1. If a > 0 and X( 0 ) has mean b/a and variance σ 2 /( 2 a) , show that the process defined by is stationary and evaluate its mean and auto covariance function. 2. Evaluate EZ 4 t for the ARCH(1)...

1. Ifa >0 andX(0)has meanb/aand varianceσ
²
/(2a), show that the process defined by is stationary and evaluate its mean and auto covariance function.

2. EvaluateEZ4
_t
for the ARCH(1) process with 0<>
₁
1 and {e_t
} ∼ IID N(0,1). Deduce thatEX
⁴

_t

 ∞ if and only if 3α
²
₁
1.