For Question 3.1, using the equation from page 28, does it solve to 1/200 because p1 = 0 since all of the terms are independent in a whilte noise process, meaning that the covariance is 0?
[NEAS: Yes]
NEAS, the problem was solved using equation 3.2.6. Please confirm whether this equation should be memorized for the Fall 2010 sitting.
[NEAS: The exercise shows the exact solution. The final exam problems can be solved by the approximation.]
NEAS:
Do we need to know equation 3.2.6 for the final exam? Module 3 says we will not be tested on it, however it is used in the solution to practice problem 3.2.
(I was able to solve the problem using equation 3.2.5, but I just want to make sure that we are not responsible for knowing equation 3.2.6.)
Thanks.
TS Module 3 Trends
(The attached PDF file has better formatting.)
Time series practice problems means and correlations
*Question 3.1: Var()
A white noise process Yt = åt has 200 observations, with ã0 = 1.
What is Var()?
A. 0.001
B. 0.002
C. 0.005
D. 0.010
E. 0.050
Answer 3.1: C
ã0 = ó2 = 1.
Var() = (1/200)2 × 200 × ó2 = 1/200 = 0.005
(See Cryer and Chan page 28)
Var( ) = (ã0 / n) × [(1 + 2 × ñ1 × (n-1)/n ] = 1/200 = 0.00500
*Question 3.2: Autoregressive process
A stationary time series Y of 300 observations has ñk = (½)|k| for all k and ã0 = 1.
A. 0.01
B. 0.03
C. 0.05
D. 0.15
E. 0.30
Answer 3.2: A
Var() ≈
= (1.5)/(0.5) × 1/300 = 0.01000