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Need help with a time series question

Hi Guys,

I cannot get past this question. For the first part I have been calculating the variance of X(t) so as to get it in the form similar to the result the question looks for but I can't quite get it out.

Any help would be much appreciated

Nappy

Re: Need help with a time series question

Hey Nappy.

Assuming I.I.D for the e(t) processes, you can use Var[aX + bY] = a^2Var[X] + b^2Var[Y] where a and b are non-deterministic quantities not related to the X's or Y's in any way (completely independent).

Since you know the sequence is summable, then it should be part of l^2 which means that the inner product of <x,x> (x is your sequence represented as an infinite vector) should also be finite (summable) so the sum of variances should be summable.

Re: Need help with a time series question

Is it enough to say as we know the sequence is summable <x,x> will also be summable and therefore will be less than infinity?

Re: Need help with a time series question

It should be, but I don't know what your lecturer expects.

You may have to use properties that relate l^1 norms to l^2 norms. l^1 is just that the normal series is summable and l^2 is the space where the squared terms are summable. There are theorems in mathmatics that relate the various norms and l^1 norm is finite, then l^2 should be as well.

Since I don't know what your lecturer expects, you will have to think about what is adequate and what isn't.