#!/usr/bin/env python3
# coding: utf-8
# @Author: ArthurBernard
# @Email: arthur.bernard.92@gmail.com
# @Date: 2019-02-20 10:39:56
# @Last modified by: ArthurBernard
# @Last modified time: 2019-05-23 17:31:40
""" Classical econometric time-series models.
Pure-NumPy implementations of moving-average, autoregressive and
GARCH-family processes used to simulate or fit return series. Parameter
estimation is delegated to the Cython routines in
:mod:`fynance.estimator` via :func:`get_parameters`, a single
maximum-likelihood entry point for all four model types.
Main entry points
-----------------
- :func:`MA` — Moving Average process.
- :func:`ARMA` — AutoRegressive Moving Average.
- :func:`ARMA_GARCH` — ARMA with GARCH(p, q) conditional variance.
- :func:`ARMAX_GARCH` — ARMA-GARCH with exogenous regressors.
- :func:`get_parameters` — fit the parameters of any of the above.
"""
# Built-in packages
# External packages
import numpy as np
import pandas as pd
# Local packages
from fynance.models.econometric_models_cy import *
__all__ = [
'get_parameters', 'MA', 'ARMA', 'ARMA_GARCH', 'ARMAX_GARCH'
]
# =========================================================================== #
# PARAMETERS FUNCTION #
# =========================================================================== #
[docs]
def get_parameters(params, p=0, q=0, Q=0, P=0, cons=True):
""" Get parameters for ARMA-GARCH models.
Helper that splits the flat ``params`` vector returned by
maximum-likelihood estimation into the structured groups expected
by the model evaluation routines: AR coefficients ``phi``, MA
coefficients ``theta``, GARCH ARCH/GARCH coefficients
``alpha``/``beta``, and constants ``c`` and ``omega``. Pass the
same ``p, q, Q, P, cons`` configuration that was used at the
estimation step (see :mod:`fynance.estimator`).
Parameters
----------
params : np.ndarray[np.float64, ndim=1]
Array of model parameters.
p, q, Q, P : int, optional
Order of model, default is 0.
cons : bool, optional
True if model contains constant, default is True.
Returns
-------
phi : np.ndarray[np.float64, ndim=1]
AR parameters.
theta : np.ndarray[np.float64, ndim=1]
MA parameters.
alpha : np.ndarray[np.float64, ndim=1]
First part GARCH parameters.
beta : np.ndarray[np.float64, ndim=1]
Last part GARCH parameters.
c : float
Constant of ARMA part.
omega : float
Constants of GARCH part.
See Also
--------
ARMAX_GARCH, ARMA_GARCH, ARMA, MA.
"""
i = 0
if cons:
c = params[i]
i += 1
else:
c = 0.
if p > 0:
phi = params[i: p + i]
i += p
else:
phi = np.array([0.], dtype=np.float64)
if q > 0:
theta = params[i: q + i]
i += q
else:
theta = np.array([0.], dtype=np.float64)
if Q > 0 or P > 0:
omega = params[i]
i += 1
if Q > 0:
alpha = params[i: Q + i]
i += Q
else:
alpha = np.array([0.], dtype=np.float64)
if P > 0:
beta = params[i: P + i]
i += P
else:
beta = np.array([0.], dtype=np.float64)
else:
omega = 0.
alpha = np.array([0.], dtype=np.float64)
beta = np.array([0.], dtype=np.float64)
return phi, theta, alpha, beta, c, omega
# =========================================================================== #
# MODELs #
# =========================================================================== #
[docs]
def MA(y, theta, c, q):
r""" Moving Average model of order `q` s.t:
.. math:: y_t = c + \theta_1 * u_{t-1} + ... + \theta_q * u_{t-q} + u_t
Parameters
----------
y : np.ndarray[np.float64, ndim=1]
Time series.
theta : np.ndarray[np.float64, ndim=1]
Coefficients of model.
c : np.float64
Constant of the model.
q : int
Order of MA(q) model.
Returns
-------
u : np.ndarray[ndim=1, dtype=np.float64]
Residual of the model.
Examples
--------
>>> y = np.array([3, 4, 6, 8, 5, 3])
>>> MA(y=y, theta=np.array([0.8]), c=3, q=1)
array([ 0. , 1. , 2.2 , 3.24 , -0.592 , 0.4736])
See Also
--------
ARMA_GARCH, ARMA, ARMAX_GARCH
"""
# Set type of variables
if isinstance(y, pd.DataFrame) or isinstance(y, pd.Series):
y = np.asarray(y)
elif isinstance(y, list):
y = np.asarray(y)
y = y.astype(np.float64).reshape([y.size])
if isinstance(theta, list):
theta = np.asarray(theta)
theta = theta.astype(np.float64).reshape([theta.size])
# Compute residuals
u = MA_cy(y, theta, np.float64(c), int(q))
return u
[docs]
def ARMA(y, phi, theta, c, p, q):
r""" AutoRegressive Moving Average model of order `q` and `p` s.t:
.. math::
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
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.
c : np.float64
Constant of the model.
p : int
Order of AR(p) model.
q : int
Order of MA(q) model.
Returns
-------
u : np.ndarray[np.float64, ndim=1]
Residual of the model.
See Also
--------
ARMA_GARCH, ARMAX_GARCH, MA.
"""
# Set type variables and parameters
y = np.asarray(y, dtype=np.float64).reshape([y.size])
theta = np.asarray(theta, dtype=np.float64)
phi = np.asarray(phi, dtype=np.float64)
# Compute residuals
u = ARMA_cy(y, phi, theta, float(c), int(p), int(q))
return u
[docs]
def ARMA_GARCH(y, phi, theta, alpha, beta, c, omega, p, q, Q, P):
r""" AutoRegressive Moving Average model of order q and p, such that:
.. math::
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:
.. math::
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}
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.
"""
y = np.asarray(y, dtype=np.float64).reshape([y.size])
theta = np.asarray(theta, dtype=np.float64)
phi = np.asarray(phi, dtype=np.float64)
alpha = np.asarray(alpha, dtype=np.float64)
beta = np.asarray(beta, dtype=np.float64)
u, h = ARMA_GARCH_cy(
y, phi, theta, alpha, beta, float(c), float(omega), int(p), int(q),
int(Q), int(P)
)
return u, h
[docs]
def ARMAX_GARCH(y, x, phi, psi, theta, alpha, beta, c, omega, p, q, Q, P):
r""" AutoRegressive Moving Average model of order q and p, such that:
.. math::
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:
.. math::
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}
Parameters
----------
y : np.ndarray[np.float64, ndim=1]
Time series.
x : np.ndarray[np.float64, ndim=2]
Time series of external features.
phi : np.ndarray[np.float64, ndim=1]
Coefficients of AR model.
psi : np.ndarray[np.float64, ndim=1]
Coefficients of external features.
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 the 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
--------
ARMA_GARCH, ARMA, MA.
"""
# Set array variables
y = np.asarray(y, dtype=np.float64).reshape([y.size])
x = np.asarray(x, dtype=np.float64)
theta = np.asarray(theta, dtype=np.float64)
phi = np.asarray(phi, dtype=np.float64)
psi = np.asarray(psi, dtype=np.float64)
alpha = np.asarray(alpha, dtype=np.float64)
beta = np.asarray(beta, dtype=np.float64)
# Compute residuals and volatility
u, h = ARMAX_GARCH_cy(
y, x, phi, theta, psi, alpha, beta, float(c), float(omega), int(p),
int(q), int(Q), int(P)
)
return u, h
