If I had to guess, it's the kind of person who is probably some math postdoc with 20 PhDs who slightly disagrees with some tiny assumption somewhere that would take an hour to explain with analysis the "rigorous" way. You're right though, and it annoys me too. This is a super helpful video and is perfect for someone trying to get their head around unit roots.
I am just getting into machine learning and this series of videos gives me all the math and stats background knowledge I need for understanding the time series, thank you!
OMG man you explain everything sooooo well and that's not easy to do because you talk about very complicated stuff !!! looking so forward to watch all your videos
Fantastic Ritvik. I benefitted. Normally I use the family tree to explain and understand Time Series. The grandpa grandson genealogy examples that work equally good. But this one is more direct
At 5m21s you say that phi^t * a_0 is a constant, so has variance zero. But...seems to be a function of t to me? These videos have been incredibly helpful, thanks so much :)
Even in |phi|infinity. So, doesn't this violate the constant variance conditiion as a_1, a_2 and so on all will have different variances (meaning it is actually changing over time)?
but if we have to take the first difference to get to stationarity, then are we not limited to only making predictions of differences? instead of making prediction of the absolute level of the variable itself, such as sales?
@ritvikmath Hi, i've watched both the invertibility videos, but i'm struggling to understand how we get the first part of line 2: a_t = phi^t a_0 + ... Please can you help me understand this?
Would you please comment on how did you get the phi^t * a_0 term in the MA(infinity) form? In the other video where you discuss invertibility condition, we only had epsilon terms.
In case of example-(3)-graphical-data, can we not rotate the x-axis anti-clock wise (say here visually ~20 degrees) {a kind of transformation} like we do in PCA and get a "kind of transformed stationary" series?
In the end, you found out that the expectation of dt and the variance of dt are constant, but what about the time series? you conclude the time series now is stationary, but you only found that out about dt, not at.
Dear Anton, greetings and all the best with your use of impulse response functions. Do you still need help? I could help... A brief discussion may get you off the ground.
@@TheTijuT Cheers Tiju, I figured it out on my own by now through textbooks. Took me a while but according to my supervisor I did a good job... Thank you anyways :)
Man your videos are amazing and super intuitive so please keep making the thanks!!! I've got just one question. In the last example for dt = at - a_t-1, did you get dt = et using the assumption that phi=1 so the at_1 terms cancel out? If you did then would you need to first test that phi is a unit root so you can then use that as an assumption to make dt = et?
It's not "assumed" that phi = 1 coz we already know it is. Our time series isn't stationary when phi = 1. So to make it stationary, we take the first difference.
1. At 3:38, where did first term a0 come from? 2, 10:20 you mentioned phi = 1 so E(at) = a0, but the whiteboard shows MOD(phi) = 1, so i'm thinking can't E(at) = - a0? (There seems to be an assumption t in power is even so (-1)(-1) = 1.) 3. 11:45 variance is getting bigger as we go rightwards. What if we limited the analysis to the 1st 1/4 of the x-axis? That looks stationary. This prompts the question do people conveniently choose the range of x to model to artificially make their results look great? Related question is how far back in history to go when building time series models?
Is it just me or the order of videos in this playlist is off for others too? Like in this one he refers to a previous video on how to represent an AR model as a MA model but I haven't seen that video yet...I assume it comes later?
Very nice explanation and video, I subscribed! However, I think the explanation 2 is slightly incorrect - in case of phi < -1, plot of time series should jump from positive to negative values, I think, not monotonically decrease. Then in this case expected value should not even exist (+ or - Inf?). And in case 3 why you didn't go to the limit with calculating variance like in case 1 and 2? As answer t*sigma^2 is only partially correct. Happy to be corrected on everything :) Greeting from Poland!
Why does |phi| < 1 satisfy the stationarity condition? I get that the expected value is 0 IN THE LIMIT, but that doesn't mean that the expected value for any given t is zero. In fact, you yourself are showing that the expected value is phi^t * x_0, which would mean that for two different x_t, x_{t+k}, their expected values would be different, therefore invalidating the definition of stationarity, right? I'm obviously wrong somewhere but I cannot see why.
We had before our transformed AR into MA process as = epsilon(t) + coef*epsilon(t-1)+coef^2*epsilon(t-2)+..., but i kinda cannot get it why are we adding coef^t*a(0) here. Is it just because of how AR specified, so we 100% need to have a first data point? and even if so, why are there superscript t in coeficient, not 0? Thanks in advance for answer
Clear explanation. Could you please explain which video you are referring to when talking about the MA infinity model? May I ask how you got the first term in the AR(1) model that you have specified? Thank you very much for your time.
Hi @ritvikmath could we also use tests like the ADF and Hurst Exp to determine exactly which parts of a trending timeseries could be considered stationary?
what i dont understand is how you treat negative values, for example if phi in absolute value is 1 than you can have phi also equal to -1 and therefore the mean of the time series is not a_0 but it changes depend of the value of t, so (obviously time is continues and not desecrate ) but if you look at full days then you will have different values (-1 or 1)*a_0
I had a question. I'm confused on the meaning of "stationary". Besides having a constant mean and variance, I thought it also means that there is no autocorrelation. Here you check that the timeseries has a constant mean and variance and say that it is "stationary". So does stationarity mean only constant mean and variance?
![DDG & G Herbo - Nosey [Official Video]](http://i.ytimg.com/vi/I9Ra0Zc2NlQ/mqdefault.jpg)
WHO THE HECK disliked this masterpiece???
If I had to guess, it's the kind of person who is probably some math postdoc with 20 PhDs who slightly disagrees with some tiny assumption somewhere that would take an hour to explain with analysis the "rigorous" way. You're right though, and it annoys me too. This is a super helpful video and is perfect for someone trying to get their head around unit roots.
@Ankit Chahal BAM
CCP
@@redcat7467 double BAM
lol
This is awesome, have my time series exam in a week and was not too optimistic... you're a lifesaver!
I read and watched many many many sources. This one is far the best explanation. It explains both intuitively and mathematically well
thank you!
I think what you have explained is the essence of unit roots. Thank you for sharing! It's a gift for the world.
best teacher ever, firmly believe that the ability of teaching is a talent! Thanks
I am just getting into machine learning and this series of videos gives me all the math and stats background knowledge I need for understanding the time series, thank you!
Excited for your journey!
ritvikmath...hands down you have the best stat formulas and models explanation videos on youtube....clear, concise and exemplary..bravo!
Wow, thanks!
Man you should have been my econometrics professor. Thank you for the hard work.
Happy to help!
OMG man you explain everything sooooo well
and that's not easy to do because you talk about very complicated stuff !!!
looking so forward to watch all your videos
I've just found your channel. You're giving out there quality man. Congrats!!!
Thanks so much for it, really great explanation and easy to understand. Watching from Brazil, congrats! You are great.
You're very welcome!
Excellent, the best explain about the AR(1) model of stationary!
Fantastic Ritvik. I benefitted. Normally I use the family tree to explain and understand Time Series. The grandpa grandson genealogy examples that work equally good. But this one is more direct
Glad it was helpful!
Really good video!! Didn't understand these AR and Unit Roots definitions but you managed to explain this in a simple talk
Glad it was helpful!
You're awesome This is a really well-spoken and intriguing video. Thanks for sharing!
please provide a direct link to the video you mention at 3:26 AR as MA inf as it is not in the earlier videos in this playlist.
Greatest explanation ever! you just saved my whole thesis
You're so good at this. Your videos rock man.
I appreciate that!
You are a genius man. I salute you.
At 5m21s you say that phi^t * a_0 is a constant, so has variance zero. But...seems to be a function of t to me?
These videos have been incredibly helpful, thanks so much :)
very fluid and Breez to watch!! is it possible to connect and seek your guidance further. Cheers!! Vivek
Great video, could you explain where comes from the name "root" in this topic?
thanks for the videos with clear explanation. I look forward to watching the dickey fuller test, is it gonna be uploaded yet?
Dude, this was amazing.
Good introduction, this helped a lot. Thank you!
Glad it was helpful!
Amazing explanation man! THANK YOU!!!!!
My pleasure!
thanks dude !
Excellent video. What’s the relation between unit root and eigenvalues?
thank you so much for dumb this down for me. Cant wait for your next content
Honestly this is brilliant, thanks you
Very good explanation of unit root. Thank you.
This is amazing!!
Thank u so much for making such a great tutorial!! But may i knw why the variance of dt is sigma squared??
Amazing explanation! Good job!
Glad you liked it!
man, what a life saver! thanks for the video
Superb awesome and splendid
Even in |phi|infinity. So, doesn't this violate the constant variance conditiion as a_1, a_2 and so on all will have different variances (meaning it is actually changing over time)?
but if we have to take the first difference to get to stationarity, then are we not limited to only making predictions of differences? instead of making prediction of the absolute level of the variable itself, such as sales?
this great. keep it up!
awesome man
Thanks!
Why does the error term e sub (t-k), have the same coefficient phi? Don't error terms have no coefficients with mean zero?
did he ever release the video about roots for ar(2) models?
@ritvikmath Hi, i've watched both the invertibility videos, but i'm struggling to understand how we get the first part of line 2: a_t = phi^t a_0 + ...
Please can you help me understand this?
Awesome explanation
In unit root case wont be expectation oscillatory? as mod phi =1 not phi=1
is there a precise definition of the unit root?
Thank You very much ! Your videos are amazing
Tks a lot! very good
Would you please comment on how did you get the phi^t * a_0 term in the MA(infinity) form? In the other video where you discuss invertibility condition, we only had epsilon terms.
good work !
In case of example-(3)-graphical-data, can we not rotate the x-axis anti-clock wise (say here visually ~20 degrees) {a kind of transformation} like we do in PCA and get a "kind of transformed stationary" series?
Thanks a lot! More time series videos please!
please arrange all videos in sequence...that would help...not able to follow the content properly
I love you :')
Thanks for the help!
No problem 😊
Thank you so much for this concept.
It is very confusing otherwise.
😀😀
I am confused when you was explaining the VARIANCE part. I am not sure how you derive it.
Thanks for the video mate!
well explained!
You are awesome! When is the video about the characteristics equation coming? I cannot find it :/ Maybe anyone can help me?
Thanks a lot man
Didn't understand a think. plz someone tell me anything I have missed out before this video , although i have watched the previous 4 videos
Can you re-explain why an AR(1) model is the same as MA(inf)? It wasn't super clear
He made a good video on it that will explain it better than I can,
In the end, you found out that the expectation of dt and the variance of dt are constant, but what about the time series? you conclude the time series now is stationary, but you only found that out about dt, not at.
thank you so much!!!
You're welcome!
Awesome video
this was really helpful!
I'm so glad!
Thank you i like your method
Where is characteristic function video?
Could suggest the book you follow?
Awesome!!
awesome, thank you!
I love you
Tired of paying a visit to one's barber just before recording a video...one just get the trimmer...and voilà!
7:23
This is his "how an AR(1) is the same thing as MA(infinity)" video: ruclips.net/video/q0vz7dGlZL0/видео.html :)
bro thanks a lot
I disliked this video, haven't gone to class all semester and cant understand a thing
I am angry at two people who disliked this very helpful video!
probably my statistics professor lol
Thank you for breaking this down man. You really have a special knack for this. We need more content! 😉
You explain this topic so good and understandable. The world needs more teachers like you 👍🏻 thank you!
Wow, thank you!
really u the only youtuber whos digging this deep, i hope you continue and panel data plz its the trend nowdays
Nice explanation. One question - Why did the variance term has powers of two, should it not include odd powers as well : phi, phi^3, phi^5 ...
Impulse Response Function Please! I want to apply it in my Bachelor Thesis in Finance but struggle to get the hang of it :(
Dear Anton, greetings and all the best with your use of impulse response functions. Do you still need help? I could help... A brief discussion may get you off the ground.
@@TheTijuT Cheers Tiju, I figured it out on my own by now through textbooks.
Took me a while but according to my supervisor I did a good job... Thank you anyways :)
I am studying IRF too. Interesting stuff.
Man your videos are amazing and super intuitive so please keep making the thanks!!!
I've got just one question. In the last example for dt = at - a_t-1,
did you get dt = et using the assumption that phi=1 so the at_1 terms cancel out?
If you did then would you need to first test that phi is a unit root so you can then use that as an assumption to make dt = et?
It's not "assumed" that phi = 1 coz we already know it is. Our time series isn't stationary when phi = 1. So to make it stationary, we take the first difference.
I look forward to watching the Dickey-Fuller or the Augmented DF.
Thank you for your time and for being so clear! 😊
Your videos have been really helpful for my study this semester. Thank you so much. Keep up the great work :)
1. At 3:38, where did first term a0 come from?
2, 10:20 you mentioned phi = 1 so E(at) = a0, but the whiteboard shows MOD(phi) = 1, so i'm thinking can't E(at) = - a0? (There seems to be an assumption t in power is even so (-1)(-1) = 1.)
3. 11:45 variance is getting bigger as we go rightwards. What if we limited the analysis to the 1st 1/4 of the x-axis? That looks stationary. This prompts the question do people conveniently choose the range of x to model to artificially make their results look great? Related question is how far back in history to go when building time series models?
Is it just me or the order of videos in this playlist is off for others too? Like in this one he refers to a previous video on how to represent an AR model as a MA model but I haven't seen that video yet...I assume it comes later?
Best explanation. Would have been best if the playlist was arranged
Hi Ritvik, can we have the play list in a sequence ?
For the first case, we have checked mean and variance but we did not check seasonality. Don't we also need to check that to be sure it is stationary?
Very nice explanation and video, I subscribed! However, I think the explanation 2 is slightly incorrect - in case of phi < -1, plot of time series should jump from positive to negative values, I think, not monotonically decrease. Then in this case expected value should not even exist (+ or - Inf?).
And in case 3 why you didn't go to the limit with calculating variance like in case 1 and 2? As answer t*sigma^2 is only partially correct.
Happy to be corrected on everything :) Greeting from Poland!
This is so helpful! GREAT video!! Saver of my Econometrics module!! Thank you so much!!!
Great to hear!
You summarize the important facts so easy and understandable. Thank you so much.
Going through all your videos about Time Series... great videos, thanks a lot!
Glad you like them!
Why does |phi| < 1 satisfy the stationarity condition? I get that the expected value is 0 IN THE LIMIT, but that doesn't mean that the expected value for any given t is zero. In fact, you yourself are showing that the expected value is phi^t * x_0, which would mean that for two different x_t, x_{t+k}, their expected values would be different, therefore invalidating the definition of stationarity, right? I'm obviously wrong somewhere but I cannot see why.
We had before our transformed AR into MA process as = epsilon(t) + coef*epsilon(t-1)+coef^2*epsilon(t-2)+..., but i kinda cannot get it why are we adding coef^t*a(0) here. Is it just because of how AR specified, so we 100% need to have a first data point? and even if so, why are there superscript t in coeficient, not 0? Thanks in advance for answer
Clear explanation. Could you please explain which video you are referring to when talking about the MA infinity model? May I ask how you got the first term in the AR(1) model that you have specified? Thank you very much for your time.
Hi @ritvikmath could we also use tests like the ADF and Hurst Exp to determine exactly which parts of a trending timeseries could be considered stationary?
what i dont understand is how you treat negative values, for example if phi in absolute value is 1 than you can have phi also equal to -1 and therefore the mean of the time series is not a_0 but it changes depend of the value of t, so (obviously time is continues and not desecrate ) but if you look at full days then you will have different values (-1 or 1)*a_0
I had a question. I'm confused on the meaning of "stationary". Besides having a constant mean and variance, I thought it also means that there is no autocorrelation. Here you check that the timeseries has a constant mean and variance and say that it is "stationary". So does stationarity mean only constant mean and variance?