H2 - H2 HW1 (due Jan. 17). Exercise 3.1 from the textbook...

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Unformatted text preview: H2 HW1 (due Jan. 17). Exercise 3.1 from the textbook and Problem 1 For the autocovariance function, { } 1 2 1 2 1 2 ( , ) ( ) ( ) = t t t t E X t X t , show that { } 1 2 1 2 1 2 ( , ) ( ) ( ) = t t t t E X X t t . Problem 2 Show that a strictly stationary process with 2 { } t E X < is weakly stationary. Problem 3 Consider t t X t Z = + + , where and are known constants and { } 2 ~ WN(0, ) t Z . Is t X stationary? Why? Problem 4 Let { } 2 ~ IID(0, ) t Z . Determine the mean and ACVF of 1 = t t t X Z Z , and state whether it is stationary. Problem 5 Using R, generate records of length 500 of AR(1) with 0.5 = and MA(1) with 0.5 = and compute their ACFs. ________________________________________________________________________________________________________ A process is called second-order stationary (or weakly stationary ) if its mean is a constant and its autocovariance function (ACVF) depends only on the lag:...
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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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H2 - H2 HW1 (due Jan. 17). Exercise 3.1 from the textbook...

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