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