VolatilityResult

Defined in fynance.estimator

class VolatilityResult(params, std_errors, loglik, aic, bic, conditional_vol, std_residuals, model, dist, n_obs)

Bases: object

Fitted GARCH-family volatility model (see fit_volatility).

Attributes:

paramsdict of str to float

Fitted parameters, keyed by name (omega, alpha, [gamma,] beta, [nu]).

std_errorsdict of str to float

Standard error of each parameter (NaN when the observed-information Hessian is not positive definite).

loglikfloat

Maximised log-likelihood.

aic, bicfloat

Akaike / Bayesian information criteria, 2k - 2ll and k ln(n) - 2ll with k parameters and n observations.

conditional_volnumpy.ndarray

In-sample conditional standard deviation \(\sigma_t\), shape (n_obs,).

std_residualsnumpy.ndarray

Standardized residuals \(y_t / \sigma_t\), shape (n_obs,).

model{‘garch’, ‘gjr’, ‘egarch’}

Conditional-variance specification.

dist{‘normal’, ‘t’}

Innovation density.

n_obsint

Number of observations the model was fit on.

forecast(h=1, n_sims=10_000, seed=0)

Multi-step conditional-variance forecast.

Returns \(\mathbb E[\sigma_{T+k}^2 \mid \mathcal F_{T-1}]\) for k = 1, \dots, h (T = n_obs). The one-step value is exactly the filter’s next-step variance.

For garch / gjr the forecast is the closed-form recursion toward the unconditional variance: after the exact one-step step, the leverage indicator is replaced by its expectation \(\mathbb E[\mathbf 1[\varepsilon < 0]] = 1/2\) (symmetric innovations), giving persistence \(\alpha + \beta + \gamma / 2\). For egarch (log-variance form) no closed form exists, so the forecast is a seeded Monte-Carlo average over n_sims simulated innovation paths.

Parameters:

hint, optional

Forecast horizon (number of steps). Default 1.

n_simsint, optional

Number of Monte-Carlo paths (egarch only). Default 10000.

seedint, optional

Seed for the Monte-Carlo draws (egarch only). Default 0.

Returns:

numpy.ndarray

Variance forecasts, shape (h,).

simulate(T, seed=0)

Simulate a return path from the fitted parameters and innovation.

Runs the fitted model’s conditional-variance recursion forward, drawing unit-variance innovations from the fitted dist (Gaussian, or standardized Student-t with nu degrees of freedom), and returns the mean-zero simulated returns \(y_t = \sigma_t z_t\).

Parameters:

Tint

Length of the simulated path.

seedint, optional

Seed for the innovation draws. Default 0.

Returns:

numpy.ndarray

Simulated returns, shape (T,).