined by tau0, tau1 and rho.

This model has no parameters since the smoothing parameter is fixed.

Examples

Daily RiskMetrics 2006 process

>>> from arch.univariate import RiskMetrics2006
>>> rm = RiskMetrics2006()

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.