3
$\begingroup$

I've seen this question asked a few times but I still haven't seen a place where I can get some good examples on how to convert an arima() output in R to equation form.

So far, my understanding is that to convert an $AR(1)$ model in R to equation form, you need to follow this form:

$$(x_t − \mu) = \varphi_1(x_{t−1} − \mu) + a_t$$

So for example, if you run $ARIMA(1,0,0)$ in R and get the following output:

Call: arima(x = xt, order = c(1, 0, 0))

Coefficients:

         ar1  intercept
      0.3536     0.0017 
s.e.  0.0385     0.0004

sigma^2 estimated as 4.69e-05:  log likelihood = 2099.57,  aic =
-4193.15

To turn that into an equation, you would do:

$$(x_t − 0.0017) = 0.3536(x_{t−1} − 0.0017) + a_t$$ $$\implies x_t = 0.0017 + 0.3536(x_{t−1}) − 0.0006 + a_t$$ $$\implies x_t = 0.0011 + 0.3536(x_{t−1}) + a_t$$

So that would be your actual $AR(1)$ equation. Is this correct? As opposed to just plugging in the R output in to the $AR(1)$ form. So the following is wrong:

$$x_t = 0.0017 + 0.3536(x_{t−1}) + a_t$$

Note the difference in intercepts or "means". Also, would the sigma^2 term be the variance of the white noise term so that: $$a_t = N(0,4.69e-05)$$

Is there a good place to view examples of how to convert different $ARIMA$ models to an equation. Like $ARIMA(1,0,0)$, $ARIMA(2,0,0)$, $ARIMA(n,0,0)$, $ARIMA(0,0,1)$, $ARIMA(1,0,1)$, etc...

$\endgroup$
1

1 Answer 1

2
$\begingroup$

You have correctly identified that arima's reported "intercept" estimates are in fact mean estimates, and you have written the model in a correct form. This is discussed more, here: http://www.stat.pitt.edu/stoffer/tsa2/Rissues.htm

$\endgroup$

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.