Dave, The code on SUB-OPTIMAL APPROACH. "The sub-optimal approach is to estimate the AR parameters using high-order Yule Walker equations, fitting overdetermined least squares equations by minimizing squared error. Filter the original signal with the inverse AR filter to produce MA residuals. Estimate MA parameters of residuals ". Do you mind if i send mine also ? ARMA GUY>Dave, > >You can send the code to me, I have also implemented something of such >using MATLAB inbuilt functions (ARYULE, lpc, filter etc). My email is >arma_ann at yahoo.com. The only disadvantage i saw in that is that the >coefficients obtained for both AR and MA are not same with what i usedfor>generating the system especially when the variance of additive white >gaussian noise is very high or the SNR is very low. > >Rune, > >Thanks for the suggestion on the model order. My own task is just on the >model coefficients, I am presently evaluating the use of correct model >order. The next step is to use different model orders for the AR and MA >part respectively. > > >ARMA GUY. >>>Hi All, >>> >>>I am working on ARMA coefficient determination using a data sequence.I>>>have no idea of the underlying system from which the data wasgenerated>>. >>>What i only have is the data and thsi si as shown in the vector form >>below. >>> >>> >>>If the data is labeled >>>d = [d(1),d(2),d(3),d(4),d(5),d(6),d(7),d(8),d(9),d(10),d(11),...... >>>d(45)] >>> >>>if the ARMA equation is >>>y(n) = a(1)y(n-1) + a(2)y(n-2) + b(0)w(n) + b(1)w(n-1) >>> >>>and the main task is to determine the value of a(1),a(2), b(0) and >b(1). >> >>> >>>In order to do that, i am trying to model the data as the output of an >>>ARMA system driving by white noise, w= w(1),w(2),w(3),w(4)...w(n). >>> >>>My questions are >>> >>>1) Is it logical to assume that w (white noise) above is similar to x >in >>>the ARMA equation. >>> >>>2) If yes to question (1) above, for example can i assume that using >the >>>ARMA equation above, d(5) was generated by >>> >>>d(5) = a(1)d(4) + a(2)d(3) + b(0)w(5) + b(1)w(4) >>> >>>similarly >>> >>>d(25) = a(1)d(24) + a(2)d(23) + b(0)w(25) + b(1)w(24) >>> >>> >>> I have been told not to use any of the least square approach in >>>determining my ARMA coefficents and not to use any of the sub optimal >>>technique but to formulate it along that line. >>> >>>Thanks for anticipated response. >>>ARMA-GUY >>> >>> >>> >>> >>> >> >>ARMA-guy - >> >>The w is the driving white noise process. Any system noise, etc.,should>>be modeled seperately. >> >>To solve for the AR and MA parameters simultaneously (optimal) you need >to >>solve nonlinear equations usng an iterative algorithm on the estimated >>autocorrelation sequence. No convergence is garanteed (see text by Kay >or >>the Matlab system identification toolbox by Ljung). Or you can use a >high >>order AR approximation that involves linear equations (see text by >>Marple). >> >>A bootstrap method is the system identification approach; estimate >>parameters using linear system identification equations, filter to >produce >>residuals, use residuals to drive estimated ARMA filter, iterate...This >is >>also not garanteed to converge. >> >>The sub-optimal approach is to estimate the AR parameters using >high-order >>Yule Walker equations, fitting overdetermined least squares equationsby>>minimizing squared error. Filter the originalsignal with the inverse AR >>filter to produce MA residuals. Estimate MA parameters of residuals. >> >>I hope this helps. I do have Matlab code for this if you are in need. >Let >>me know. >> >>Dave >> >> >> >