40054a - ) } against t . (b) Plot the time series {5 Z ( t...

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STATISTICS 4005 ASSIGNMENT 4 Due date: March 19, 2004 1. Identify the following as specific ARIMA models: (a) Z t = 2 . 3 Z t - 1 - 1 . 6 Z t - 2 + 0 . 3 Z t - 3 + a t + 0 . 2 a t - 1 (b) Z t = 1 . 4 Z t - 1 - 0 . 4 Z t - 2 + a t - 0 . 5 a t - 1 - 0 . 3 a t - 2 (c) Z t = 1 . 2 Z t - 1 - 0 . 36 Z t - 2 + a t - a t - 1 + 0 . 25 a t - 2 2. Consider the IMA(1,1) model Z t = Z t - 1 + 0 . 2 + a t - 0 . 5 a t - 1 where Z t = 0 for t < - 10. Suppose Z t can also be written in the form Z t = Z 0 t + β 0 + β 1 t where Z 0 t is an IMA(1,1) model with E ( 5 Z 0 t ) = 0 where 5 Z 0 t = Z 0 t - Z 0 t - 1 . Find the values of β 0 and β 1 . 3. Find the partial autocorrelations φ 11 , φ 22 and φ 33 of the MA(1) process Z t = a t - 0 . 7 a t - 1 . 4. Consider an AR(1) series of length 100 with φ = 0 . 7. (a) Would you be surprise if r 1 = 0 . 6? (b) Would r 10 = - 0 . 15 be unusual? 5. A stationary time series of length 144 produced sample partial autocorrelations of φ 11 = 0 . 9 , φ 22 = - 0 . 8, and φ kk = 0 . 002 , k 3. Based on this information alone, what model would we tentatively specify for the series? Explain. 6. Denote { Z ( t ) , t = 1 , . . . , 111 } be the time series of the data set “dataset2.xls”. (a) Plot the time series { Z ( t
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Unformatted text preview: ) } against t . (b) Plot the time series {5 Z ( t ) } against t . (c) Plot the time series {5 2 Z ( t ) } against t . (d) Plot the autocorrelation of { Z ( t ) } with Maximum Lag k = 36. (e) Plot the autocorrelation of {5 Z ( t ) } with Maximum Lag k = 36. (f) Plot the autocorrelation of {5 2 Z ( t ) } with Maximum Lag k = 36. (g) Plot the partial autocorrelation of {5 Z ( t ) } with Maximum Lag k = 36. (h) Plot the partial autocorrelation of {5 2 Z ( t ) } with Maximum Lag k = 36. (i) Specify a tentative ARIMA model for the { Z ( t ) } . Explain. NOTE: The data set “dataset2.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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This note was uploaded on 01/20/2012 for the course STA 4005 taught by Professor ? during the Spring '08 term at CUHK.

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