# A2 - show non-constancy of error variance? iv. provide a...

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STA 4005B ASSIGNMENT 2 Due date: February 15, 2008 1. Suppose Z t = a t - 0 . 3 a t - 1 + 0 . 3 a t - 2 - 0 . 4 a t - 3 where σ 2 a = 4. Find V ar ( 1 100 100 X t =1 Z t ) 2. Fit the monthly series (refer to data1.xls) by the following two models: (a) Z t = β 0 + β 1 cos(2 πft ) + β 2 sin(2 πft ) + X t where f = 1 12 with E ( X t ) = 0. (b) A seasonal mean model. That is Z t = μ t + X t with E ( X t ) = 0 and μ t = β 1 , t = 1 , 13 , 25 ,..., 133 ( i.e for Jan ); β 2 , t = 2 , 14 , 26 ,..., 134 ( i.e for Feb ); . . β 12 , t = 12 , 24 , 36 ,..., 144 ( i.e for Dec ) . (c) With each ﬁt, i. provide a multiple time series plot of the data and ﬁtted values. ii. provide a time series plot of the residuals. Do the residuals oscillate in a predictable manner? iii. provide a plot of the residuals against the ﬁtted values. Does the plot
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Unformatted text preview: show non-constancy of error variance? iv. provide a histogram (with Options: Lower bound=-14, Upper bound=14 and Interval width=2 in Splus) and a Q-Q plot of the residuals. Do the residuals look like normal? v. provide an autocorrelation plot of the residuals, to lag 36. (d) For each model, calculate the ﬁtted value and the actual residual for June, 1968. (e) Which model would you prefer? Why? NOTE: The data set ’data1.xls’ can be downloaded from http://www.cuhk.edu.hk/wbt...
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## This note was uploaded on 11/02/2011 for the course STAT 4005 taught by Professor Wu,kaho during the Spring '08 term at CUHK.

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