What are Seasonal ARIMA Models

[@nickchristensen7148]

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

[@AricLaBarr]

Glad you like them!

[@askerj9774]

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-mc7op]

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.

[@kaynkayn9870]

Dude, you're so right. The way he just broke it down to t-12 makes so much sense. Just made it so much simplier to understand mathematically, it's just in a factor of 12...

[@kubakuba7786]

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

[@alijafarzadeh8267]

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

[@rabiasaeedmalik6946]

Thank you Eric for existing.

[@EmporerMeh]

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

[@carllu5827]

The quality over quantity of this man

[@m.raedallulu4166]

You are a wonderful professor, sir!

[@nataliatenoriomaia1635]

Thanks for the great videos on Time Series!

[@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?

[@AricLaBarr]

Hey Pablo! That all depends on whether you have an additive or multiplicative model. The structure in how we write the ARIMA(p,d,q)(P,D,Q) is the same regardless for consistency. However, if we had a multiplicative model then yes you would have additional affects. These multiplied effects are essentially effects that permeate out of the main effects. Here though I am just looking at additive. Hope this helps!

[@lucasm4299]

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

[@AricLaBarr]

Hey Lucas! That is because there are differences being taken! The original series Y_t is differenced to be come W_t which is what we build our ARIMA model off of.

[@alikhan-zz5jc]

Excellent Presentation God Bless You

[@konstantinospantazis2624]

Amazing videos! Thank you. Keep it up

[@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.

[@AricLaBarr]

Your formulation is correct! When it comes to looking at PACF and ACF plots, they are hard to do when you have mixed models. For an AR process, you look in the PACF because the ACF is exponentially decreases in an AR process. The reverse is true for an MA process. But that means for both you have exponential decreases in both PACF and ACF which makes it hard to truly see the patterns. That is why we typically do grid searches to find reasonable starting points and then adjust from there. When it comes to making these things stationary, we start with seasonality first. Sometimes seasonality correction will correct for trend at the same time. This is not true in reverse. Hope this helps!

[@Rundtj45]

Amazing. Thanks very much

[@gabriellara9954]

amazing explanation. thank you for putting this out there

[@sandipprabhu]

So well explained. Great!!

[@amra.haleem5175]

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

[@nishikataneja2184]

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

[@AricLaBarr]

First take a seasonal difference of 12, so Y_t - Y_(t-12) = W_t Then the rest is on the W_t: W_t = a_0 + a_1 * W_(t-1) + a_2 * W_(t-2) + a_3 * W_(t-3) + a_4 * W_(t-12) + a_5 * W_(t-24) + b_1 * e_(t-1) + b_2 * e_(t-2) + e_t

[@tochoXK3]

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

[@AricLaBarr]

Then you would take two differences FIRST. First you take the seasonal difference as in the video, then another difference before you start worrying about the AR and MA terms.

[@ajinkyaajinkya6725]

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

[@AricLaBarr]

So you have a couple of differences here. Let's let Y_t - Y_(t-6) = W_t for your seasonal difference. Then let's W_t - W_(t-1) = Z_t for your regular difference. From there we add lags at the season and regular: Z_t = w + a_1*Z_(t-1) + a_2*Z_(t-6) + b1*e_(t-1) + b2*e_(t-6) + e_t Hope this helps!

[@me-hn4bs]

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

[@AricLaBarr]

It is always good practice to take seasonal differences first IF you have seasonal data. A lot of times, if you remove the season through seasonal differences, you will also remove the trend as well!

[@me-hn4bs]

@@AricLaBarr thank you so much !!!

[@Nett6799]

Good one

[@7_Maverick_7]

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

[@AricLaBarr]

Hey Rohit, The D = 1 is the seasonal difference. So the original Y(t) - Y(t-12) is that D = 1 difference.

[@plamenyankov8476]

Great!

[@alexzano7957]

why use a additive model and not a multiplicative model?

[@AricLaBarr]

I think an additive model is easier for people to conceptual understand and grasp due to the additive effects. Could easily do a multiplicative model as well, but only have 5 minutes :-)

[@alexzano7957]

@@AricLaBarr I know you have only five minutes,but it's not easier with a first explanation with backshift operator?

[@AricLaBarr]

Having explained the backshift operator to students many times over the years, that is not a concept that could have been fit in this video and kept it under 5 minutes :-) Maybe another video on multiplicative models with the backshift operator in it would be something I could look at in the future though! Thanks for the idea!

[@alexzano7957]

@@AricLaBarr thanks for your answer ! I think I would have understood certain concepts better with a professor like you

[@AricLaBarr]

Thank you very much for the kind words!

[@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

[@Grand-Mono]

@@hyperadapted Thank you so much for the enlightened Sir! I'm literally just watching youtube tutorials, I'm literally had no background in stats, and calculus for data science