ARMAX_GARCH

Defined in fynance.models.econometric_models

ARMAX_GARCH(y, x, phi, psi, theta, alpha, beta, c, omega, p, q, Q, P)

AutoRegressive Moving Average model of order q and p, such that:

\[y_t = c + \phi_1 * y_{t-1} + ... + \phi_p * y_{t-p} + \psi_t * x_t + \theta_1 * u_{t-1} + ... + \theta_q * u_{t-q} + u_t\]

With Generalized AutoRegressive Conditional Heteroskedasticity volatility model of order Q and P, such that:

\[ \begin{align}\begin{aligned}u_t = z_t * h_t\\h_t^2 = \omega + \alpha_1 * u^2_{t-1} + ... + \alpha_Q * u^2_{t-Q} + \beta_1 * h^2_{t-1} + ... + \beta_P * h^2_{t-P}\end{aligned}\end{align} \]

Parameters:

ynp.ndarray[np.float64, ndim=1]

Time series.

xnp.ndarray[np.float64, ndim=2]

Time series of external features.

phinp.ndarray[np.float64, ndim=1]

Coefficients of AR model.

psinp.ndarray[np.float64, ndim=1]

Coefficients of external features.

thetanp.ndarray[np.float64, ndim=1]

Coefficients of MA model.

alphanp.ndarray[np.float64, ndim=1]

Coefficients of MA part of GARCH.

betanp.ndarray[np.float64, ndim=1]

Coefficients of AR part of GARCH.

cnp.float64

Constant of the model.

pint

Order of AR(p) model.

qint

Order of MA(q) model.

Qint

Order of MA part of GARCH.

Pint

Order of AR part of GARCH.

Returns:

unp.ndarray[np.float64, ndim=1]

Residual of the model.

hnp.ndarray[np.float64, ndim=1]

Conditional volatility of the model.

See also

ARMA_GARCH, ARMA, MA.