Mr Lambert. Your videos have completely reversed my view on stats and econometrics. I have switched from confusion and disdain of the course to understanding and ALMOST enjoying it. Thank you.
Hi Ben. I' m so grateful I've found your videos. It has helped me a lot on being more critical towards all machine learning approaches on time series. You're extremely gifted. Continue the excellent work!
so can two variables with different covariances but both covariance stationary (like those two in the top right figure) form a linear regression model?
Alex Cheung It doesn't. Because the assumption is not about the working of OLS but about the series being stationary. Stationarity absolutely requires constant covariance with respect to time, thus Xt in the bottom left corner is not stationary (and Yt would not be either had it the same covariance structure). However, your OLS estimate of Beta might actually work in the case of both being non-covariance stationary while still having the same covariance structure over time.
Great informative video! How do we know if a process is covariance-stationary? Is there any formal way of testing if a time series is covariance-stationary or not? Like a dickey-fuller test
***** Use rank ADF and rank KPSS test together to test whether or not the process is unit root stationary, unit root non-stationary, fractionally integrated or indeterminate. Applying the rank transformation makes the stationary tests more robust to non-linearity and non-normality. If you're hardcore, I would recommend the Forward Backward Range Unit Root test.
Hi, the top right graph does not show two variables which are supposed to be linked. It merely shows two types of processes with different AR parameters. Hope that helps! Best, Ben
Hi Ben, after watching your video, I am still confused with the meaning of con(x(t), x(t-1)). What's the meaning behind the covariance between the value of X at two consecutive times? That confuses me a lot. Could you please make an example and explain to me? I am taking the FRM exam and I really want to make sure I understand the topic deeply. Thanks!
I am confused because I hold the opinion that covariance is sort of "inner-correlation" between TWO RV's. But in this problem, Xt and Xt-1 are not two RVs, they are the values of a single variable X at two different times. I know this video is made 6 years ago but I hope you could see my question and respond. Please help!!
Hi, Thanks for your message. I am only using Y here to mean a particular dependent variable, and X to mean an independent variable. The idea is that we are trying to explain movements in Y with movements of X. There is no real distinction per se, they are only labels of two variables. Hope that helps! Ben
Ben Lambert well this isn't the only video that i've seen that in. It seems like you're using Xt as the dependent variable since it's on the vertical axis... and also, what's the difference between t+1 and t-1 as in Xt-1 or Xt+1??
Ben Lambert I also see in the graph on the bottom left that you wrote Xt and Yt together... I do appreciate it you can reply back to me or if I message you more often because I have an econometrics midterm this week and I'm really stressed out because I don't know what I'm doing :(
Mr Lambert.
Your videos have completely reversed my view on stats and econometrics. I have switched from confusion and disdain of the course to understanding and ALMOST enjoying it.
Thank you.
yeah same here,, ALMOST.. lol
I must be wierd-I LOVE econometrics! But this course has helped MASSIVELY! My notes from this are actually useable!
Thanks Ben. You have an amazing talent in making difficult concepts clear! Your work has been my go-to source during my Masters!
Very well explained. Would recommend this channel to any student studying econometrics
Hi Ben. I' m so grateful I've found your videos. It has helped me a lot on being more critical towards all machine learning approaches on time series. You're extremely gifted. Continue the excellent work!
Once again this is explained way better then anywhere else!!
better than anywhere else, say for example, professors in uni.
Thank you for the great explanations. They really help a lot!
Awesome explain! Very nice to understand the covarince stationary in graphically.
Really really helpful! Thank you so much! The graphs are great demonstrations.
great videos, man! keep up! these videos helped me a lot.
Very good video. Really miss your new videos
Thank you Ben! This helps me a lot!
This was amazingly helpful !!! Thank uYou so much!
Hi, glad to hear it was helpful. All the best, Ben
So cov(xt) and cov(yt) should equal a constant?
Beautiful video!
Mesmerising
so can two variables with different covariances but both covariance stationary (like those two in the top right figure) form a linear regression model?
Isnt Xt+h one particular value and Xt another value.. So what does it mean when you say covariance between these two values?
what if yt and xy BOTH sharing the same covariance structure like the one on the bottom left? Does it satisfy the assumption?
Same question
Alex Cheung It doesn't. Because the assumption is not about the working of OLS but about the series being stationary. Stationarity absolutely requires constant covariance with respect to time, thus Xt in the bottom left corner is not stationary (and Yt would not be either had it the same covariance structure). However, your OLS estimate of Beta might actually work in the case of both being non-covariance stationary while still having the same covariance structure over time.
Great informative video! How do we know if a process is covariance-stationary? Is there any formal way of testing if a time series is covariance-stationary or not? Like a dickey-fuller test
***** Use rank ADF and rank KPSS test together to test whether or not the process is unit root stationary, unit root non-stationary, fractionally integrated or indeterminate.
Applying the rank transformation makes the stationary tests more robust to non-linearity and non-normality. If you're hardcore, I would recommend the Forward Backward Range Unit Root test.
what about the graph in the top right, will that give a spurious relation? each timesies independantly has a constant covariance
Hi, the top right graph does not show two variables which are supposed to be linked. It merely shows two types of processes with different AR parameters. Hope that helps! Best, Ben
Hi Ben, after watching your video, I am still confused with the meaning of con(x(t), x(t-1)). What's the meaning behind the covariance between the value of X at two consecutive times? That confuses me a lot. Could you please make an example and explain to me? I am taking the FRM exam and I really want to make sure I understand the topic deeply. Thanks!
I am confused because I hold the opinion that covariance is sort of "inner-correlation" between TWO RV's. But in this problem, Xt and Xt-1 are not two RVs, they are the values of a single variable X at two different times. I know this video is made 6 years ago but I hope you could see my question and respond. Please help!!
Thank you so so much!!!
Thank you so much.
Thank you!!
Very helpful!! Than you :)
i'm super confused about the whole difference between Xt and Yt. what's the difference? Why use Xt instead of Yt?
Hi, Thanks for your message. I am only using Y here to mean a particular dependent variable, and X to mean an independent variable. The idea is that we are trying to explain movements in Y with movements of X. There is no real distinction per se, they are only labels of two variables. Hope that helps! Ben
Ben Lambert
well this isn't the only video that i've seen that in. It seems like you're using Xt as the dependent variable since it's on the vertical axis... and also, what's the difference between t+1 and t-1 as in Xt-1 or Xt+1??
Ben Lambert
I also see in the graph on the bottom left that you wrote Xt and Yt together... I do appreciate it you can reply back to me or if I message you more often because I have an econometrics midterm this week and I'm really stressed out because I don't know what I'm doing :(