40055 - θ(b Find an estimate of the noise variance σ 2...

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STATISTICS 4005 ASSIGNMENT 5 Due date: April 2, 2004 1. Find the partial autocorrelations φ 11 , φ 22 and φ 33 of the MA(1) process Z t = a t - 0 . 6 a t - 1 . 2. From a series of length 100, we have computed r 1 = 0 . 8 , r 2 = 0 . 6, r 3 = 0 . 5 ¯ Z = 3, and a sample variance of 4. If we assume that an AR(2) model with a constant term is appropriate, how can we get (simple) estimates of φ 1 , φ 2 , θ 0 , and σ 2 a ? 3. If { Z t } satisfies an AR(1) model with φ = 0 . 7, how long a series do we need to estimate the true φ = ρ 1 with 95% confidence that our error is no more than ± 0 . 1. 4. Consider an MA(1) process for which it is known that the mean is zero. Based on a series of length 3, we observe Z 1 = 0 , Z 2 = - 1 . 2, and Z 3 = 0 . 6. (a) Find the conditional least-squares estimate of
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Unformatted text preview: θ . (b) Find an estimate of the noise variance σ 2 a . (Hint: Iterative meth-ods are not needed in this simple case.) 5. Consider the dataset is in ‘dataset3.xls’ Suppose the AR(2,2) model W t = φ 1 W t-1 + φ 2 W t-2 + a t , W t = ∇ 2 Z t do fit the data. Find the estimates of φ 1 and φ 2 by (a) the method of moments; (b) conditional least squares; (c) using the ARIMA command. NOTE: The data set “dataset3.xls” can be downloaded from http://www.sta.cuhk.edu.hk/khwu/courses/sta4005/ under the subsection Time Series Data used for Assignments....
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