1
$\begingroup$

I obtained the following output from the function auto.arima(): enter image description here

Is this the correct way to write the equation? enter image description here

Or should it be like this? enter image description here

Improve this question
$\endgroup$

1 Answer 1

Reset to default
1
$\begingroup$

Hi: you don't difference the error terms. So, the arima(1,1,2) is:

$ y_{t} - y_{t-1} = \mu + \phi (y_{t-1}-y_{t-2}) + \theta_{1} \epsilon_{t-2} + \theta_2 \epsilon_{t-1} + \epsilon_t$.

So, the left side is for the $d=1$ term. The first term is the mean ( what you refer to as drift ? ), the second term is the $p= 1$ term and the third and fourth terms are the $q=2$ MA terms.

Sometimes there is the possibility the $\mu$ is put as part of the $\phi$ term rather than alone but I'd have to look at the code for auto.arima in R and don't have time at the moment. I hope this helps.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

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