The property of the sum of random errors

[nacrointfin]

Hi all:

If two random errors (a, b) are independent and each is in GARCH process. Do the sum of these two random errors (c = a + b) still be GARCH process? Any comment or reference is welcome.

Best,

Nacrointfin

[TomDoan]

No. Just take a simple example --- one process is ARCH(1), the other is just ARCH(0). If you check the expansion, you'll see that there's no way to get the variance as an ARCH or GARCH recursion.