# References for this ARMA two step method estimation

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.

• It might be easiest if you just contacted the author of the slides directly. – Stephan Kolassa May 8 at 14:39
• 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. – Cristián Antuña May 8 at 14:42
• Thanks for the advice! I will write him. – Cristián Antuña May 8 at 14:47
• Will do it if I get it. – Cristián Antuña May 8 at 14:51
• For the record, I sent the author an email a month ago and got no answer yet... – Cristián Antuña Jun 13 at 16:43