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.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

step-by-step explanation: