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I have been given a basic task designed to assess my knowledge of ARCH/GARCH modelling, which involves fitting the models on 2 lots of time-series index returns.

What are the brief steps I need to follow?

1) Identify if my data is firstly Stationary, then Hetereoskedastic and finally Autocorrelated? (How can I do this?) (ADF test? ARCH LM test?)

2) Fit the model? (what are the steps involved in doing this?) (In a book i've read there is least square approach, and maximum likelihood approach?) (What do I need to look for)

So far I have spent 3-4 days reading, I have a basic understanding of this process but I feel like my knowledge has a lot of gaps and I'm struggling to put it all together.

If someone could outline a simple procedure, what I need to look for etc It'd be of great help!

I'm using the software STATA.

Harry
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  • Have you read the following: [this](http://stats.stackexchange.com/questions/77925/procedure-for-fitting-an-arma-garch-model/128866#128866), [this](http://stats.stackexchange.com/questions/143517/arma-garch-estimation-process-in-practice/143521#143521), [this](http://stats.stackexchange.com/questions/143035/the-use-of-garch/143040#143040), [this](http://stats.stackexchange.com/questions/136302/how-to-identify-the-arch-and-garch-lag-lenght-in-dcc-garch-model/136334#136334), and [this](http://stats.stackexchange.com/questions/87600/arma-garch-estimation-in-sequence/128745#128745)? – Richard Hardy Apr 10 '15 at 14:51
  • First link is too specific to that particular persons needs, the second link seems great, Thanks! The other links are useful in parts. I was hoping for an answer that simplifies the whole process into a rough guide I can follow and research individually (if I need to). – Harry Apr 10 '15 at 15:01
  • I see. One option is to wait until someone answers your question properly; the second is to draft a rough guide yourself, post it and ask if it looks fine. – Richard Hardy Apr 10 '15 at 15:03
  • If anyone is reading this, I'd be grateful to learn how you would approach this task! – Harry Apr 10 '15 at 16:42
  • Chapters 7 and 8 of Sean Becketti's ITSUS book walks you through these steps. That's about as brief as it gets, but much too long to excerpt here. – dimitriy Apr 10 '15 at 18:15
  • Thanks Dimitriy, I've downloaded the book I think it's exactly what I need. – Harry Apr 12 '15 at 00:46
  • @RichardHardy I've estimated an ARIMA(3,0,5) model to my data, and then fitted an ARCH(5) and separately a GARCH(1,1) onto the residuals, both of which show insignificant (0.45 p value) Portmanteau white noise test and improvements on AIC and BIC. Is it still better for me to estimate the ARMA and ARCH/GARCH part simultaneously? What is the procedure to do this, is it doable with STATA? – Harry Apr 12 '15 at 15:09
  • Simultaneous estimation is better because you get consistent and efficient estimates. Meanwhile, stagewise estimation of ARMA+GARCH with non-empty MA part leads to inconsistent estimates. I do not use Stata but I am pretty sure simultaneous estimation of ARMA+GARCH can be done in Stata. – Richard Hardy Apr 12 '15 at 18:15
  • @RichardHardy I emailed my lecturer and he told me we just need to fit ARCH and GARCH models onto our data (once checking for stationarity etc), without doing the ARMA part first. I'm guessing this just involves fitting variations of the models and then comparing AIC and BIC for optimum fit? – Harry Apr 25 '15 at 11:38
  • Yes, I think so, too. Just be aware that when a group of models have the same number of parameters, both AIC and BIC will favour whichever model delivers the highest likelihood (since the penalty term in AIC and BIC will be the same for all the models in the group). If the group of models is quite large, picking the AIC- or BIC-selected model will be nothing more but data dredging which should be avoided. Unfortunately, I am not aware of any *simple* solution to this problem; I am also no expert in the *complicated* solutions whatever they are. – Richard Hardy Apr 25 '15 at 11:58
  • Hello again! Sorry to keep coming back. Can you confirm if what I've done is correct? So far I've confirmed the stationarity of my data (Log returns tested using ADF test), then confirmed the presence of ARCH effects (Using ARCH-LM test). Is it wise to square my log returns and then fit ACF & PACF graphs? In order to give clues for lag selection for ARCH etc? I have a feeling that I can only do this for ARIMA models, however I don't know the technicalities of why. After this step am I free to simply fit ARCH (1), ARCH (1,1) etc and then confirm the best fit using AIC/BIC... – Harry May 07 '15 at 09:03
  • ... whilst being aware of the guidance you gave above. My task requires me to show a thorough understanding of ARCH/GARCH models, I just want to be sure I haven't missed anything. Thanks in advance – Harry May 07 '15 at 09:03
  • Ok, ignore my query regarding ACF/PACF for ARCH lag selection, we can't do it because we are "trying to model the evolution over time of an unobservable phenomena... we are one more degree of separation from observable phenomena" - taken from Sean Becketti - ITSUS. I'd be greatful for comments on the other points. – Harry May 07 '15 at 10:49

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