🔒 How to determine the range of p and q values for ARIMA/SARIMA using ACF and PACF plots ?

[random hull]

I’m building ARIMA / SARIMA models and want to systematically choose the range of p and q values based on ACF and PACF plots.
Given example ACF and PACF plots:

1. How should I interpret the threshold values (or upper bounds) for p and q?
2. More specifically, how can I avoid large ranges for pdq combinations and restrict p, q to some meaningful values suggested by the plots?

Considering the plots given in the images, can anyone please help me for appropriate way to minimize the range for pdq combinations
EOD I'll be using

p_vals = range(0, p_upper_bound)
d_vals = range(0, 1)
q_vals = range(0, q_upper_bound)

pdq_combinations = list(product(p_vals, d_vals, q_vals))

and then fit, predict, evaluate the ARIMA, SARIMA models for each order and select the pdq values which will give least rmse

[wraith spoke]

@random hull

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[warm flint]

hmmm better you ask on huggingface discord 😉

[random hull]

is that another server or a channel in this server ?

[warm flint]

Nothing against the pros here... but here is only basic and pure Python help, less about what you can do with it and applications.
Its another server, google
huggingface discord
you will find ...

[random hull]

i did it seems like I need to have a hugging face account for it and authorize the server to access it

thanks for the help
I'll ask the same question there

[shadow sequoia]

I doubt hf would help, that's more for deep learning folks

[random hull]

hmm let's see

[shadow sequoia]

if my rusty statistics knowledge serves, you look at peaks of the pacf to determine max ar, and peaks of acf for max ma
though if both show geometric-y decay, you have an ar-ma and you usually determine it through other stats like aic

for example here, they don't even talk about looking at (p)acf, and only about aic/bic/aicc

and also, are you doing this because you're hitting a computational wall or smthn?

[random hull]

ohh so you mean to say pacf & acf are outdated now ?

[shadow sequoia]

well I wouldn't say outdated
but when you have an ar-ma model it complicates things and you can't easily look at acf/pacf to determine what p q you should use

(as well as, my statistics is really rusty, so the more ml side of me is just quietly whispering just throw more compute at it)

[random hull]

well I'm given an assignment to solve, and they taught us only pacf & acf
I asked the same question to the trainers, but they refused to ans it as it'll be used in my assignments and can be considered as a copy.

not sure how exactly but I believe it's conceptual knowledge I'm after

so instead of arguing with them I thought of getting some help from discord 😅

[shadow sequoia]

well sure, in theory (again iirc 😅 ):
AR(p) - pacf shuts off (basically 0) after p, geometric decay of acf
MA(q) - acf shuts off (basically 0) after q, geometric decay of pacf
ARMA(p, q) - both acf/pacf look like they have geometric decay

[random hull]

okay so considering this

from acf plot I have attached
q should be ranging from 4 to 6

and from pacf plot, p should be 3 or 4

is the understanding correct ?

for the better results I shall go with following pdq_combinations

p_vals = range(1, 6)
d_vals = range(0, 1)
q_vals = range(1, 4)

pdq_combinations = list(product(p_vals, d_vals, q_vals))

correct ?

[shadow sequoia]

if you want to strictly look at what falls or doesn't fall into the bands
pacf has 1, 4, 5, 7, with 1 and 5 looking more out there, so p could potentially be 1 or 5 like you have ar(1) or ar(5) (or ar(4) or ar(7))
acf has 1 and 2 (maybe even 4), so q could potentially be 1 or 2 (or 4) like you have ma(1) or ma(2) (or ma(4))

ig if you really want to be thorough from that you're gonna check p from 1-7 and q from 1-4, note that setting it too high might make it overfit easier tho

and in the end it honestly might just be arma(1, 1) lul

and (if you've been taught this) you can use something like the adf test to check if the original series is stationary, if it's not then d=0 is not needed

[random hull]

yeah I did the adf test, the p-value came out to be 0.0039 which is way lesser than 0.05 so d has to be 0
still I don't want to take any chances hence I'm going [0, 1]

[shadow sequoia]

in practice many packages come with autoarima which usually has a good enough default (p, q, d) range it fits & checks thru, and gives you the best one

[random hull]

oh really

[shadow sequoia]

for example statsforecast.AutoARIMA

[shadow sequoia]

yeah fitting an arima is really not that intense given how beefy modern pcs are comparatively

[random hull]

basically this assignment stuff that I'm doing right now is not the way they use in real life

it's just for understanding how it works underneath

[shadow sequoia]

technically it doesn't check through the entire parameter grid and uses a heuristic, but you get the idea
as the end user you just have 1 big my_model = AutoARIMA() then my_model.fit( ... ) instead of having to loop yourself

[random hull]

ohh that's interesting

though it must be needing a lot of time right ?
as underneath it needs to find the appropriate p,d,q fit the model, and do some extra stuff as well

[shadow sequoia]

well, always depends on how much data you have, like if you have thousands of time series each with thousands of observations or smthn
or like if your data is very long seasonality it's also p bad

(though I'm not sure if ppl would actually use in those cases, might just resort to a deep learning model)

[random hull]

yeah I think that's the case with every business use case

[shadow sequoia]

I don't really have personal experience tbh
if you look online you'll see both being said (that ARIMA is being used, and also it's not being used)
I'd ask someone like Edd, he seems way more knowledgeable than me on this type of stuff

[random hull]

edd ?

[shadow sequoia]

ye, another helper in this server named Edd
I'm a bit afraid to ping other ppl tho

[random hull]

ohh

well I'm not really comparing but you're quite knowledgable too

at least much much better than me

I'm like totally new to this overall ML field

[shadow sequoia]

on the other hand, nixtla (who maintains statsforecast) is very focused on making performant impl's of forecasting algos so it's probably not that bad

[random hull]

right
I just had a look at the release history for statsforecast I got to say
They've maintained it quite well

https://pypi.org/project/statsforecast/#history

[shadow sequoia]

nixtla's probably the leading team to look when you just want performant forecasting

[random hull]

right

[wraith spoke]

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