Hello Mario, I am a big fan of your videos in your dynamic regression playlist. I’ve been recently learning about transfer function models in a time series textbook by William S Wei and another by Montgomery, however the lack of adequate examples makes it difficult to learn. I’ve learned about how to read the cross correlation function with its many patterns, however I know that often you cannot find your parameters “b, r, s” by viewing the CCF of the original time series. This might be due to non stationary data. Wei discusses how to “prewhiten” the input series with an ARIMA model and then “filter” the output series with the same model. This is extremely confusing for me, since we are using a model to filter the output series that may not be appropriate for it. Do you have any insight on this process? Another question I have for you regards the process before prewhitening and filtering. In both textbooks, Wei and Montgomery claim that before you prewhiten your input series and filter your output series, both series must be stationary. Of course this includes applying box-cox transformations where necessary, which is easy enough. Then, if the input series requires differencing, then I feel comfortable applying an ARIMA(1,1,1) model, for example. But to make the output series stationary, would I difference and then apply the same ARIMA(1,1,1) model? Wouldn’t that be differencing twice, which is too much? Sorry for being confusing and/or too hypothetical, I am just trying to learn as much as I can to use these transfer function models in practice. Thanks for your time and great job on the videos!
Hi Andrew, Thanks for your comment. I think that you have better insights than you think. Regarding your second point, I totally agree that taking differences and then applying ARIMA(1,1,1) is like an ARIMA(1,2,1). The first point is trickier. Filtering the data is not innocuous at all. Wei's claim is based on the (not always correct) assumption that filtering a signal leaves the noise Gaussian, which is not correct in general. Usually, this is not relevant as you don't want a "true model" of your time series but a "good tool" to make forecasts. I guess that this is behind the whole philosophy of those books (if it works....). Going back to the estimation part, estimating b,r,s (or whatever) is not hard only for the non-stationarity of the problem. More often than not, the problem is that there is not enough information in the series to "identify" (that's the technical name) all the parameters and hyperparameters. My approach (in research) is far from this overall framework of transfer functions. I try to understand one potential generating model of that time series and then use Bayesian methods to estimate it. Again, thanks for your insightful comments.
@@MarioCastroPonce Ok, I realize my second question was just a little careless because I checked Wei’s equations for transfer function models and only the PHI(B) and THETA(B) expressions are used to filter the output series. The order of differencing only depends on the series themselves. Thanks for that. You make some great points that I never really thought about before, which is the “if it works” thought process behind Wei and pretty much all other time series authors whose books I’ve read. I am curious about what you mean by using using Bayesian methods to estimate parameters of a working model. I’m still an undergrad so I unfortunately don’t know a lot of terminology. Thank you very much for your thoughtful reply and taking the time to make such informative videos. Your channel is a hidden gem.
@@andrewdisher2086 Thank you. I'm considering to create a kind-of ebook using the videos and the code and leave it for free online (probably by late September). Say tuned just in case...
Hello Mario, I am a big fan of your videos in your dynamic regression playlist. I’ve been recently learning about transfer function models in a time series textbook by William S Wei and another by Montgomery, however the lack of adequate examples makes it difficult to learn.
I’ve learned about how to read the cross correlation function with its many patterns, however I know that often you cannot find your parameters “b, r, s” by viewing the CCF of the original time series. This might be due to non stationary data. Wei discusses how to “prewhiten” the input series with an ARIMA model and then “filter” the output series with the same model. This is extremely confusing for me, since we are using a model to filter the output series that may not be appropriate for it. Do you have any insight on this process?
Another question I have for you regards the process before prewhitening and filtering. In both textbooks, Wei and Montgomery claim that before you prewhiten your input series and filter your output series, both series must be stationary. Of course this includes applying box-cox transformations where necessary, which is easy enough. Then, if the input series requires differencing, then I feel comfortable applying an ARIMA(1,1,1) model, for example. But to make the output series stationary, would I difference and then apply the same ARIMA(1,1,1) model? Wouldn’t that be differencing twice, which is too much?
Sorry for being confusing and/or too hypothetical, I am just trying to learn as much as I can to use these transfer function models in practice. Thanks for your time and great job on the videos!
Hi Andrew,
Thanks for your comment. I think that you have better insights than you think.
Regarding your second point, I totally agree that taking differences and then applying ARIMA(1,1,1) is like an ARIMA(1,2,1).
The first point is trickier. Filtering the data is not innocuous at all. Wei's claim is based on the (not always correct) assumption that filtering a signal leaves the noise Gaussian, which is not correct in general. Usually, this is not relevant as you don't want a "true model" of your time series but a "good tool" to make forecasts. I guess that this is behind the whole philosophy of those books (if it works....).
Going back to the estimation part, estimating b,r,s (or whatever) is not hard only for the non-stationarity of the problem. More often than not, the problem is that there is not enough information in the series to "identify" (that's the technical name) all the parameters and hyperparameters.
My approach (in research) is far from this overall framework of transfer functions. I try to understand one potential generating model of that time series and then use Bayesian methods to estimate it.
Again, thanks for your insightful comments.
@@MarioCastroPonce Ok, I realize my second question was just a little careless because I checked Wei’s equations for transfer function models and only the PHI(B) and THETA(B) expressions are used to filter the output series. The order of differencing only depends on the series themselves. Thanks for that.
You make some great points that I never really thought about before, which is the “if it works” thought process behind Wei and pretty much all other time series authors whose books I’ve read. I am curious about what you mean by using using Bayesian methods to estimate parameters of a working model. I’m still an undergrad so I unfortunately don’t know a lot of terminology.
Thank you very much for your thoughtful reply and taking the time to make such informative videos. Your channel is a hidden gem.
@@andrewdisher2086 Thank you. I'm considering to create a kind-of ebook using the videos and the code and leave it for free online (probably by late September). Say tuned just in case...
@@MarioCastroPonce Looking forward to it!
And How to predict? I try but always error. Anw my independent variable are 3🤔