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How to use Maximum Likelihood estimation technique to asses time correlated noise in the time series. I want to use MLE to characterize the amplitude of stochastic processes please help me
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MLE is used to fit a distribution, and in your situation I suppose a noise model. A least squares might work as well for normally distributed noise or errors but the fit statistics may be way off and you may have to use a HAC estimator to get an unbiased estimation of the fit statistics. To start with use the Durbin-Watson test (dwtest) to check for serial correlation in the residuals. Now to your question, is there a specific error model you are interested in? What is the distribution of you errors? is it normal or another distribution? MATLAB has mle to fit distributions based on data, as long as you can specify what distribution you want.