Time series, normal distribution?

[MaxManus]

Homework Statement

If I have a time series model

x_1 = my + epsilon_1
x_i = my + a(x_{i-1} - my) + epsilon_i

epsilon_i are iid standard normal.

Can I then say that
y = a_1 x_1+a_2 x_2 + ... a_n x_n

is multi normal?

The Attempt at a Solution

All the x-es are normal since they are built up of previous epsilons thich are independent and normal.

But the x-es are not independent so can I then say that a linear combination of them is normal

 

[sunjin09]

absolutely, any linear combinations of joint Gaussian plus whatever constant is still joint Gaussian (in your case, iid Gaussian is a special joint Gaussian)

 

[MaxManus]

Thanks for the help.