Currently preparing for my masters thesis (not economy related). I hardly had any statistics courses during my studies, but now I need knowledge of time series analysis in order to create a forecasting model. Within just 3 days consuming videos on this channel, my understanding of time series analysis went from virtually 0 to something that at least allows me to read relevant papers and understand the basic concept of the proposed models within. This guy is amazing
You're amazing. I'm taking a time series course and the professor isn't so great at explaining any of these concepts. Really appreciate you and your videos! Please keep them coming.
Outstanding video, Any chance there is a video where you code this or solve an example with some values for those constant in the final equation for Z(t) Thanks a lot
Hi, your video is excellent, making time series much more understandable. But I couldn't find the video specific for Augmented Dickey-Fuller test in your videos. As you mentioned in this video, there is another video on ADF test. Thanks!
Stationarity in Time series The models like AR, MA assume our time series to be stationary stationary - mean constant, std dev constant and no seasonality non - lot of fluctuations in the data. first there were immense fluctuations, now less -> different std dev - mean is not constant. of a time chunk - seasonality - periodic trend over time how to check? 1. visually 2. global vs local tests (global mean =|= local mean) 3. augmented duckey fuller test how to make it stationary yt = b0 + b1 t + Et ( mean not constant in the graph) new series Zt = yt - yt-1 Zt = b1 + Et - Et-1 E(Zt) = b1 (mean of new series) (Et and Et-1 are constants from some distribution with mean 0) Var(Zt) =
Good explanation, thanks. However, I am a bit confused with the condition on seasonality and wikipedia says seasonal cycles do not prevent a time series to be stationary. Could you share an example of a stationary time series that is white noise? Arent't f(x) = cos(x) and g(x) = sin(x) stationary?
Excellent video!! great and concise explanation! But i just have one question left. What we forecast is the ts after differencing, but do we need to recover the differenced ts back to the original one? Will the forecast be the same? Or there is just no need to convert it back? Thanks in advance!
Ive been struggling to understand third condition of stationarity until now. I had an intuition it was something like seasonality but it was really not clear for me. Ty.
I have been watching your amazing teaching videos which are so intuitive. Would it be possible for you to post the sheet notes you work on somewhere? It would be easier for us to make notes on top of those instead of trying to make our own sheets. Thank you!
This explanation assumes “ strict sense” stationarity yes? There’s a slightly relaxed definition of stationarity called the “ wide sense” stationarity. I think the white noise process falls under ‘wide sense’ stationarity.
Thanks for the video! I am just a little bit confused by the example in the end of the video. As the time series has already been modeled by the linear regression model, then why do we need to do the differencing to create a new series for modeling using AR/MA/ARMA? So in the end, to model such series, we need to combine both linear regression and AR/MA/ARMA? Or is it that we use AR/MA/ARMA to substitute the linear regression model? Thanks!
Why do you say that, in example number 3, the mean rule is not violated? If we look at different intervals, like in example number 2, then the mean will not be constant (for instance, taking the first half of a period and the entire period).
That's a great question! You are right that we can always find two intervals with different means but the idea of stationarity has more to do with whether the mean is consistently getting higher or lower. In the second graph, the mean is consistently rising whereas in the third graph, the mean is centered around 0. Hopefully that helps a bit!
stationerity assumes variance is constant. But hetroskedecity says variance is time specific. But in time series we see present of stationerity and hetroskdecity as well. How is this explained? shd these two not be mutually exclusive
Doubt You said the mean for chart no. 3 is 0, as the local and global means are 0 but, the mean for chart no.3, varies locally depending upon where you take the interval. Eg. for half of the cycle it is different than 1/4 cycle
This doesnt make sense to me as the criteria we learn in class is different. "Stationarity means that the mean and the variance of the process are independent of time / constant over time". Examples in our class would rather look at the first graph as seasonality Second would be right. but third is stationary. But in general we have many graphs with bigger and smaller fluctuations but are still stationary. So the statement around time series "1" is in direct opposition to what we are learning. a stationary time series can still have higher and lower peaks but as long as that is constant over time it should be good? Im so confused.
The video about AR showed a seasonal time series (milk). In this video it says that stationary means there is no seasonality and stationary is important because then models like AR can be used. Those are conflicting statements. So I am confused. Who can help?
Hi. I have understood your lecture on stationary but in the end of video I couldn't get that mean part how non zero error et is zero. Could you please explain that part.
Hey @ritvikmath, I tried using ADF and KPSS on 3 sample datasets, similar to the ones in your video. One dataset violates the constant mean, the other thd constant variance, and lastly one with seasonality. However, it seems that both the ADF and KPSS are returning the datasets to be stationary for both non-constsnt deviation and the seasonality dataset. It accurately tests non-constant mean datasets. Any thoughts as to why that would happen?
In the white noise video you said white noise is not predictable. But now you are saying if a data is white noise than it is stationary which literally means it is predictable no? What is the explanation here... I'm new to statistics and don't understand really.
Quick question, there is a seasonality in my timeseries data but as per augmented dicky fuller test, my timeseries is stationary. Now I am confused. Could you please provide more context to why this might be happening?
Can't the process of taking a non-stationary random variable and making it stationary be generalized by saying the analysis works for processes whose derivative is some constant B_1.
Does anyone know why would we take the difference of the time series y and do our calculations Z, rather than fit a linear regression through y to remove the effect of Beta1*t to get a new time series (Y), where Y is stationary?
hello there, i have a query that,if i have a stationary time series data, then no matter how many sub-sequence i get form it. All the sub_seq should should be stationary. but what i observe is p_value is changing,. and even some sub_seq are throwing up p-value to be >0.05(means non-stationary).why is it so ??
Thank you but I am afraid, you are confused between seasonal and cyclical components because at 3:45 your data is all seasonal but just 3rd one is cyclical. Please consider then discuss again :)
you saved my life in my master study
Is this playlist good for ma eco student?
Currently preparing for my masters thesis (not economy related).
I hardly had any statistics courses during my studies, but now I need knowledge of time series analysis in order to create a forecasting model.
Within just 3 days consuming videos on this channel, my understanding of time series analysis went from virtually 0 to something that at least allows me to read relevant papers and understand the basic concept of the proposed models within.
This guy is amazing
You're amazing. I'm taking a time series course and the professor isn't so great at explaining any of these concepts. Really appreciate you and your videos! Please keep them coming.
Best math teacher I have ever had the pleasure of being taught by! ❤
Been following since I found your Ridge regression video. You're incredible, keep up the great work!
I appreciate it!
OMG your visual example and explanation are very clear and easy to follow. Thank you so much for making such a thoughtful video!
I've watched a bunch of videos now, started on SVM. The quality and pedagogy of these videos is superb! Great job!
Your videos are amazing, you make time series easier. Keep the good work
Thanks!
Such videos are the reason why I still love RUclips
so easy to understand, I've watched everything on RUclips but this is where things start to make sense lolllll
Damn, I was struggling to grasp this in my Finance class 8 years ago, and finally it landed!! You nailed it man!! Thnx a lot
no problem !
Seriously amazing, learned more from watching your videos for a hour then countless grad school lectures.
Fantastic Video!! The stationary has been puzzled me for a long time, this is the simplest and easiest video to understand!!
Really wish id discovered this channel before my semester ended
Thank you very much for such amazing class !
you are seriously a life savor, much love
Thanks this corrected a lot of my misunderstanding!
Great to hear!
Can you answer why B1t - B1t-1 = B1?
Nice explained! I would like to see one practical example that would further elaborate this matter. Anyway great video and thanks!
Thanks! And good suggestion
Very concise and clear explanation...
Incredible useful for our my masters thesis
Man !
your explanation is a life saver for Me thanks a lot :)
You are absolutely master piece
Concept of stationarity is nicely explained
I like the pictorial way of u teaching time series makes it 1000x more appreciable. Tnks alot
U are amazing.. i finally understand what time series are .. keep it up .. 🤩🤩🤩
No problem!
Thank you for this helpful video
Glad it was helpful!
Great work, super nice and simple explanations! You rock :D
Yeah you are really great hope you continue to make the awesome videos ❤️❤️❤️
Thanks for clearing up the question about whether we can do a transformation like Zt to make the series stationary.
Damn I need to refresh on some stuff but this helps out so much 🙏
Thanks!
thank you for the video
Excellent guide, thanks
Found another gem on youtube :)
Ritvik, this was the most clear explanation of stationary I have ever found. THANK YOU!!!
Excellent! Thank you!
excellent work. Your great sharings save me
hey no problem!
thank you so much
perfect video, thanks!
Thanks for the video!
Just insane! Thank you so much
Very well explained. Can you pl include a video on ADF test and how to interpret the P value?
there is seasonality in your example...there's an upward trend, as well as seasonality about the trend
Outstanding video,
Any chance there is a video where you code this or solve an example with some values for those constant in the final equation for Z(t)
Thanks a lot
Well paced. Please keep it up!
Hi, your video is excellent, making time series much more understandable. But I couldn't find the video specific for Augmented Dickey-Fuller test in your videos. As you mentioned in this video, there is another video on ADF test. Thanks!
Great explanation !
CAN SOMEONE PLEASE EXPLAIN WHY DO WE NEED STATIONARITY FOR ARMA PROCESS PLEASE? WHAT WILL HAPPEN IF IT IS NOT STATIONARY?
Thank you very much, love it
youre the best!
Stationarity in Time series
The models like AR, MA assume our time series to be stationary
stationary - mean constant, std dev constant and no seasonality
non - lot of fluctuations in the data. first there were immense fluctuations, now less -> different std dev
- mean is not constant. of a time chunk
- seasonality - periodic trend over time
how to check?
1. visually
2. global vs local tests (global mean =|= local mean)
3. augmented duckey fuller test
how to make it stationary
yt = b0 + b1 t + Et ( mean not constant in the graph)
new series
Zt = yt - yt-1
Zt = b1 + Et - Et-1
E(Zt) = b1 (mean of new series) (Et and Et-1 are constants from some distribution with mean 0)
Var(Zt) =
great explanation! Thanks
wonderful video
Hi! Thank you a lot. Could you make some videos on cointegration and causality. Concepts are very tricky for me
thank you
You're welcome
Good explanation, thanks. However, I am a bit confused with the condition on seasonality and wikipedia says seasonal cycles do not prevent a time series to be stationary. Could you share an example of a stationary time series that is white noise? Arent't f(x) = cos(x) and g(x) = sin(x) stationary?
tx sir
Excellent video!! great and concise explanation! But i just have one question left. What we forecast is the ts after differencing, but do we need to recover the differenced ts back to the original one? Will the forecast be the same? Or there is just no need to convert it back? Thanks in advance!
May I know how is it that the beta1 t - beta1 t-1 equates to beta1?
By Assuming they are slope coefficients of the same process & t,t-1 are not independent
@@Hassan_MM. thank you!
Ive been struggling to understand third condition of stationarity until now. I had an intuition it was something like seasonality but it was really not clear for me. Ty.
nice content
I have been watching your amazing teaching videos which are so intuitive. Would it be possible for you to post the sheet notes you work on somewhere? It would be easier for us to make notes on top of those instead of trying to make our own sheets. Thank you!
Great !
Hey! Amazing content! However, I get lost in these formulas. Could you reccommend any course or book to learn more about these formulas? Thanks!
This explanation assumes “ strict sense” stationarity yes? There’s a slightly relaxed definition of stationarity called the “ wide sense” stationarity. I think the white noise process falls under ‘wide sense’ stationarity.
Thanks for the video! I am just a little bit confused by the example in the end of the video. As the time series has already been modeled by the linear regression model, then why do we need to do the differencing to create a new series for modeling using AR/MA/ARMA? So in the end, to model such series, we need to combine both linear regression and AR/MA/ARMA? Or is it that we use AR/MA/ARMA to substitute the linear regression model? Thanks!
thanks
For the 3rd example, is the mean constant over different time intervals ?
I have the same question!
Sir in the variance step k^2 should cancel other k^2 and should be zero… please clarify!
hello, could you please elaborate a little bit more on the 2K2, 8:56. Thanks
Why do you say that, in example number 3, the mean rule is not violated? If we look at different intervals, like in example number 2, then the mean will not be constant (for instance, taking the first half of a period and the entire period).
That's a great question! You are right that we can always find two intervals with different means but the idea of stationarity has more to do with whether the mean is consistently getting higher or lower. In the second graph, the mean is consistently rising whereas in the third graph, the mean is centered around 0. Hopefully that helps a bit!
stationerity assumes variance is constant. But hetroskedecity says variance is time specific. But in time series we see present of stationerity and hetroskdecity as well. How is this explained? shd these two not be mutually exclusive
much better than the professor!!!
Doubt
You said the mean for chart no. 3 is 0, as the local and global means are 0 but, the mean for chart no.3, varies locally depending upon where you take the interval. Eg. for half of the cycle it is different than 1/4 cycle
Can you do a practical example of going from the differences back to y, the variable that we really want to forecast.
Very good video, may I know what is Yt here representing?
How do you use seosonality on time series if you cannot have it with stationary data?
This doesnt make sense to me as the criteria we learn in class is different.
"Stationarity means that the mean and the variance of the process are independent of time / constant over time".
Examples in our class would rather look at the first graph as seasonality
Second would be right.
but third is stationary.
But in general we have many graphs with bigger and smaller fluctuations but are still stationary. So the statement around time series "1" is in direct opposition to what we are learning. a stationary time series can still have higher and lower peaks but as long as that is constant over time it should be good?
Im so confused.
The third is considered stationary tbh
Can you talk about ergodicity?
I dont understand why var(Zt) = 2k^2. Can someone explain it to me, please?
Thanks for the videos.. could you pls make a video on Dickey Fuller test
The video about AR showed a seasonal time series (milk). In this video it says that stationary means there is no seasonality and stationary is important because then models like AR can be used. Those are conflicting statements. So I am confused. Who can help?
Shouldn't it be Yt instead of just t in the equation. Can someone please explain??
8:55 Condition 3 of seasonality isnt satisfied right, graph is not cyclic, how is Zt stationary?
is the variance of (eps_t - eps_t-1)=2K^2=(eps_t + eps_t-1)=??????????????????? the left is minus the right is plus??.. thank you
Hi, what is unit root and why is it not a stationary ts?
How is the mean constant in the third plot? It's only zero if we take the time frame as 2π.
I am missing something ps help.
so, so helpful.....
Common. The third case has by no means constant mean !!
Hi. I have understood your lecture on stationary but in the end of video I couldn't get that mean part how non zero error et is zero. Could you please explain that part.
Why stationarity is important? and why the non stationary data getting captured correctly by ml models but not by arima?
Can you clarify on how you forecast y-t from z-t? May be with a simple example
Hey @ritvikmath, I tried using ADF and KPSS on 3 sample datasets, similar to the ones in your video. One dataset violates the constant mean, the other thd constant variance, and lastly one with seasonality. However, it seems that both the ADF and KPSS are returning the datasets to be stationary for both non-constsnt deviation and the seasonality dataset. It accurately tests non-constant mean datasets. Any thoughts as to why that would happen?
In the white noise video you said white noise is not predictable. But now you are saying if a data is white noise than it is stationary which literally means it is predictable no? What is the explanation here... I'm new to statistics and don't understand really.
Quick question, there is a seasonality in my timeseries data but as per augmented dicky fuller test, my timeseries is stationary. Now I am confused. Could you please provide more context to why this might be happening?
Can't the process of taking a non-stationary random variable and making it stationary be generalized by saying the analysis works for processes whose derivative is some constant B_1.
Is this correct? The Beta1 should not stand alone. It should be imo Beta1*(t - tsub(-1)).
Does anyone know why would we take the difference of the time series y and do our calculations Z, rather than fit a linear regression through y to remove the effect of Beta1*t to get a new time series (Y), where Y is stationary?
Can you please explain the time series by using R ?
Thanks for the suggestion, I'll try to include more R along with Python :)
hello there, i have a query that,if i have a stationary time series data, then no matter how many sub-sequence i get form it. All the sub_seq should should be stationary. but what i observe is p_value is changing,. and even some sub_seq are throwing up p-value to be >0.05(means non-stationary).why is it so ??
Thank you but I am afraid, you are confused between seasonal and cyclical components because at 3:45 your data is all seasonal but just 3rd one is cyclical. Please consider then discuss again :)