In this question you will consider ergodicity and time series averages. Consider the following MA (2) time series model: Y₁ = t 01€t-1 - 0₂€t-2 (a) Explain with a diagram and no more than 4-5 sentences the dif- ference between an ensemble average and a time series average.
In this question you will consider ergodicity and time series averages. Consider the following MA (2) time series model: Y₁ = t 01€t-1 - 0₂€t-2 (a) Explain with a diagram and no more than 4-5 sentences the dif- ference between an ensemble average and a time series average.
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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Transcribed Image Text:In this question you will consider ergodicity and time series averages.
Consider the following MA(2) time series model:
Y₁ = €t — 0₁€t−1 - 0₂€t-2
(a) Explain with a diagram and no more than 4-5 sentences the dif-
ference between an ensemble average and a time series average.
Expert Solution
Step 1
The ensemble average is the average of a large number of independent realizations of the same stochastic process, where each realization is treated as a member of a probability distribution. It represents the long-term behaviour of the process, and it is often used in theoretical analysis. The time series average, on the other hand, is the average of a single realization of the process over a certain time period. It represents the behaviour of the process at a specific time window, and it is often used in empirical analysis.
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