Very interesting, thanks for this video. I have just one question, about how you explain at the end of the video, why a VAR model have more parameters to estimate compared to a VARM model, in case of multivariate analysis? VARM model need to estimate autoregressive and moving average parameters, VAR only autoregressive. From the example you have done in the video is not so clear, could you explain please?
Sure! It all has to deal with the moving average. With just AR pieces in the model, you can use least squares estimation to estimate things. However, to pull off the moving average pieces you need to estimate with iterative maximum likelihood (think iteratively estimation where we add a new observation into the training data one at a time to estimate the model). To do that iterative MLE you need partial derivatives on the multivariate scale. This is just a LOT of partial derivatives which makes things harder (taking much longer) than least squares.
Hey there. Thanks for your explanation. I am not clear on how you came about 320 parameters for AR(12). I counted 300 coefficients (60 for each eqn) and 5 constants.
Sure thing! The extra 15 parameters come from the correlation that gets estimated between each of the series in the multivariate sense as well. The errors have a multivariate gaussian distribution with a needed covariance matrix that needs estimating. That 5x5 matrix is symmetric so it only needs 15 terms to estimate. Hope this helps!
Thanks for your interest! Maybe in the future. For now, the next series is underway with anomaly detection. For seasonal VAR though, you just extend the VAR model much like the seasonal ARIMA model video.
Hi, quick question ... What if instead of y1, y2, etc being target variables they were just observations of the same variable? How would you set up a model in that case? Thanks
That is how the basic ARIMA models are structured. Imagine a variable a just a collection of observations. If that is what you have then you only have one target variable. At that point you can use any of the basic time series models like ARIMA, Exponential Smoothing, Prophet, etc. You can check out the videos on those as well as I think that would be what you are looking for!
This has to be the most entertaining overview of vector autoregression ive seen. Amazing!!
"Right?" "Don't answer that", brings me back all the memory at IAA!!
I wish you do video lectures on ANY topic ... great non-monotonous voice that never lets me sleep :) I get general ideas very well from your videos.
Wow in only 5 minutes! that deserves a huge like !!!
Thank you. Super useful
The VARMA(p,q) formula at 3:40 seems wrong. Shouldn't the coefficient matrices A and B be different for each lag? So A(i), B(j) instead of A1, B1?
Great catch! I knew that copy and paste would come back to bite me eventually :-)
Love your videos!!!
Very interesting, thanks for this video. I have just one question, about how you explain at the end of the video, why a VAR model have more parameters to estimate compared to a VARM model, in case of multivariate analysis? VARM model need to estimate autoregressive and moving average parameters, VAR only autoregressive. From the example you have done in the video is not so clear, could you explain please?
Sure! It all has to deal with the moving average. With just AR pieces in the model, you can use least squares estimation to estimate things. However, to pull off the moving average pieces you need to estimate with iterative maximum likelihood (think iteratively estimation where we add a new observation into the training data one at a time to estimate the model). To do that iterative MLE you need partial derivatives on the multivariate scale. This is just a LOT of partial derivatives which makes things harder (taking much longer) than least squares.
Looking forward to the Baysian part :)
Hey there. Thanks for your explanation. I am not clear on how you came about 320 parameters for AR(12). I counted 300 coefficients (60 for each eqn) and 5 constants.
Sure thing! The extra 15 parameters come from the correlation that gets estimated between each of the series in the multivariate sense as well. The errors have a multivariate gaussian distribution with a needed covariance matrix that needs estimating. That 5x5 matrix is symmetric so it only needs 15 terms to estimate.
Hope this helps!
thank you, hope more video about these topics, do you have AR and MA model ?
** video of AR and MA
I do! Here are the links:
ua-cam.com/video/Mc6sBAUdDP4/v-deo.html
ua-cam.com/video/zNLG8tsA_Go/v-deo.html
ua-cam.com/video/dXND1OEBABI/v-deo.html
Could you please post a video about SVAR model? Thanks!!!
Thanks for your interest! Maybe in the future. For now, the next series is underway with anomaly detection.
For seasonal VAR though, you just extend the VAR model much like the seasonal ARIMA model video.
Hi, quick question ... What if instead of y1, y2, etc being target variables they were just observations of the same variable? How would you set up a model in that case? Thanks
That is how the basic ARIMA models are structured. Imagine a variable a just a collection of observations. If that is what you have then you only have one target variable. At that point you can use any of the basic time series models like ARIMA, Exponential Smoothing, Prophet, etc. You can check out the videos on those as well as I think that would be what you are looking for!
😌
2:30 lmao
Ok, you lost me there in the end. I don't have enough RAM between my ears and my brain hit a memory overflow condition...