Time Series Talk : Seasonal ARIMA Model

[@muhammadzhafranbahaman6401]

Wow! You just condensed a 3 hours lecture into an 11-minute video. You sir deserve a medal!

[@boxu2148]

I binged your time series videos.. Love it so much! Please keep this series going

[@ritvikmath]

more time series vids coming up soon!

[@theh1ve]

3 years old and still providing value! Thanks

[@ritvikmath]

Woo thanks!

[@GaganiMethsara]

this series is the best time series vedios that I have seen. Thank you so much

[@PianoMan333]

Hey dude you got some of the most clear, concise and informative videos on KZbin regarding these econometric subjects. Thanks for all your efforts!

[@ritvikmath]

Glad it was helpful!

[@xxyyzz007]

This was explained so clearly that being a beginner in time series, I understood it quite well. Was applying all the codes in Python, but this really helped me understand the basics behind it. Thank you. Will check out more of these videos.

[@EdeYOlorDSZs]

I'm going to have to study this a bit more to select the proper ARIMA models for my analysis but this is a step in the right direction already!

[@akashpb1865]

Brilliantly explained ... I like teachers who explain things like you mathematically 👍🏼

[@ritvikmath]

Happy to help

[@lydiachong1274]

This is an excellent video. I spent hours trying to understand how pdqPDQm related to the final model in the end and you got through to me. Thank you x

[@ritvikmath]

No problem!

[@roytescaro6313]

"Ok? That was... very very confusing" totally killed me, you just won a new sub!

[@statisticianj.3837]

Thank you a lot for making this Time Series Analysis playlist! I just finished a course on Time Series, and these videos really helped.

[@lch9429]

amazing video on helping people to understand time-series concept, thank you so much. pls publish more videos on times series. if possible, hope u can do some video regarding Markov Switching, GARCH, VECM :)

[@홍성의-i2y]

6:29 The order of placing the operators matters. It cannot be switched. For all AR, MA, Integration parameters, seasonal ones come first, because we first need to make them "seasonally fair." 8:26 The lag operator (explained in kzbin.info/www/bejne/jIGxmp2HZ7Fmjq8) is a linear operator, so we can apply the rules of the linear operator. It really helps in making the relationship into a simple format, and this is the beauty of the lag operator.

[@dr.merlot1532]

My Grandmother completely understood this video!

[@claudiofranceschi3416]

Excelent explanation. It makes the topic to clear.

[@MrMoore0312]

Ritvik, foremost long time viewer and love all of your content dude! Please keep up this great work of yours. Not sure if you would be up for any replying to math questions, or if you just leave that to other commentators down here. On that note, I will leave the question all the same. Cheers! What i understand: ARIMA(1,1 1)(1,1,1)sub4 ==> (1-phi1Lag)(1-capitalphi1Lag^4)(1-Lag)(1-Lag^4)Ysubt = (1+sigma1Lag)(1+capitalsigma1Lag^4)Esubt unsimplified ARIMA(1,0,0)(0,1,1)sub4 ==> (1-phi1Lag)(1-Lag^4)Ysubt = (1+capitalsigma1Lag^4)Esubt unsimplified My question is about generalization in theory. I think the process you laid out for determining the order of each ordinary and seasonal component will be simple enough for me to gather, but i am more concerned with turning the wrong corner on this next point. Would the following be correct? ARIMA(2,0,0)(0,1,1)sub4 ==> (1-phi1Lag^2)(1-Lag^4)Ysubt = (1+capitalsigma1Lag^4)Esubt unsimplified It seems to be just too simple, only having to change (1-phi1Lag) to (1-phi1Lag^2) in the first term if I were to increase the order of the ordinary AR component by 1 in this way. However, I can can continue to original process you laid out by expanding the polynomial and then writing a new Zeta function to simply nicely. Any and all help or direction would be greatly appreciated!! Thanks!

[@alteshaus3149]

More time series please!!! I have watched already all of them

[@홍성의-i2y]

This is my personal understanding, and I think this is correct. The season-wise differentiation in SARIMA, that is y_{t-12}-y_t, is done for fair comparison w.r.t. season. So instead of comparing the values themselves, we are displaying the seasonal jumps. Then what if the jump in December is way bigger than that of June? The answer that I think is that SARIMA does not assume this. At least it is assuming that the jump is similar (both mean-wise and variance-wise). If we believe that there exists some big difference in that, we would need to apply some transformed model. For example, we may do twice-differencing for December and once-differencing for June.

[@KienTran-bc9dr]

Damit this is really nice and clear. Instantly subscribed and will bringe through your contents for sure!

[@ritvikmath]

Awesome, thank you!

[@josefjosef1524]

I watched your ARIMA video and this one. Really really helpful! Thumbs up! :)

[@b.vinaykumar1994]

4 years old yet it's the simplest ❤

[@HenningPhysics]

First of all, I would like to thank you for great series in this subject. You explain extremely well and your examples are extremely clarifying! I saw some questions below similar to mine, however I think that it's a bit "weird" someone simply dropping direct questions without showing that they put indeed some thoughts on it. Therefore, I will try to do so and explain my reasoning (it might also be helpful to other people): I want to understand better how to spot the seasonal parameters graphically, similar to what we have done for (p,d,q) in the ARIMA model. As far as I understood when you take the model (1, 0, 0)(0, 1, 1)_4, the (p, d, q) you find in the usual way: analyzing the PACF and ACF, for p and q, respectively. For obtaining d you analyze whether or not your timeseries has a trend, upwards or downwards. Accordingly, in your example, you observe that you have a direct correlation to the previous event by analyzing PACF, no trend and that's all (1, 0, 0). Now you move towards the seasonality analysis: you observe that when you built your equation, it has a similar structure *as if* you have removed a trend, but now for the season (in your case you have a quarterly data therefore it is 4)! And now you have some information about this **new data **, z_t, which the corresponding equation for z_t has a new d = 1 and a new q = 1 and the new p would be zero, since there is no direct correlation with previous values. Okay, now comes my conclusion: If I have a seasonal data, I can make a seasonal difference (in your case a_t - a_{t-4}) to obtain a new equation (z_t). I can plot the PACF and ACF for this new variable to obtain the P and Q, respectively. Furthermore, if my new variable, z_t, has a trend I can make some difference process to remove the trend which would give me the D. Then the three seasonal parameters are obtained by analyzing the new variable z_t. Am I right? Thanks once more, best regards from the South hemisphere!

[@ankitbiswas8380]

shouldnt you plot the PACF and ACF only after you have removed the trend of the seasonal component i.e. after getting the D ?

[@joyxu1072]

Hey thank you so much, I appreciated the useful and clear contents you posted. I followed every single video about time series here. Could you do a code example on modeling SARIMA, that will be very helpful. Thanks!

[@josevilhena8523]

Amazing video!! Thank you so much.

[@wl3637]

thanks for your amazing video can u explain why some of the (p,d,q) are not same as (P,Q,M) value when we use seasonal ARIMA?

[@matheusgaignoux2283]

You save my life! Thanks a lot dude!!!!!!

[@manifold4448]

Thanks a lot for these videos! I have a question, is it possible to statistically test for seasonality (and the factor, if seasonal) without looking at a time series plot? In the case of seasonal model, the ADF tests whether there is stochastic or deterministic seasonality but this is tested after the choice has been made to model the seasonality with m as factor. For my work I'm trying to develop a generic forecasting model and the only solution I can think of is building an image recognition model that identifies time series patterns in the plotted data. The latter would be quite an operation on itself.

[@hameddadgour]

Great presentation!

[@kronnologic]

Hey, great set of videos, I've devoured most of them!! However I didn't find any about SARIMAX and neither about regressions with ARIMA errors. I'm very interested in quantifying certain events that have occurred in my time series. Give it a thought, keep up the good work, kind sir!

[@woodl8654]

It saved my day, thank you

[@talentflame5557]

omg too good, bro too good hats off

[@bhavinmoriya9216]

Thanks a lot for awesome video. In the video, it was very clear m = 4. In general how would you figure out P, D, Q? Suppose you take say, Google stock, then how would you figure out P, D, Q, S (I suppose S is same as m, isn't it?). One more question -- if D=2 and m = 4, are we gonna take, (1-B^(2*4))?

[@taramorovatdar3710]

Thanks for the great videos, I am a little bit confused here. If the time series have seasonality then it is not stationary and we cant use the ARMA model but it seems we can use SARIMA! does that mean that for the SARIMA model we don't need to check for stationarity? I have five-month data that looks to have weekly seasonality(data is per hour) so can I apply SARIMA?

[@phi-vunguyen4911]

Thanks so much for your great videos on time series, i wonder why did you stop at SARIMA, how about ARIMAX and SARIMAX, looking forwards to it! :)

[@alecvan7143]

awesome videos!!

[@ritvikmath]

Thanks!

[@melaniemerchant1949]

very well explained

[@sihongliu5464]

This man is literally teaching better than my UC Berkeley Professor Ruoqi Yu who teaches Introduction to Time Series (STAT 153) this 2022 spring semester :)) :((

[@douglasmatheus9123]

Amazing videos, thank you so much!! , just a question professor, if a sarima model is for example (1,0,1) (1,1,1)6, we should still call sarima even with the fact that the integration is 0?

[@PinkFloydTheDarkSide]

Could you please create a playlist for all your time-series videos? It will be helpful to navigate sequentially. Thank you.

[@proserpinaabao176]

Thank You so much.,. God Bless.,.

[@satoshikiminoto2909]

how can Y^4 * Y^1 = Y^5 ? I think Y^4 is the former period value for 4 round( it isn't for the last 4 day) and Y^1 is yesterday so i don't think it can multiply to Y^5. please correct me if i wrong. Thank you.

[@asmitatcs9826]

Hi Ritwick , great videos. Keep up the good work. Could you please post a video on SARIMAX or ARIMAX , and pose another for TSLM(time series linear models)? Thanks in advance

[@yiyis1807]

I need help writing a SARIMA model I have obtained mathematically. My model is ARIMA(2,1,0)(0,1,0) period 12. I understand what the different parts actually mean but get very lost trying to write out the mathematical model. I have tried to follow other examples but as the models differ it makes it hard to apply it to what I have.

[@woodypham6474]

Realworld sales are not simple as we thought. Think about competitors promotion effect on company sales. Seasonal sales pattern are distorted by promotion and competition effect.

[@nishikataneja2184]

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

[@aakuthotaharibabu8244]

glad u became a math major

[@praveen2hearts]

How to choose the Seasonailty paramers like P,D and Q?

[@hannahnelson4569]

Good video!

[@me-hn4bs]

please I have some questions the first question is do we start by first differences or seasonal differences the second question is how to write the formula when the difference is > 1 because that B will change the third question is what is the formula for additive model

[@jalillahrach9449]

does the series z^t at the end is stationary ?

[@proserpinaabao176]

I hope you can upload video regarding the crime trend in relation to COVID 19 Pandemic.

[@PinkFloydTheDarkSide]

So how do I decide whether I should remove the seasonality and use ARIMA or use SARIMA instead while keeping the seasonality?

[@meghanap3468]

Great video! Thank you! Just one question. How do you account for two seasonal patterns in the series? For example, weekly and hourly seasonality. How do you select the value of m?

[@TheMehrdadIE]

I wonder how we can identify the P,D,Q for a time series.

[@robertchen7058]

Thank you for these awesome videos! Quick question, Since sarima and arima both involves differenced data, when you're doing acf and pacf analysis for determining p, P, q and Q, would you be generating acf and pacf of the original data or the differenced data? I have a feeling that it's the original data, and I did something wrong when I differenced a data (to make it stationary) and then use AR to model it, when I checked acf and pacf of the differenced data, the plots indicate that the differenced data was basically white noise, and that was very disturbing to me, because that suggests that the best prediction I can for tomorrow is to use today's data.

[@seyedalisadati3677]

Hello dear professor I deeply thank you for your wonderful lesson on Arima , But I have a ques, in the last examplw that you gave in the video the order of nonseasonal differences was zero what about if it was 1 , will the Z(t) become= Y(t)-Y(t-4) again? or you said that Y(t-1)-Y(t-5)=Z(t-1) so for instance I we had Y(t-1)-Y(t-7) what would term become according to Z(t)? another thing ,sorry if I am asking a lot , our professor said that the MA coefficients will appear with negative sing not positive...I mean=(1-teta1B1-teta2B2.....-tetaqBq)*error Thanks again

[@raoulcousins7243]

In this example, your variance looks non-constant. Is that a problem here? How do you address it?

[@navaneethsen]

Does seasonality come into existence only when we have data for multiple year? Is is still valid if we have only two months of data?

[@lovebroman9335]

Thank you so much!

[@anjigolla4853]

My dataset will store the values of CO2 for every 5 seconds on every day (DataTime--->CO2 value), so now I have only one month data. On every day in-between 2:30pm to 3:30pm CO2 values are increasing (>0), remaining all time in all days 0. So, I want consider this as seasonal period,. So, what is the value I need to consider as m value for this condition. Please anyone help how to select seasonal period for hourly/daily ?

[@sarimzahid3481]

the model has a nice name ;)

[@ritvikmath]

Time series people seem to really like models with nice names haha

[@fathimabinthashraf6037]

could you please explain how to write ARIMA(2,1,2)(1,1,1)[12]

[@yashvijain2229]

I have one doubt someone please help me. How do we choose the values of P, D and Q?

[@sachinsinghchauhan9861]

Hi!! Can you please explain how to choose PDQ

[@PratapO7O1]

how to find m if seasonality occurs every 3 years?

[@alhajinabiejunior1983]

Hello Sir, can you please help me to derive the equation for SARIMA (1,1,0)x(1,1, 0,12)

[@nikhiljagtap6799]

sir my project is crime forecasting i use auto.arima code in r then my ARIMA model is (0,0,0) so i confuse how to forecast them plz solve my querry

[@IAKhan-km4ph]

Very Nice. I used SPSS for ARIMA the model is (3,1,1) (3,1,1). Would you please write the model equation. The data is monthly temperature from 2002 to 2020. I can share my paper as well.

[@antoniorivera6556]

yes please!! share it!

[@yinstube]

Amazing!!!

[@bilalsohail3732]

great work (Y)

[@Otisawide]

Thank you!

[@jongcheulkim7284]

Thank you.

[@raltonkistnasamy6599]

Thanks man

[@ritvikmath]

You're welcome!

[@hiroshiperera7107]

Wow

[@r0nniecoleman]

king shit

[@ulysseskoudou962]

She

[@cusescholar3582]

This series has been great, but this explanation was the worst by far. Considering redoing this one.