def test_remove_parameter():
ds = Docstring(good)
ds.remove_parameters('x')
assert 'x : int' not in str(ds)
ds = Docstring(good)
ds.remove_parameters(['x', 'y'])
assert 'x : int' not in str(ds)
assert 'y : float' not in str(ds)
with pytest.raises(ValueError):
Docstring(good).remove_parameters(['w'])
ds = remove_parameters(good, 'x')
assert 'x : int' not in ds
assert isinstance(ds, str)
class ArmaProcess(object):
r"""
Theoretical properties of an ARMA process for specified lag-polynomials.
Parameters
----------
ar : array_like
Coefficient for autoregressive lag polynomial, including zero lag.
Must be entered using the signs from the lag polynomial representation.
See the notes for more information about the sign.
ma : array_like
Coefficient for moving-average lag polynomial, including zero lag.
nobs : int, optional
Length of simulated time series. Used, for example, if a sample is
generated. See example.
Notes
-----
Both the AR and MA components must include the coefficient on the
zero-lag. In almost all cases these values should be 1. Further, due to
using the lag-polynomial representation, the AR parameters should
have the opposite sign of what one would write in the ARMA representation.
See the examples below.
The ARMA(p,q) process is described by
.. math::
y_{t}=\phi_{1}y_{t-1}+\ldots+\phi_{p}y_{t-p}+\theta_{1}\epsilon_{t-1}
+\ldots+\theta_{q}\epsilon_{t-q}+\epsilon_{t}
and the parameterization used in this function uses the lag-polynomial
representation,
.. math::
\left(1-\phi_{1}L-\ldots-\phi_{p}L^{p}\right)y_{t} =
\left(1+\theta_{1}L+\ldots+\theta_{q}L^{q}\right)\epsilon_{t}
Examples
--------
ARMA(2,2) with AR coefficients 0.75 and -0.25, and MA coefficients 0.65 and 0.35
>>> import statsmodels.api as sm
>>> import numpy as np
>>> np.random.seed(12345)
>>> arparams = np.array([.75, -.25])
>>> maparams = np.array([.65, .35])
>>> ar = np.r_[1, -arparams] # add zero-lag and negate
>>> ma = np.r_[1, maparams] # add zero-lag
>>> arma_process = sm.tsa.ArmaProcess(ar, ma)
>>> arma_process.isstationary
True
>>> arma_process.isinvertible
True
>>> arma_process.arroots
array([1.5-1.32287566j, 1.5+1.32287566j])
>>> y = arma_process.generate_sample(250)
>>> model = sm.tsa.ARIMA(y, (2, 0, 2), trend='n').fit(disp=0)
>>> model.params
array([ 0.79044189, -0.23140636, 0.70072904, 0.40608028])
The same ARMA(2,2) Using the from_coeffs class method
>>> arma_process = sm.tsa.ArmaProcess.from_coeffs(arparams, maparams)
>>> arma_process.arroots
array([1.5-1.32287566j, 1.5+1.32287566j])
"""
# TODO: Check unit root behavior
def __init__(self, ar=None, ma=None, nobs=100):
if ar is None:
ar = np.array([1.0])
if ma is None:
ma = np.array([1.0])
with warnings.catch_warnings():
warnings.simplefilter("ignore", np.ComplexWarning)
self.ar = array_like(ar, "ar")
self.ma = array_like(ma, "ma")
self.arcoefs = -self.ar[1:]
self.macoefs = self.ma[1:]
self.arpoly = np.polynomial.Polynomial(self.ar)
self.mapoly = np.polynomial.Polynomial(self.ma)
self.nobs = nobs
@classmethod
def from_roots(cls, maroots=None, arroots=None, nobs=100):
"""
Create ArmaProcess from AR and MA polynomial roots.
Parameters
----------
maroots : array_like
Roots for the MA polynomial
1 + theta_1*z + theta_2*z^2 + ..... + theta_n*z^n
arroots : array_like
Roots for the AR polynomial
1 - phi_1*z - phi_2*z^2 - ..... - phi_n*z^n
nobs : int, optional
Length of simulated time series. Used, for example, if a sample
is generated.
Returns
-------
ArmaProcess
Class instance initialized with arcoefs and macoefs.
Examples
--------
>>> arroots = [.75, -.25]
>>> maroots = [.65, .35]
>>> arma_process = sm.tsa.ArmaProcess.from_roots(arroots, maroots)
>>> arma_process.isstationary
True
>>> arma_process.isinvertible
True
"""
arpoly = np.polynomial.polynomial.Polynomial.fromroots(arroots)
mapoly = np.polynomial.polynomial.Polynomial.fromroots(maroots)
# As from_coeffs will create a polynomial with constant 1/-1,(MA/AR)
# we need to scale the polynomial coefficients accordingly
return cls(np.r_[1, -np.asarray(-1 * arpoly.coef[1:] / arpoly.coef[0])],
np.r_[1, np.asarray(mapoly.coef[1:] / mapoly.coef[0])],
nobs=nobs)
@classmethod
def from_coeffs(cls, arcoefs=None, macoefs=None, nobs=100):
"""
Create ArmaProcess from an ARMA representation.
Parameters
----------
arcoefs : array_like
Coefficient for autoregressive lag polynomial, not including zero
lag. The sign is inverted to conform to the usual time series
representation of an ARMA process in statistics. See the class
docstring for more information.
macoefs : array_like
Coefficient for moving-average lag polynomial, excluding zero lag.
nobs : int, optional
Length of simulated time series. Used, for example, if a sample
is generated.
Returns
-------
ArmaProcess
Class instance initialized with arcoefs and macoefs.
Examples
--------
>>> arparams = [.75, -.25]
>>> maparams = [.65, .35]
>>> arma_process = sm.tsa.ArmaProcess.from_coeffs(ar, ma)
>>> arma_process.isstationary
True
>>> arma_process.isinvertible
True
"""
arcoefs = [] if arcoefs is None else arcoefs
macoefs = [] if macoefs is None else macoefs
return cls(
np.r_[1, -np.asarray(arcoefs)],
np.r_[1, np.asarray(macoefs)],
nobs=nobs,
)
@classmethod
def from_estimation(cls, model_results, nobs=None):
"""
Create an ArmaProcess from the results of an ARIMA estimation.
Parameters
----------
model_results : ARIMAResults instance
A fitted model.
nobs : int, optional
If None, nobs is taken from the results.
Returns
-------
ArmaProcess
Class instance initialized from model_results.
See Also
--------
statsmodels.tsa.arima.model.ARIMA
The models class used to create the ArmaProcess
"""
nobs = nobs or model_results.nobs
return cls(
model_results.polynomial_reduced_ar,
model_results.polynomial_reduced_ma,
nobs=nobs,
)
def __mul__(self, oth):
if isinstance(oth, self.__class__):
ar = (self.arpoly * oth.arpoly).coef
ma = (self.mapoly * oth.mapoly).coef
else:
try:
aroth, maoth = oth
arpolyoth = np.polynomial.Polynomial(aroth)
mapolyoth = np.polynomial.Polynomial(maoth)
ar = (self.arpoly * arpolyoth).coef
ma = (self.mapoly * mapolyoth).coef
except:
raise TypeError("Other type is not a valid type")
return self.__class__(ar, ma, nobs=self.nobs)
def __repr__(self):
msg = "ArmaProcess({0}, {1}, nobs={2}) at {3}"
return msg.format(
self.ar.tolist(), self.ma.tolist(), self.nobs, hex(id(self))
)
def __str__(self):
return "ArmaProcess\nAR: {0}\nMA: {1}".format(
self.ar.tolist(), self.ma.tolist()
)
@Appender(remove_parameters(arma_acovf.__doc__, ["ar", "ma", "sigma2"]))
def acovf(self, nobs=None):
nobs = nobs or self.nobs
return arma_acovf(self.ar, self.ma, nobs=nobs)
@Appender(remove_parameters(arma_acf.__doc__, ["ar", "ma"]))
def acf(self, lags=None):
lags = lags or self.nobs
return arma_acf(self.ar, self.ma, lags=lags)
@Appender(remove_parameters(arma_pacf.__doc__, ["ar", "ma"]))
def pacf(self, lags=None):
lags = lags or self.nobs
return arma_pacf(self.ar, self.ma, lags=lags)
@Appender(
remove_parameters(
arma_periodogram.__doc__, ["ar", "ma", "worN", "whole"]
)
)
def periodogram(self, nobs=None):
nobs = nobs or self.nobs
return arma_periodogram(self.ar, self.ma, worN=nobs)
@Appender(remove_parameters(arma_impulse_response.__doc__, ["ar", "ma"]))
def impulse_response(self, leads=None):
leads = leads or self.nobs
return arma_impulse_response(self.ar, self.ma, leads=leads)
@Appender(remove_parameters(arma2ma.__doc__, ["ar", "ma"]))
def arma2ma(self, lags=None):
lags = lags or self.lags
return arma2ma(self.ar, self.ma, lags=lags)
@Appender(remove_parameters(arma2ar.__doc__, ["ar", "ma"]))
def arma2ar(self, lags=None):
lags = lags or self.lags
return arma2ar(self.ar, self.ma, lags=lags)
@property
def arroots(self):
"""Roots of autoregressive lag-polynomial"""
return self.arpoly.roots()
@property
def maroots(self):
"""Roots of moving average lag-polynomial"""
return self.mapoly.roots()
@property
def isstationary(self):
"""
Arma process is stationary if AR roots are outside unit circle.
Returns
-------
bool
True if autoregressive roots are outside unit circle.
"""
if np.all(np.abs(self.arroots) > 1.0):
return True
else:
return False
@property
def isinvertible(self):
"""
Arma process is invertible if MA roots are outside unit circle.
Returns
-------
bool
True if moving average roots are outside unit circle.
"""
if np.all(np.abs(self.maroots) > 1):
return True
else:
return False
def invertroots(self, retnew=False):
"""
Make MA polynomial invertible by inverting roots inside unit circle.
Parameters
----------
retnew : bool
If False (default), then return the lag-polynomial as array.
If True, then return a new instance with invertible MA-polynomial.
Returns
-------
manew : ndarray
A new invertible MA lag-polynomial, returned if retnew is false.
wasinvertible : bool
True if the MA lag-polynomial was already invertible, returned if
retnew is false.
armaprocess : new instance of class
If retnew is true, then return a new instance with invertible
MA-polynomial.
"""
# TODO: variable returns like this?
pr = self.maroots
mainv = self.ma
invertible = self.isinvertible
if not invertible:
pr[np.abs(pr) < 1] = 1.0 / pr[np.abs(pr) < 1]
pnew = np.polynomial.Polynomial.fromroots(pr)
mainv = pnew.coef / pnew.coef[0]
if retnew:
return self.__class__(self.ar, mainv, nobs=self.nobs)
else:
return mainv, invertible
@Appender(str(_generate_sample_doc))
def generate_sample(
self, nsample=100, scale=1.0, distrvs=None, axis=0, burnin=0
):
return arma_generate_sample(
self.ar, self.ma, nsample, scale, distrvs, axis=axis, burnin=burnin
)