Never have I ever seen arch/garch models explained with this level of intuitiveness before. Thanks Prof. I have a few questions tho as this doesn't perfectly look similar to how it's written in textbooks. You explain that in the variance equation for ARCH1 the return variance at time t+1 depends on the lagged squared return (that's the variance) at time t, but isn't reserved for the GARCH model ? Because that's how almost every econometrics textbook explains it. And is the lagged squared "forecasted value" in the variable equation in GARCH as shown in the video, equivalent to the lagged squared error ? Again isn't that supposed to be seen in ARCH? I feel like things got mixed up for me.
So it really depends on terminology. A lot of econometric books will refer to the return at the error term because they are finding volatility for errors from another model as compared to the raw returns themselves!
Great video. thank you. You explain it well and in a non-boring manner. So, in the variance formula, the assumption is that it's the population variance with 1/t. for the sample variance with 1/(t-1) this assumption won't work.
Exactly! In the end, it really is just an approximation anyway. The goal is to try and get a good estimate of variance in the smallest time frame possible. That is why squared returns are a decent estimate of this value!
If the averages aren't 0 then you can model them! Maybe it is a basic model of just the overall average where you can just subtract that from your data before moving to GARCH modeling. But it could be more complicated! You could easily use an ARIMA model to forecast and model the mean then look at the residuals left from your model to use GARCH models on those!
Thank you very much, Profs, for this very handy video. I've been learning the Arch and Garch model and have really been struggling to deal with the notation and expression in the papers. Your way of addressing the problem is really straightforward and inspiring. Btw, could you pls help me to get a grasp of the residual terms in a GRACH model?. It's been making me confused for some time As we know, after estimating the parameters of a Garch model, for example, GARCH(1,1) model. So we can forecast the return of tomorrow's stock by the equation: r_(t+1) = σ _(t+1)* ε_(t+1) where σ _(t+1) is our forecast volatility for tomorrow from our GARCH (1,1) model and ε_(t+1) is i.i.d from N(0,1) distribution. That means the forecast return tomorrow is still unknown since ε_(t+1) is a random variable. So where we can get the fitted return for tomorrow and calculate the residual afterward?
More than happy to help! The goal isn't to get the return from these models, but just the volatility. You also have to be careful because we are assuming normality, but it is the actual variance of that normality that we are trying to model! For example, a lot of the times we assume that the returns are normally distributed around 0 but the ARCH/GARCH model is trying to model the variance of those normally distributed returns. Hope this helps!
Those charts are created in Excel/PowerPoint. I find them really good at created professional charts in an easy way. Now, I don't use Excel for the analysis at all, but it is good for charting!
Wached mit 1 hour video and couldn't understand the concept and you just explained it in 5 mins, amazing
Excellent explanation, that makes the notation much easier to understand. Thank you for this great video and sharing your knowledge
Glad it was helpful!
That video had to be recorded...
You and rikvitmath make the best econometrics videos on whole UA-cam
Mind blowing! Practically made it easy to relearn the ARCH/GARCH framework. Thanks for sharing with us.
Glad it was helpful!
Sweet explanation, loved it! Thank you very much!
You're very welcome!
Very good and concise video!
Thank you for this excellent video!
Oh wow, such a great video!
Hilarious explanation - thank you!
Excellent video!
Great Video! Thank you for sharing
Thanks for watching!
Never have I ever seen arch/garch models explained with this level of intuitiveness before. Thanks Prof. I have a few questions tho as this doesn't perfectly look similar to how it's written in textbooks. You explain that in the variance equation for ARCH1 the return variance at time t+1 depends on the lagged squared return (that's the variance) at time t, but isn't reserved for the GARCH model ? Because that's how almost every econometrics textbook explains it. And is the lagged squared "forecasted value" in the variable equation in GARCH as shown in the video, equivalent to the lagged squared error ? Again isn't that supposed to be seen in ARCH? I feel like things got mixed up for me.
So it really depends on terminology. A lot of econometric books will refer to the return at the error term because they are finding volatility for errors from another model as compared to the raw returns themselves!
Awesome explanation 👍
Thanks for these videos, I love the channel!
Great video. thank you. You explain it well and in a non-boring manner.
So, in the variance formula, the assumption is that it's the population variance with 1/t. for the sample variance with 1/(t-1) this assumption won't work.
Exactly!
In the end, it really is just an approximation anyway. The goal is to try and get a good estimate of variance in the smallest time frame possible. That is why squared returns are a decent estimate of this value!
@@AricLaBarr thank you very much for taking the time to reply. it does make sense.
What do you do if the average of the returns are not zero?
Excellent video by the way
If the averages aren't 0 then you can model them! Maybe it is a basic model of just the overall average where you can just subtract that from your data before moving to GARCH modeling. But it could be more complicated! You could easily use an ARIMA model to forecast and model the mean then look at the residuals left from your model to use GARCH models on those!
Thank you very much, Profs, for this very handy video. I've been learning the Arch and Garch model and have really been struggling to deal with the notation and expression in the papers. Your way of addressing the problem is really straightforward and inspiring.
Btw, could you pls help me to get a grasp of the residual terms in a GRACH model?. It's been making me confused for some time
As we know, after estimating the parameters of a Garch model, for example, GARCH(1,1) model. So we can forecast the return of tomorrow's stock by the equation: r_(t+1) = σ _(t+1)* ε_(t+1) where σ _(t+1) is our forecast volatility for tomorrow from our GARCH (1,1) model and ε_(t+1) is i.i.d from N(0,1) distribution. That means the forecast return tomorrow is still unknown since ε_(t+1) is a random variable. So where we can get the fitted return for tomorrow and calculate the residual afterward?
More than happy to help! The goal isn't to get the return from these models, but just the volatility. You also have to be careful because we are assuming normality, but it is the actual variance of that normality that we are trying to model!
For example, a lot of the times we assume that the returns are normally distributed around 0 but the ARCH/GARCH model is trying to model the variance of those normally distributed returns. Hope this helps!
Great video! Is it possible to teach something about the Barndorff-Nielsen and Shephard Model?
Thanks for your interest! Maybe in the future. For now, the next series is underway with anomaly detection.
2:20 Sir how to create these charts?? Do we have to do this in E-views or Excel???
Those charts are created in Excel/PowerPoint. I find them really good at created professional charts in an easy way. Now, I don't use Excel for the analysis at all, but it is good for charting!
Hello sir, should we have stationary data for applying GARCH model?
Yes! Now, a lot of times we do ARCH/GARCH models on residuals from other models so they should naturally be stationary (at least around the mean).
the clue begins after 2:38
Hi
I need a follow up on this.
Point me in the right direction
Happy to help. Follow-up on the concepts or how to implement these?