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Suppose that {ut : t ≤T}is a time series of independent observations with mean zero and common variance σ²= 4. Suppose further that {x, : t = T} is a time series satisfying: X₁= 0.6 X÷-₁ + U₁ + 0.1 U₁-₁ - 0.2 U₁2 + 5. Find the mean value, µ = E(x₁), of the time series. Compute o(h), the autocovariance function and p(h), the autocorrelation function of the process. Plot their graphs. c) If X100 = 10.0 would you expect X₁02 to be above or below the mean of the process? d) a) b) Find the values of Þ11, Þ22 and Þ33 - the values of the partial autocorrelation function (PAFC) at lags 1, 2 and 3 respectively.

Suppose that {ut : t ≤T}is a time series of independent observations with mean zero and common variance σ²= 4. Suppose further that {x, : t = T} is a time series satisfying: X₁= 0.6 X÷-₁ + U₁ + 0.1 U₁-₁ - 0.2 U₁2 + 5. Find the mean value, µ = E(x₁), of the time series. Compute o(h), the autocovariance function and p(h), the autocorrelation function of the process. Plot their graphs. c) If X100 = 10.0 would you expect X₁02 to be above or below the mean of the process? d) a) b) Find the values of Þ11, Þ22 and Þ33 - the values of the partial autocorrelation function (PAFC) at lags 1, 2 and 3 respectively.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 25EQ
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Suppose that {ut: t = T}is a time series of independent observations with mean zero and common variance o²= 4. Suppose further that {x, : t = T} is a time series satisfying: xt = 0.6 Xt-1 + ut + 0.1 Ut-1 - 0.2 Ut-2 +5. a) Find the mean value, µ = E(x₁), of the time series. b) Compute o(h), the autocovariance function and p(h), the autocorrelation function of the process. Plot their graphs. c) If X100 = 10.0 would you expect X102 to be above or below the mean of the process? ರ d) Find the values of Þ11, Þ22 and Þ33 - the values of the partial autocorrelation function (PAFC) at lags 1, 2 and 3 respectively.
Transcribed Image Text:Suppose that {ut: t = T}is a time series of independent observations with mean zero and common variance o²= 4. Suppose further that {x, : t = T} is a time series satisfying: xt = 0.6 Xt-1 + ut + 0.1 Ut-1 - 0.2 Ut-2 +5. a) Find the mean value, µ = E(x₁), of the time series. b) Compute o(h), the autocovariance function and p(h), the autocorrelation function of the process. Plot their graphs. c) If X100 = 10.0 would you expect X102 to be above or below the mean of the process? ರ d) Find the values of Þ11, Þ22 and Þ33 - the values of the partial autocorrelation function (PAFC) at lags 1, 2 and 3 respectively.
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