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.
What is Var()?
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