Thanks for the great video! I had a small doubt which probably is stupid/rudimentary but still if you could clear? At 8:32, why are we assuming epsilons are serially uncorrected if the very premise of proving the yt's mean 0 and stationary covariance properties in wold's representation was that it doesn't satisfy all 3 properties of 0 mean, stationary cov and serial uncorrelation (which by definition makes Wold's representation unnecessary) as at 2:58 Thanks!
Setting Yt = epsilont satisfies the template of the Wold's theorem (here, you are assuming b0=1 and all other b's to be zero). This simple Yt is indeed zero mean and also covariance stationary, but the problem with this Yt is that there is no link between its value at time t and any value of its lagged values (at times prior to t) i.e. autocovariance for all lags is zero. As proved later on this video, using the templated specification provided by Wold's theorem, autocovariances comes out to be non-zero (dependent on the chosen b's, but not on time).
Thank you, Don Joseph. Yup I should have. I assume its difficult to edit / replace videos on UA-cam, but I'll definitely take note of this aspect for future.
Clear explanation, thanks for this
Thank you. Very good explanation
Please keep making time series videos
Thanks for the great video! I had a small doubt which probably is stupid/rudimentary but still if you could clear?
At 8:32, why are we assuming epsilons are serially uncorrected if the very premise of proving the yt's mean 0 and stationary covariance properties in wold's representation was that it doesn't satisfy all 3 properties of 0 mean, stationary cov and serial uncorrelation (which by definition makes Wold's representation unnecessary) as at 2:58
Thanks!
Setting Yt = epsilont satisfies the template of the Wold's theorem (here, you are assuming b0=1 and all other b's to be zero). This simple Yt is indeed zero mean and also covariance stationary, but the problem with this Yt is that there is no link between its value at time t and any value of its lagged values (at times prior to t) i.e. autocovariance for all lags is zero.
As proved later on this video, using the templated specification provided by Wold's theorem, autocovariances comes out to be non-zero (dependent on the chosen b's, but not on time).
Very clear explanation. Thanks a lot!!
Glad that the video was helpful, Qianyun.
Amazingly explained...!!
Thank you Brijesh for the kind words of appreciation.
Thanks for the useful video. it would be great if you can explain or give a formal definition of the Wold Representation in the start.
Thank you, Don Joseph. Yup I should have. I assume its difficult to edit / replace videos on UA-cam, but I'll definitely take note of this aspect for future.
Awesome boss
the wold = ZA WARUDO