3. Let {X} be an autoregressive process of order one, usually written as AR(1).(a) Write down an equation defining X₁ in terms of an autoregression coefficient aand a white noise process {} with variance σ².Explain what the phrase "{} is a white noise process with variance o?" means.(b) Derive expressions for the variance 70 and the autocorrelation function Pk, k0,1,. of the {X} in terms of o2 and a.Use these expressions to suggest an estimate of a in terms of the sample autocor-relations {k}.(c) Suppose that only every second value of X is observed, resulting in a time seriesY X2, t = 1, 2,....Show that {Y} forms an AR(1) process. Find its autoregression coefficient, sayd', and the variance of the underlying white noise process, in terms of a and o².(d) Given a time series data set X1, ..., X256 with sample mean = 9.23 and sampleautocorrelations ₁ = -0.6, 2 = 0.36, 3 = -0.22, p = 0.13, 5 = -0.08,estimate the autoregression coefficients a and a' of {X} and {Y}.

Answered: 3. Let {X} be an autoregressive process…

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter4: Writing Linear Equations

Section: Chapter Questions

Problem 12CR

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