I ran the auto.arima()command in R on a set of data and it chose the appropriate model to be ARIMA(0,1,0).

I know ARIMA(0,0,0) is just white noise, but what does ARIMA(0,1,0) mean?

  • 6
    $\begingroup$ ARIMA(0,1,0) is random walk. $\endgroup$ – Richard Hardy Oct 27 '17 at 18:10
  • 2
    $\begingroup$ @RichardHardy I try to look online before posting a question. Post the comment as an answer. Its good to have a reference $\endgroup$ – EconJohn Oct 27 '17 at 18:45

ARIMA(0,1,0) is random walk.

It is a cumulative sum of an i.i.d. process which itself is known as ARIMA(0,0,0).

  • 2
    $\begingroup$ a bit short as an answer $\endgroup$ – g3o2 Oct 27 '17 at 19:00
  • 1
    $\begingroup$ @g3o2, the real answer is in the first line. To make it artificially longer, I have added the second line. (OK, this is a joke. The second line gives the definition of a random walk.) I gave the name and the definition, and that was sufficient for the OP. I do believe in the virtue of brevity. There is plenty of information online on random walk, and the purpose of Cross Validated is not to duplicate it. $\endgroup$ – Richard Hardy Oct 27 '17 at 19:44
  • $\begingroup$ "Brevity is acceptable, but fuller explanations are better." (quoted from CV help) $\endgroup$ – g3o2 Oct 29 '17 at 16:06
  • $\begingroup$ @g3o2, thank you. I think my answer is full already (even the first line is a full answer), so there is no tradeoff between completeness and brevity anymore. But I appreciate the tip and I will see if I can add something that is still relevant without expanding into unrelated topics. $\endgroup$ – Richard Hardy Oct 29 '17 at 17:15
  • $\begingroup$ @g3o2, From a highly-upvoted answer on Meta: If it answers the question in a self-contained way, I don't think an answer's length particularly matters. For very short answers, it would be nice if the answerer provided a bit of "bonus" information (background, support for their answer, etc), but I think this extra effort should be more of a social norm than a hard and fast rule. I will try my best at that bonus information :) $\endgroup$ – Richard Hardy Oct 29 '17 at 17:30

An ARIMA(0, 1, 0) series, when differenced once, becomes an ARMA(0, 0), which is random, uncorrelated, noise.

If $X_1, X_2, X_3, \ldots$ are the random variables in the series, this means that

$$X_{i+1} - X_{i} = \epsilon_{i + 1}$$

where $\epsilon_1, \epsilon_2, \ldots$ is a sequence of centered, uncorrelated random variables.


$$ X_{i+1} = X_i + \epsilon_i $$

reveals that we have a random walk.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.