TS Module 4: Variance of mean homework assignment
(The attached PDF file has better formatting.)Homework assignment: Variance of mean
An MA(2) process Yt
has N observations, with ó2e
= 1, –1 è1
+1, –1 è2
+1. What values of è1 and è2 maximize the variance of , the average of the Y values?What values of è1 and è2 minimizes the variance of , the average of the Y values?
Your answer should give a line of values for each part, such as è1
How should we reason through this homework assignment? Rachel:
Write the value of in terms of the å’s: yj
+ (1 – è1
+ (1 – è1
Most of the terms have (1 – è1
; only the two terms at the beginning and the two terms at the end have fewer è’s. Ignore these beginning and end terms (assuming n is large).
All the å’s are independent. We choose è1
to maximize or minimize (1 – è1
, which is easy.
For the homework assignment, ignoring the end terms is fine. If N is small, the answer differs slightly, and the calculations are messy.