https://lectures.quantecon.org/jl/linear_models.html#stationarity-and-ergodicity

Hi All,

Many thanks for the fascinating lectures !!

Am struggling a bit with equation 14.

Was wondering if anyone could provide a proof .

alex

https://lectures.quantecon.org/jl/linear_models.html#stationarity-and-ergodicity

Hi All,

Many thanks for the fascinating lectures !!

Am struggling a bit with equation 14.

Was wondering if anyone could provide a proof .

alex

Hi Alex, glad to hear that you are enjoying them so far.

As for your question, are you referring to the PDF or online lectures? Perhaps you could provide us with a link to the relevant section of the online lectures?

Regards, John.

Hey John

Thanks so much for your swift answer.

Am using the online version - link:

“Lectures.quantecon.org/jl/linear_models.html#stationarity-and-ergodicity”

In the Autocovariance paragragh Equation 14 is just before the above link. Intuitively I was expecting to see some forms of transpose of A in the equation as A is not necessarily symetric. Also there is no mention of C… Am certain am missing something very basic…

Again many thanks and congratulations for what you have put together which is really impressive.

Meilleures salutations / Best regards

Alex

Hey Alex,

I’m at the airport (Changi airport, en route to Tokyo) so it’s a bit awkward to do the calculations, but I did a quick check for the case j=1 and the claim seems to be true. Why don’t you try verifying that case as well and see how you go? Have a look at the definition of Sigma_t, just before equation (7). You’re aiming for the left hand side of (14) to equal A Sigma_t when j=1. This works for me, with the shock term involving C dropping out since future shocks are independent of current state and shocks.

I hope that helps

John.