A4 - t . (b) Plot the time series {5 Z ( t ) } against t ....

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STATISTICS 4005 ASSIGNMENT 4 Due date: March 28, 2008 1. Consider the process Z t = a t - 0 . 4 a t - 1 - 0 . 4 a t - 2 + 0 . 4 a t - 3 . Find the partial autocorrelation φ 11 , φ 22 and φ 33 . 2. Show that an IMA(1,1) process Z t - Z t - 1 = a t - θa t - 1 can be written in the form Z t = ¯ Z t - 1 ( λ ) + a t where a t ’s are white noises, λ = 1 - θ and ¯ Z t - 1 ( λ ) = λ X j =1 (1 - λ ) j - 1 Z t - j . 3. From a series of 144 observations, we calculate r 1 = - 0 . 73 , r 2 = 0 . 51 , r 3 = - 0 . 38 , r 4 = 0 . 02, and | r k | ≤ 0 . 09 for k > 4. On the basis of this information alone, what ARIMA model would we tentatively specify for the series. Explain. 4. A stationary time series of length 121 produced sample partial autocorrelations of φ 11 = 0 . 8 , φ 22 = - 0 . 6 , φ 33 = 0 . 08, and φ 44 = 0 . 00. Based on this information alone, what model would we tentatively specify for the series? Explain. 5. Denote { Z ( t ) , t = 1 ,..., 111 } be the time series of the data set “iowa.xls”. (a) Plot the time series { Z ( t ) } against
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Unformatted text preview: 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 = 30. (e) Plot the autocorrelation of {5 Z ( t ) } with Maximum Lag k = 30. (f) Plot the autocorrelation of {5 2 Z ( t ) } with Maximum Lag k = 30. (g) Plot the partial autocorrelation of { Z ( t ) } with Maximum Lag k = 30. (h) Plot the partial autocorrelation of {5 Z ( t ) } with Maximum Lag k = 30. (i) Plot the partial autocorrelation of {5 2 Z ( t ) } with Maximum Lag k = 30. (j) Specify a tentative ARIMA model for the { Z ( t ) } . Explain. NOTE: The data set ’data2.xls’ can be downloaded from http://www.cuhk.edu.hk/wbt...
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