Suppose that {ut: t =T}is a time series of independent observations with mean zero and common variance ♂²= 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.
Suppose that {ut: t =T}is a time series of independent observations with mean zero and common variance ♂²= 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.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Suppose that {ut: t =T}is a time series of independent observations with mean zero
and common variance ♂²= 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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