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Could someone give me a step-by-step example of time series prediction using ARIMAX or ARMAX model? The example doesn't need to be long or complicated. It could be for example forecasting temperature with past data of only ten values (e.g [15, 16, 17, 15, ..., 12])

You don't have to calculate autocorrelation etc. step-by-step but I need it to be clear A) What are you doing and why, B) Which data you're using to get what etc..

For example, I would like to see the procedure of finding AR-, MA-, and X- lags, possible integrations, finding the error terms $y_i - \widehat{y}_i = e_i$, solving the coefficients for AR-, MA- and X-parts and making the predictions.

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    $\begingroup$ I am no time series expert, by any means, but there are some good examples in the SAS documentation (especially helpful if you are using SAS, of course, but pretty nice even if you aren't). $\endgroup$ – Peter Flom - Reinstate Monica Apr 8 '13 at 10:28
  • $\begingroup$ Thank you for your help =) I would prefer nonetheless example here =) I don't want examples involving functions, I would love an example done by hand (to some level) =). Like you would be defining an algorithm and what it does at each step =) $\endgroup$ – jjepsuomi Apr 8 '13 at 10:35
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ARIMA models are prone to failure. You need to run a tournament(parallel) and not do this in a series mentality. Also, you likely didn't get to see all the resources you need to build your model well. For example, are you looking for outliers first and then look for the ARIMA structure? Are you looking for seasonal pulses or level shifts or changes in time trend, parameters(ie CHOW test) or variance(ie TSAY test)?

If I were to document all the steps then we wouldn't be in business. Your posts over the past few months certainly indicate you are trying to build an automatic modeling approach too! Take a look at this as it will give you more critical details.

http://www.autobox.com/cms/index.php/blog/entry/build-or-make-your-own-arima-forecasting-model

Feel free to post some example data or send one to us and we can discuss in detail the example.

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  • $\begingroup$ Hi and thank you for your answer =) To answer your question, I don't know what an outlier is. My book didn't mention this definition, I just want a concrete example whether it was imagenary or not. Where can I find an algorithm which shows me the steps in detail? I want to see what's going on under the hood, I want an example, I don't care what it is about ;D It is hard to understand the ideas, because it is so hard to find concrete examples. If I were to teach you dancing, it's not enough to talk about swing and sway in theory. I must show u what it looks like and how and why to do it. $\endgroup$ – jjepsuomi Apr 8 '13 at 19:06
  • $\begingroup$ Ok, great. Did you click on the link I provided? There are examples there. $\endgroup$ – Tom Reilly Apr 8 '13 at 19:24
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    $\begingroup$ Post an example dataset and we can do an indepthOr this one which has real data autobox.com/cms/index.php/blog/entry/you-paid-that-much $\endgroup$ – Tom Reilly Apr 8 '13 at 19:31

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