Generate AR(1) process {X_t}. Compute the first difference Y_t = X_t - X_(t-1). Draw ACF and PACF of {Y_t}. What can you say about this process? Is it again a AR(1) process? What can you say in general?
For the AR(2) processes with the following parameters, determine if AR(2) processes are stationary. Without drawing the graphs, what can you say about ACFs.

(a) ϕ1=1.2, ϕ2=−0.2

(b) ϕ1=0.6, ϕ2=0.3

(c) ϕ1=1.2, ϕ2=−0.7

(d) ϕ1=−0.8, ϕ2=−0.7

For the process Xt = ϕXt−2+Zt, determine the range of ϕ for which the process is stationary.

the functions have the same rate of change i think. i narrowed it down to this answer and "the rate of change of tour 1 is greater" but i got it wrong using that answer so im assuming its the answer above. (this is a question i also answered from the iready site if anyone needs a reference)

x^2 + 81

we can factor this using difference of square binomials.

rewrite the equation:

x^2 - (-81)

factor:

(a^2 - b^2) = (√a^2 + √b^2)(√a^2 - √b^2)

(x^2 - (-81) = (x + √-81)(x - √-81)

we can remove the - from under the radical by multiplying it by i.

(x^2 - (-81) = (x + i√81)(x - i√81)

(x^2 - (-81) = (x + 9i)(x - 9i)

we can check our answer by using foil:

x^2 - 9ix + 9ix - 81i^2

x^2 - 81^2

i^2 = -1

x^2 + 81

sorry for any inconvenience this may have caused try again

try again.