(d) You are told that o² = 1, 0₁ = 0.2 and 02 = -0.1 is the variance for the time series mean estimator less efficient or more efficient than the T = 20 sample size ensemble average i.i.d. case? Justify your answer with a relevant calculation and explanation using the formula in Equation (1) provided above in part (c) of this question.

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In this question you will consider ergodicity and time series averages.
Consider the following MA (2) time series model:
Ytt 01€t-1 - 0₂€t-2
-
Var (Y) = 7+²7 ²2 (1-1)
T
(2-1) +2 +
(-0₁ +010₂)
(1 + 0² +02)
(1 + 0² +02)
(1)
(d) You are told that o² = 1, 0₁ = 0.2 and 0₂ = -0.1 is the variance
for the time series mean estimator less efficient or more efficient
than the T = 20 sample size ensemble average i.i.d. case?
Justify your answer with a relevant calculation and explanation
using the formula in Equation (1) provided above in part (c) of
this question.
Transcribed Image Text:In this question you will consider ergodicity and time series averages. Consider the following MA (2) time series model: Ytt 01€t-1 - 0₂€t-2 - Var (Y) = 7+²7 ²2 (1-1) T (2-1) +2 + (-0₁ +010₂) (1 + 0² +02) (1 + 0² +02) (1) (d) You are told that o² = 1, 0₁ = 0.2 and 0₂ = -0.1 is the variance for the time series mean estimator less efficient or more efficient than the T = 20 sample size ensemble average i.i.d. case? Justify your answer with a relevant calculation and explanation using the formula in Equation (1) provided above in part (c) of this question.
Expert Solution
Step 1

Given:-

            To compare the variance of the time series which means the variance estimator T = 20.

The average sample lesson is:

                         Var Y¯ = σ2T               = 120               = 0.05

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