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I have been told numerous times that an ARIMA(0,1,1) is indifferent from an ARIMA(1,1,0), but I am unsure why this is the case.

Could someone please help explain this to me?

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    $\begingroup$ This does not look right... $\endgroup$ – Richard Hardy Dec 8 '15 at 12:05
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    $\begingroup$ So you are essentially asking for the difference between an AR(1) and an MA(1). This is a very broad question and there are many differences so I don't think your claim is correct. $\endgroup$ – JohnK Dec 8 '15 at 12:06
  • $\begingroup$ Sorry for the confusion. What I am asking is why does an ARIMA(0,1,1) offer almost identical estimates to ARIMA (1,1,0)? $\endgroup$ – Gabriella101 Dec 8 '15 at 12:08
  • $\begingroup$ if the AR(1) coefficient in the first model is the mirror image of the MA(1) coefficient in the second model the two models are functionally the same as they have equivalent pi weights and equivalent psi weights. This would be true if the AR(1) coefficient was .333333 and the MA(1) coefficient was -.3333333 $\endgroup$ – IrishStat Dec 8 '15 at 12:21

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