H6 - H6 HW3(due Jan 31 Exercise 4.4 from the textbook and Problem 1 Explore the correlation structure of the following models X t =.7 X t-1.5 X t-2

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H6 HW3 (due Jan. 31). Exercise 4.4 from the textbook and Problem 1 Explore the correlation structure of the following models, 12 .7 .5 , .7 .3 , tt t t t t X XX XZ Z Z −− =−+ =+ Z by simulating their realizatins of 500 observations and computing ACFs and PACFs. Comment on how these cut off. Problem 2 Sample mean 100 0.157 X = was computed from a sample of size 100 generated from a MA(1) process with mean μ and 2 0.6, 1 θσ = −= . Construct an approximate 95% CI for . Are the data compatible with the hypothesis that 0 = ? _________________________________________________________________________________________________________ Confidence Intervals (CIs) for the Mean of a Stationary Time Series is estimated from data by the sample mean 1 1 n nn t X X n = = . For ARMA models, v ~N , X n ⎛⎞ ⎜⎟ ⎝⎠ & , where for large , n v( h h ) γ =−∞ = , or () , 2 X hh γσ ρ = 2 V , X X n σ & , where for large , . n 1 V12 ( ) h h = Then an approximate 100(1 )% α (or 1 )) CI for is given by 1/ 2 2 VV , X X Xz αα σσ −+ , where is the 2 z 2 quantile of the standard normal distribution. Example 1 An approximate 95% CI (or 0.95 CI) for is given by
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This note was uploaded on 09/23/2009 for the course MATH 200 taught by Professor Gur during the Spring '09 term at Accreditation Commission for Acupuncture and Oriental Medicine.

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H6 - H6 HW3(due Jan 31 Exercise 4.4 from the textbook and Problem 1 Explore the correlation structure of the following models X t =.7 X t-1.5 X t-2

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