def ma(X, Q, M):
"""Moving average estimator.
This program provides an estimate of the moving average parameters
and driving noise variance for a data sequence based on a
long AR model and a least squares fit.
:param array X: The input data array
:param int Q: Desired MA model order (must be >0 and <M)
:param int M: Order of "long" AR model (suggest at least 2*Q )
:return:
* MA - Array of Q complex MA parameter estimates
* RHO - Real scalar of white noise variance estimate
.. plot::
:width: 80%
:include-source:
from spectrum import arma2psd, ma, marple_data
import pylab
# Estimate 15 Ma parameters
b, rho = ma(marple_data, 15, 30)
# Create the PSD from those MA parameters
psd = arma2psd(B=b, rho=rho, sides='centerdc')
# and finally plot the PSD
pylab.plot(pylab.linspace(-0.5, 0.5, 4096), 10 * pylab.log10(psd/max(psd)))
pylab.axis([-0.5, 0.5, -30, 0])
:reference: [Marple]_
"""
if Q <= 0 or Q >= M:
raise ValueError('Q(MA) must be in ]0,lag[')
#C Fit a high-order AR to the data
a, rho, _c = yulewalker.aryule(X, M, 'biased') #! Eq. (10.5)
#add an element unity to the AR parameter array
a = np.insert(a, 0, 1)
#C Find MA parameters from autocorrelations by Yule-Walker method
ma_params, _p, _c = yulewalker.aryule(a, Q, 'biased') #! Eq. (10.7)
return ma_params, rho
def ma(X, Q, M):
"""Moving average estimator.
This program provides an estimate of the moving average parameters
and driving noise variance for a data sequence based on a
long AR model and a least squares fit.
:param array X: The input data array
:param int Q: Desired MA model order (must be >0 and <M)
:param int M: Order of "long" AR model (suggest at least 2*Q )
:return:
* MA - Array of Q complex MA parameter estimates
* RHO - Real scalar of white noise variance estimate
.. plot::
:width: 80%
:include-source:
from spectrum import arma2psd, ma, marple_data
import pylab
# Estimate 15 Ma parameters
b, rho = ma(marple_data, 15, 30)
# Create the PSD from those MA parameters
psd = arma2psd(B=b, rho=rho, sides='centerdc')
# and finally plot the PSD
pylab.plot(pylab.linspace(-0.5, 0.5, 4096), 10 * pylab.log10(psd/max(psd)))
pylab.axis([-0.5, 0.5, -30, 0])
:reference: [Marple]_
"""
if Q <= 0 or Q >= M:
raise ValueError('Q(MA) must be in ]0,lag[')
#C Fit a high-order AR to the data
a, rho, _c = yulewalker.aryule(X, M, 'biased') #! Eq. (10.5)
#add an element unity to the AR parameter array
a = np.insert(a, 0, 1)
#C Find MA parameters from autocorrelations by Yule-Walker method
ma_params, _p, _c = yulewalker.aryule(a, Q, 'biased') #! Eq. (10.7)
return ma_params, rho