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st: A cry for help on ARMA with weak autocorrelation


From   "Dmytro Andriychenko" <dmytro@blueyonder.co.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: A cry for help on ARMA with weak autocorrelation
Date   Wed, 5 May 2010 19:49:37 +0100

Dear Statalist,

I have been recently asked to fit a univariate model for a particular
stationary time series. I thought ARMA will be the obvious choice, but when
I looked at the autocorrelation within the series, I found that the first
two lags are not significant and the few significant ones are only
marginally so (see corrgram output below). 

I guess I can still do the estimates, but I am very much wondering if ARMA
is appropriate modeling technique here. Is it even valid? Portmanteau
statistics is not rejecting hypothesis of no autocorrelation and Q stats
suggest marginal significance at lag 3,5 and 7 in the first series.

The question is:  is it even appropriate to be building ARMA in the light of
such weak autocorrelation, especially that the first two lags are not
significant? If ARMA is not appropriate, then what can it be?

If anyone can help me with that, or better still point me towards a
reference that would explain that, I would very much extremely appreciate
that. I have been reading books on econometrics for over a week, but still
cannot conclusively answer the question.

Thank you,

Dmytro
 
                                          -1       0       1 -1       0
1
 LAG       AC       PAC      Q     Prob>Q  [Autocorrelation]  [Partial
Autocor]
----------------------------------------------------------------------------
---
1       -0.0516  -0.0516   1.3555  0.2443          |                  |

2        0.0574   0.0551   3.0348  0.2193          |                  |

3       -0.1253  -0.1209   11.062  0.0114         -|                  |

4       -0.0248  -0.0401   11.377  0.0226          |                  |

5        0.0887   0.1020   15.417  0.0087          |                  |

6        0.0809   0.0808   18.785  0.0045          |                  |

7       -0.1274  -0.1468   27.146  0.0003         -|                 -|

8        0.0455   0.0491   28.214  0.0004          |                  |

9       -0.0718  -0.0235   30.882  0.0003          |                  |

10      -0.0196  -0.0722   31.081  0.0006          |                  |

11       0.0029  -0.0091   31.085  0.0011          |                  |

12      -0.0930  -0.0818   35.588  0.0004          |                  |

13       0.1613   0.1684   49.154  0.0000          |-                 |-

14      -0.0064  -0.0050   49.176  0.0000          |                  |

15       0.0465   0.0277   50.305  0.0000          |                  |

16       0.0520   0.0951   51.726  0.0000          |                  |

17      -0.0261  -0.0090   52.084  0.0000          |                  |

18       0.0407   0.0249   52.955  0.0000          |                  |

19       0.0720   0.0485   55.692  0.0000          |                  |

20      -0.0093   0.0368   55.738  0.0000          |                  |

21       0.0882   0.0593   59.865  0.0000          |                  |

22       0.0209   0.0623   60.098  0.0000          |                  |

23      -0.0231  -0.0031   60.381  0.0000          |                  |

24      -0.0112  -0.0256   60.448  0.0001          |                  |

25      -0.0611  -0.0094   62.445  0.0000          |                  |

26       0.0820   0.0641   66.046  0.0000          |                  |

27      -0.0818  -0.1022    69.64  0.0000          |                  |

28      -0.0372  -0.0531   70.384  0.0000          |                  |

29      -0.0148   0.0117   70.503  0.0000          |                  |

30      -0.0195  -0.0182   70.708  0.0000          |                  |

31       0.0606   0.0384   72.693  0.0000          |                  |

32       0.0101  -0.0140   72.748  0.0001          |                  |

33       0.0248   0.0807   73.083  0.0001          |                  |

34       0.0049  -0.0336   73.096  0.0001          |                  |

35      -0.0110  -0.0529   73.162  0.0002          |                  |

36      -0.0420  -0.0467   74.129  0.0002          |                  |

37       0.0684   0.0485   76.693  0.0001          |                  |

38       0.0291   0.0632   77.159  0.0002          |                  |

39       0.0517  -0.0230   78.631  0.0002          |                  |

40      -0.0336   0.0225   79.255  0.0002          |                  |



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