I'm a math graduate student with not much knowledge in statistics. I could note that we have different techniques to estimate ARIMA parameters for a time series: using Bayes's Theorem, maximizing the likelihood function, and using the state-space model.

My question is: what is the difference between these 3 techniques and which is the best (and the best for ARIMA(1,1,0))?

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    $\begingroup$ You forgot another alternative: OLS. It will not work for models with a non-empty moving average part, but it will work for autoregressive models and thus for your example of ARIMA(1,1,0). It will be the fastest among the methods and asymptotically as accurate as likelihood maximization. It will not be as accurate in small samples since the first $p$ observations are thrown away when running OLS on an AR($p$) model. Also, state-space model is a model, not an estimation technique. I think it can be estimated by EM algorithm, but I may be wrong. $\endgroup$ – Richard Hardy Sep 12 '15 at 6:15
  • $\begingroup$ What means the "O" letter in OLS? $\endgroup$ – Mimi Sep 12 '15 at 12:27
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    $\begingroup$ "OLS" stands for "Ordinary least squares". $\endgroup$ – Richard Hardy Sep 12 '15 at 12:53

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