By NEAS - 10/17/2014 9:15:50 PM
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 = et – è1 et-1 – è2 et-2 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 + è2 = k.
Jacob: How should we reason through this homework assignment?
Rachel: Write the value of in terms of the å’s: yj = ån + (1 – è1) ån-1 + (1 – è1 – è2) ån-2 + …
Most of the terms have (1 – è1 – è2) ån-2 ; 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 and è2 to maximize or minimize (1 – è1 – è2) ån-2, 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.
|
By ekitelinger - 1/27/2018 5:16:15 PM
This looks different from the homework assignment I printed. The one that I see has exhibit 3.10 and is showing standardized residuals versus Fitted VAlues for the temp. Seasonal means model.
I’m wondering about questions C and D. For C, it asked if toy sales are higher in December (500,000) and low in February (50,000). Would you expect the residuals to have a higher variance in December or February? What’s the intuition behind this? It does not seem obvious to me.
Part D asks why this reasoning does not apply to daily temperature.
Would you please help me understand the idea behind this, or where in the book it explains this reasoning?
|
|