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
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.
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.]
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]