What are Seasonal ARIMA Models

ARIMA models are very popular, but what if you have seasonality to your data. Here we talk about the seasonal ARIMA model to account for this!

[nickchristensen]

Buddy you are unreal! You teach these topics so well. And love the humor too

[askerj]

I'm binge watching your videos. You have great a tactic to explain things in simple and understandable ways. Thank you, sir! Please, continue sharing your knowledge.

[JohnDoe-mcop]

I have been searching for three hours for a clear explanation of pdq vs PDQ. I knew the answer would be simple but everything I read just said it was the seasonal part without explaining how those lags and differencing were actually taken differently than little pdq. Finally, thank you! Always frustrating when you know it could be explained in a sentence.

[kubakuba]

omg, you're back! I'm so happy, these videos are the most helpful!

[alijafarzadeh]

And that's how it is done UNDER FIVE MINUTES. Absolutely brilliant.

[EmporerMeh]

These are literally my favourite videos on YouTube on this topic. So glad you're back! :D

[PABLOLUZPEDEMONTE]

Thank you for the excellent explanation!. One question... in the example, as there is a multiplication between the non seasonal and seasonal AR components (the p and P in ARIMA (1, 0, 1) (2, 1, 0)), shouldn't there be 2 combinations of coefficients in the resulting equation? phi1*phi2*Wt-13 and phi1*phi3*Wt-25?

[Shrikant_Anand]

Hi Aric, suppose I have ARIMA(2, 2, 2)(2, 2, 2)12, I got this model equation:
W_t = omega + phi_1*W_t-1 + phi_2*W_t-2 + capital_phi_1*W_t-12 + capital_phi_2*W_t-24 + theta_1*e_t-1 + theta_2*e_t-2 + capital_theta_1*e_t-12 + capital_theta_2*e_t-24 + e_t
where omega, phi_i, theta_j are all constants, e_t is white noise and W_t is a stationary process.
I got W_t like this: W_t = (1-L^12)^2 * (1-L)^2 * Y_t where Y_t is the original time series with both trend and seasonal difference, L the lag operator.
Is my formulation correct for the above ARIMA(2, 2, 2)(2, 2, 2)12 stated process?
I am aware that for P, p we need to look at the PACF but of which series, W_t only for both?
Similarly for the Q, q do we need to look at the ACF of W_t only for both?
I guess it does not matter whether we do seasonal differencing first(1-L^12)^2 or non-seasonal-differencing first(1-L)^2 to get W_t ?
What if the series becomes stationary after doing (1-L)^2 * Y_t and we get p(t) do we still have to apply (1-L^12)^2 on result of the previous operation p(t)?
I tried a grid search method to get the value of p, d, q, Q but want to now how to get those values from the ACF and PACF plots.
I know I have asked lot of questions but I would appreciate your help.

[nataliatenoriomaia]

Thanks for the great videos on Time Series!

[lucasm]

Note: Usually the series values are X_t and the white noise values are W_t.
Here it’s written as W_t, e_t

[amra.haleem]

Dr. Aric, would it be possible to have examples from you with real values? Thanks a lot : )

[nishikataneja]

What would be the equation for an ARIMA (3, 0, 2)(2, 1, 0)[12] process?

[gabriellara]

amazing explanation. thank you for putting this out there

[tochoXK]

So, what if there's integration and also seasonal integration?

[me-hnbs]

please I have a question do we start by first differences or seasonal differences

[ajinkyaajinkya]

what would be equation for order (1, 1, 1) (1, 1, 1)6

[rohitverma]

It is still not clear what he did with the D = 1 at the last.

[alexzano]

why use a additive model and not a multiplicative model?

[Grand-Mono]

Hi again, im new in this field. This symbol is Golden Ratio ϕ correct? It has a value right? why we use golden ratio ϕ value for time series? why we multiply golden ration ϕ for every AR value?

Same with theta