We are trying to model ARIMA procedures in MATLAB. We have been able to simulate the model using Ordinary Least Squares estimation however, we have few problems in Maximum Likelihood Estimation.
The main problem that we are facing is the computation of omega(covariance function) that is used in MLE techniques. We are not sure how the value of omega is computed. We have tried to follow the SAS estimation details manual for this formulation. In this manual, the log likelihood function is minimized by using Marquardt algorithm to minimize the following sum of squares -> |H|^(1/n) * e^(dash)*e*|H|^(1/n). Now, it is specified that omega = H*H^(dash). We have tried to compute H using Cholesky Decomposition but I believe we are getting an error due to computation of omega.
We have tried to remove the ACF of the input data series however, the computation of omega from this ACF looks dicey.
Let us know if anybody has any idea regarding this.