# Specify order of ARIMA model using autocorrelogram

How can I, using the correlograms above, specify the orders of the ARIMA model? These are the pac an ac of the differenced time series. Using AIC and BIC, I can't seem te find a proper model.

     +-----------+
|     rGDPs |
|-----------|
1. |         . |
2. |  .0105743 |
3. |  .0077057 |
4. |  .0120554 |
5. |  .0089645 |
|-----------|
6. |  .0066547 |
7. |  .0106363 |
8. |  .0049944 |
9. |  .0050993 |
10. |    .00879 |
|-----------|
11. |  .0043526 |
12. |  .0086107 |
13. |   .008379 |
14. |  .0076342 |
15. |  .0057287 |
|-----------|
16. |  .0104761 |
17. |  .0083132 |
18. |  .0046806 |
19. |  .0131731 |
20. |  .0041189 |
|-----------|
21. |  .0096865 |
22. |   .010355 |
23. |  .0078735 |
24. |  .0118189 |
25. |  .0094376 |
|-----------|
26. |  .0110931 |
27. |  .0088711 |
28. |  .0094872 |
29. |  .0087013 |
30. |  .0075502 |
|-----------|
31. |  .0077829 |
32. |  .0065832 |
33. |  .0050039 |
34. | -.0002508 |
35. |  -.007906 |
|-----------|
36. | -.0107899 |
37. | -.0171785 |
38. | -.0105772 |
39. | -.0032196 |
40. | -.0009422 |
|-----------|
41. |  .0010233 |
42. |  .0019455 |
43. | -.0002184 |
44. |  .0023556 |
45. |  .0018158 |
|-----------|
46. | -.0011978 |
47. | -.0032644 |
48. | -.0037203 |
49. | -.0042601 |
50. | -.0049648 |
|-----------|
51. | -.0038538 |
52. | -.0077257 |
53. | -.0031233 |
54. | -.0013533 |
55. |  .0007629 |
|-----------|
56. |  .0017443 |
+-----------+


These are the observations on rGDPs, quarterly data. rGDPs is already the growth rate of gdp: calculated using logs: rGDPs = log(GDPs) - log(GDPs[n-1])

Edit: Here is my raw data, where the indicators n and s represent two countries. In this question, all I posted was about 's'. http://pastebin.com/4LbkgmEr

• You should include the plots in your post! – kjetil b halvorsen Dec 8 '15 at 10:21
• Im sorry, I never included graphs before. If I click on PAC and AC, I get to see the plots, but I conclude you don't? – pk_22 Dec 8 '15 at 10:23
• Yes, I see them, but in another window, and the text then disappears. – kjetil b halvorsen Dec 8 '15 at 10:24
• So how should I fix that? – pk_22 Dec 8 '15 at 10:25
• Never mind. It worked – pk_22 Dec 8 '15 at 10:28

One can use the ACF and PACF to identify a useful model if the paramaters of that model are invariant over time AND there are no outliers/level shifts/time trends in the data. Unfortunately for you and STATA neither is true . The CHOW Test for checking constancy of parameters over time is discussed here https://en.wikipedia.org/wiki/Chow_test and here http://www.autobox.com/cms/index.php/news/188-autobox-coauthors-article-in-journal. I took your data (55 values) and used AUTOBOX which I have helped develop and found that there was a significant break point in parameters. . The actual coefficients for the first period (31 values) was while the coefficients for the second regime (24 values ) was . Unfortunately most time series packages assume constancy of parameters which is hardly ever true except for many textbook examples.

Yes Virginia there is no Santa Claus !

My comment ...

I don't think the CHOW Test is applicable for testing the dummy. The complete model should include ARIMA structure , exgoneous series and any Intervention Detected Pulses/Level Shifts.time Trends that are appropriate. Why don't you post in an (excel file .... easy for me ...) the original Y series and the exogenous series and I will take a comprehensive look at it. Taking unwarranted differences ( a transformation) or using unwarranted power transformations (like logs) is always dangerous as like drugs some are good for you and some are not ....so I will let you decide on which approach you wish to take ...original data or arbitrarily manipulated/transformed data .

edited after receipt of data for Country 1:

OP wished to identify a combined ARIMA model with 4 user suggested causals.

Here is the Actual/Fit and Forecast graph The residual plot is here along with the residual ACF . The equation is here and here and here and here with forecasts[] .

In summary there is important lag structure in the first user suggested input while the second input is not informative. There are a number of pulses and seasonal pulses and no ARIMA structure is required or needed. Incorporating good user-suggested causals is motivated in part to vitiate any otherwise neede ARIMA strucure. You should duplicate this study for Country2 and then use the CHOW Test to test the hypothesis of a common set of parameters.

• Yes, there are outliers in our data and we thought of including a dummy in our model to account for these outliers. Is this also possible? We also use regressors in our model.. It is all a bit complicated. Our supervisor told us to use Chow test on the dummy, test whether to include it or not. Is this the right approach? And how can we know which regressors to include/which are significant? Should this be done after an arima model is estimated? – pk_22 Dec 8 '15 at 11:59
• How can I send you the excel file? I have a file with the original data (of 2 countries, but when I know how to handle 1, I can do the other one also). Our supervisor explicitly told us to use the Chow test on this.. I have no clue. In the excel file, there are no growth rates yet (however, we were informed to use the log approximation on this also). – pk_22 Dec 8 '15 at 12:26
• Ok ... Now I understand ,, The CHOW Test was to be used to compare/contrast the two models ... one for Country A and the second for Country B.. What I need is the Y series ( logged/differenced) for each country and the causal series for each country. If you can't attach them here send an excel file to me at my contact info . – IrishStat Dec 8 '15 at 13:42
• I managed to attach them. You can check if it is helpful. See the edit in the post. – pk_22 Dec 8 '15 at 13:44
• Oh and the Chow test, no it is not for the countries. We want to perform an ARIMA model on both countries, seperately, and then a VAR model to see whether foreign variables also affect domestic gdp. So for ARIMA we just want two different models for the countries. And then for the dummy, we include it in our model, and then test if the coefficient is significant or not with a chow test (basically F test). Should I include interaction terms with the dummy also? I guess we do – pk_22 Dec 8 '15 at 13:46

Only the first partial autocorrelation is significant, so the AR is at most of order 1. There are three significant lags in the AC, which implies MA of order three at most. But the AC for an MA process generally tapers off more quickly, so I think this is AR(1).

• That might be true if there were no outliers and no transient/dynamic coefficients and a constant error process. .... which is not true for this data ...As it turns out it is a composite AR(1) with an AR(4) – IrishStat Dec 8 '15 at 12:11
• My answer was to the original question, which included only the AC and the PAC, and only one time series. It has evolved quite a bit since. As it stands now, it looks like whatever question is being researched would be better answered by a vector autoregression / error correction model. – BjaRule Dec 8 '15 at 15:01
• or preferably what I just posted could be useful to you .... – IrishStat Dec 8 '15 at 15:12