Hi Ben -- just curious what a random walk with drift would look like in state-space form? I just want to confirm my understanding. Ideally something where the drift term was dynamic....Thanks!
+Lizi zhu Because alpha*t is equal to (alpha+alpha+alpha...) which is the same as adding a constant t times. Now, given that the variance of a constant is zero; therefore, the variance of alpha*t is equal to zero.
Why Xo is assumed to be0? What happens if it isn't 0? It will only be added by a constant term and that will still be independent of time. So why are we assuming it to be zero?
@@johnnyjonas564 To my mind it is just made to make the sums clean and clear. It doesn't matter it it doesn't equal zero, if it equalled 5 then the expectation would be 5 and the variance for it would be zero as it is constant over time, like like the alpha coefficient is constant and therefore has a variance of zero.
4:44 - 5:03 He explained in 19 seconds what the textbook took to explain in 30 pages.
True
With you videos more people were saved from being killed in university than from a doctors hand.. thanks a lot statistical life saver!!
you're the most brilliant economics teacher on the internet! :D
Life saver!
Thank you. This is very helpful.
I think Expectation of constant term is constant so E(Xt) should be at+Xo
I would like to watch the videos of first hitting models or first passage model also.
Thank you Sir for this instructive video !
How does the summation of the alphas lead to alpha t?
Hi Ben -- just curious what a random walk with drift would look like in state-space form? I just want to confirm my understanding. Ideally something where the drift term was dynamic....Thanks!
why alpha*t doesn't enter the variance please? I think you are saying it is uncorrelated with the error terms (e0, e1, e2...) thank you!
+Lizi zhu Because alpha*t is equal to (alpha+alpha+alpha...) which is the same as adding a constant t times. Now, given that the variance of a constant is zero; therefore, the variance of alpha*t is equal to zero.
alpha * t is a constant, and a variance of a constant is 0 -- doesn't contribute to the total variance.
Really nice!
nice
Why Xo is assumed to be0? What happens if it isn't 0? It will only be added by a constant term and that will still be independent of time. So why are we assuming it to be zero?
This is an unimportant assumption.
Normally one assumes to be starting at the "origin" on some coordinate system, which can be represented with zero
@@johnnyjonas564 I believe it's an "irrelevant" assumption that we start at the origin to make every move relative and normalized.
@@johnnyjonas564 To my mind it is just made to make the sums clean and clear. It doesn't matter it it doesn't equal zero, if it equalled 5 then the expectation would be 5 and the variance for it would be zero as it is constant over time, like like the alpha coefficient is constant and therefore has a variance of zero.
game changer in 5 mins
@1:10 shouldn't this equation exclude the Xt-2 as you are substituting it out - similarly as you did in the equation before, but with of Xt-1.
He did exclude Xt-2 when substituting it out. You must have mistaken Epsilon t-2 with Xt-2.
sorry for my question, but i didn´t understand why expectation of Xo is zero.
It started in the infinite past (we assume) so no innovations (epsilons) or drifts (alpha's) happened yet.