# Time Series Analysis HW 03 Answer keys - 1 TIME SERIES...

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1 TIME SERIES ANALYSIS Assignment 3 answer keys 2.2The following trigonometric sum-difference formulas are needed: cos°± ± ²³ = cos°±³ cos°²³ ∓ sin°±³ sin°²³´°µ³ = ´°¶³ = 0implies that ´°·¸³ = 0; independent of ¹. Also, it is known that º»¼°µ³ = º»¼°¶³ = 1and that µand are uncorrelated. So, for any , ½¾²°·¸¿À, ·¸³ = ´°·¸¿À·¸³= ´ÁÂµ cos !°¹ + ℎ³# + ¶ sin !°¹ + ℎ³#\$%µ cos°!¹³ + ¶ sin°!¹³&’= º»¼°µ³ cos !°¹ + ℎ³# cos°!¹³ + º»¼°¶³ sin !°¹ + ℎ³# sin°!¹³= cos°!ℎ³ ;independent of ¹. Moreover, º»¼°·¸³ = cos°0³ = 1 < ∞. So, ¸,is stationary. Because -°ℎ³ = cos°!ℎ³is the ACVF of ¸,, by Theorem 2.1.1 it’s nonnegative definite. 2.8Write ·¸= .¸+ /·¸01= .¸+ /°.¸01+ /·¸02³ = ⋯ = .¸+ /.¸01+ ⋯ + /4.¸04+ /4¿1·¸0401.If ¸,is stationary, then on the one hand º»¼°·¸− /4¿1·¸0401³ = º»¼°·¸³ + /2°4¿1³º»¼°·¸0401³ − 2/4¿1½¾²°·¸, ·¸0401³= 8°0³ 1 + /2°4¿1³# − 2/4¿1

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Term
Fall
Professor
Irene Hueter
Tags
Trigraph, Time series analysis