Talk:Autoregressive integrated moving average

Wiki Education Foundation-supported course assignment
This article was the subject of a Wiki Education Foundation-supported course assignment, between 26 May 2020 and 3 July 2020. Further details are available on the course page. Student editor(s): Yifeng Li.

Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 15:04, 16 January 2022 (UTC)

Untitled
I removed the "too technical" tag. Feel free to reinsert it, but please leave some comments as to what you think needs explanation (along with some suggested fixes if you can). Thanks, Lunch 22:13, 22 October 2006 (UTC)

Redirect from "integrated of order zero"
This redirect seems totally inapropriate, I haven't removed the redirect because i dont know how.

The redirect is already fixed Testrider (talk) 12:54, 28 October 2011 (UTC)

Definition of ARIMA
You say that "an ARIMA(p,d,q) process is obtained by integrating an ARMA(p,q) process"

How bout random walk: xt=x(t-1)+et? Xt is an ARMA(1,0) process. but if you integrate it order 1, you get: xt-x(t-1)=et with is ARMA(0,0).

The standard definition seems to be this: Lecture Notes (pg2), which i've seen in several places

I.e. xt is ARIMA(p,d,q) if (1-L)^d is ARMA (p,q). Thus xt in the random walk example above is ARMA(1,0) or ARIMA(0,1,0) because once integrated you get an ARMA(0,0)

Anyone agree? If so, then i think the wiki page is confusing and needs somehow to be changed.

ALSO, i think we need to include ARIMA in the title which would help find it in a search.

Shades9662 23:12, 29 December 2006 (UTC)


 * On another note, maybe we should add that after differencing, if any of the new phi's (for the AR process) is equal to 0, i.e. the original phi was 1, then this will produce an AR(p-1) process after first differencing, for example. leading to ARIMA(p-1,1,0). On a side note: the reason why I'm still proposing/discussing more than editing is because I'm still new to all this. Shades9662 23:36, 29 December 2006 (UTC)

Implementation
I'd appreciate some reference as to how one actually computes solutions to an ARIMA model given data. dfrankow (talk) 20:36, 5 May 2008 (UTC)

Added a small hint on how these models are typically solved. Testrider (talk) 12:53, 28 October 2011 (UTC)

Pre-whitening
Anyone who has good technical knowledge of the application of pre-whitening would do well to take a crack at adding to this page. Here are some refs:


 * 
 * —Preceding unsigned comment added by Dfrankow (talk • contribs) 22:01, 3 October 2008 (UTC)

I(0)
Notation should be explained. The article mentions I(0) without any hint of its meaning. Also, I(1) links to the article, but there's no explanation of I(1) either. Albmont (talk) 18:18, 2 September 2008 (UTC)

Solved this by changing the redirects to Order of integration, this page refers to ARIMA for people that were actually looking for it. Testrider (talk) 13:12, 28 October 2011 (UTC)

Fixing wrong interwikis
It seems that the interwikis related to Autoregressive model, Moving average model, Autoregressive moving average model and Autoregressive integrated moving average are all mixed up. I have just fixed a few wrong interwikis (it:Modello lineare autoregressivo), but it seems that there are lots of other wrong interwikis (for example, tr:Otoregresif hareketli ortalamalar modeli interwikis to gl:Modelo autorregresivo de media móbil and to it:Modello lineare autoregressivo). Albmont (talk) 13:28, 9 October 2009 (UTC)

Seasonal ARIMA
In this article SARIMA is mentioned, however it seems to be impossible to find anything about SARIMA on wikipedia. Nor on this page nor on a seperate page. At the very least I hope the definition can be added either here or seperately. Testrider (talk) 13:04, 28 October 2011 (UTC)

I'd suggest as an intro that models can simultaneously model multiple lags, eg for one period and 12 periods. In this way a seasonal or cyclic element can be added to create a SARIMA. Similar parameters variants apply to the multiple period as for the single period, thus we have a model with six variables, written by convention as SARIMA(p,d,q)(P,D,Q) — Preceding unsigned comment added by 143.52.35.244 (talk) 10:20, 13 July 2016 (UTC)

Reinserted the "Too Technical" and "Context needed" Tags
While the material is technically accurate, it is *impossible* to learn about ARIMA from this article (While having a modest math background, I am someone who has used general-linear-model and logistic-regression modules of stat software, and understands the basics of time series, and was looking to educate myself). It desperately needs at least one running, readily understood example. Prakash Nadkarni (talk) 16:18, 14 October 2013 (UTC)

Second that. Equations are not self-evident or self explanatory. Theblindsage (talk) 09:31, 24 January 2014 (UTC)

I'd suggest some initial description of the underlying principles eg The Autoregressive Model assumes that future values will partially depend on errors made in previous predictions. It does not imply reversion to mean, though some values of parameters will model that scenario. The Moving Average model assumes future values will partially depand on previous values. It has a stationary mean, so the name may confuse. — Preceding unsigned comment added by 78.146.134.201 (talk) 14:46, 5 July 2016 (UTC)

Holt model written correctly?
The last example in the section Autoregressive integrated moving average is:


 * An ARIMA(0,2,2) model is given by $$X_t = X_{t-1} + X_{t-2} +(\alpha + \beta - 2)\varepsilon_{t-1} + (1-\alpha)\varepsilon_{t-2} + \varepsilon_{t}$$ — which is equivalent to Holt's linear method with additive errors, or Double exponential smoothing.

But the ARIMA(0, 2, 2) model is I(2) and thus has the differencing operation $$(1-L)^2 = (1-2L+L^2), $$ so the first two terms on the RHS should be $$2X_{t-1}-X_{t-2}.$$ So does the quoted passage have a couple of typos, or am I missing something? Loraof (talk) 19:00, 3 August 2016 (UTC)

Distinction between process and model
The current article contains the text:

"For this reason, no ARIMA model with d > 0 is wide-sense stationary."

Elsewhere (on Wikipedia) I have read that (non-)wide-sense stationarity is a property of processes rather than models. So, I suppose what is meant here is:

"For this reason, no process that is accurately described bu an ARIMA model with d > 0 is wide-sense stationary."

If there are no motivated and convincing objections, I intend to alter the text along these lines (in a week or two.)

There may be similar instances in the text where no proper distinction is made between processes and models.Redav (talk) 14:25, 15 July 2020 (UTC)