fynance.models.econometric_models.ARMA_GARCH¶
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fynance.models.econometric_models.ARMA_GARCH(y, phi, theta, alpha, beta, c, omega, p, q, Q, P)¶ AutoRegressive Moving Average model of order q and p, such that:
\[y_t = c + \phi_1 * y_{t-1} + ... + \phi_p * y_{t-p} + \theta_1 * u_{t-1} + ... + \theta_q * u_{t-q} + u_t\]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: - y : np.ndarray[np.float64, ndim=1]
Time series.
- phi : np.ndarray[np.float64, ndim=1]
Coefficients of AR model.
- theta : np.ndarray[np.float64, ndim=1]
Coefficients of MA model.
- alpha : np.ndarray[np.float64, ndim=1]
Coefficients of MA part of GARCH.
- beta : np.ndarray[np.float64, ndim=1]
Coefficients of AR part of GARCH.
- c : np.float64
Constant of ARMA model.
- omega : np.float64
Constant of GARCH model.
- p : int
Order of AR(p) model.
- q : int
Order of MA(q) model.
- Q : int
Order of MA part of GARCH.
- P : int
Order of AR part of GARCH.
Returns: - u : np.ndarray[np.float64, ndim=1]
Residual of the model.
- h : np.ndarray[np.float64, ndim=1]
Conditional volatility of the model.
See also
ARMAX_GARCH,ARMA,MA.