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I was doing some survey on ARMA parameters estimation methods. While on that, I found these lecture notes: http://www.phdeconomics.sssup.it/documents/Lesson12.pdf

There, the author describes a two step estimation procedure for an $ARMA(p, q)$ model. Given $p$ and $q$, basically the process is as follows:

  • First it runs the regression $Y_t = \sum_{i=1}^p \pi_iY_{t-i} + \epsilon_t$ and calculates $\hat{\epsilon} = Y_t - \sum_{i=1}^p \hat\pi_iY_{t-i}$ using OLS.

  • Then, it estimates the parameters regressing $Y_t = \sum_{i=1}^p \phi_iY_{t-i} + \sum_{i=1}^q \theta_i\hat\epsilon_{t-i}+ \epsilon_t$. Again, using OLS

  • The results from the last step are the author's estimates; $\{\hat\phi_i\}_{i=1}^p, \{\hat\theta_i\}_{i=1}^q$.

I am not asking about the merits of the procedure per se, but a reference to a textbook or paper where this method is investigated/described. I haven't been able to find any of such by myself.

Thank you very much in advance.

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  • $\begingroup$ It might be easiest if you just contacted the author of the slides directly. $\endgroup$ – Stephan Kolassa May 8 at 14:39
  • $\begingroup$ I am not an academic myself, but a practitioner. I don't know if it is considered polite for me to contact a professor for such a question. $\endgroup$ – Cristián Antuña May 8 at 14:42
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    $\begingroup$ Thanks for the advice! I will write him. $\endgroup$ – Cristián Antuña May 8 at 14:47
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    $\begingroup$ Will do it if I get it. $\endgroup$ – Cristián Antuña May 8 at 14:51
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    $\begingroup$ For the record, I sent the author an email a month ago and got no answer yet... $\endgroup$ – Cristián Antuña Jun 13 at 16:43

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