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Unformatted text preview: STAT 420 Examples for 12/06/2007 Fall 2007 1. Consider the AR(2) process for which it is known that = 0, Y t = 1 Y t 1 + 2 Y t 2 + e t Based on a series of length N = 100, we observe y 99 = 2, y 100 = 3. a) Suppose r 1 = 0.50, r 2 = 0.55. Use the method of moments to estimate 1 and 2 . YuleWalker equations for an AR(2) process: 1 = 1 + 2 1 2 = 1 1 + 2 b) Use your answers to part (a) to forecast y 101 , y 102 , and y 103 . Y N + 1 = + 1 ( Y N ) + 2 ( Y N 1 ) + e N + 1 1 + N y = () 1 N y = E N ( Y N + 1 ) = + 1 ( y N ) + 2 ( y N 1 ) Y N + 2 = + 1 ( Y N + 1 ) + 2 ( Y N ) + e N + 2 2 + N y = ( ) 2 N y = E N ( Y N + 2 ) = + 1 ( 1 + N y ) + 2 ( y N ) Y N + 3 = + 1 ( Y N + 2 ) + 2 ( Y N + 1 ) + e N + 3 3 + N y = ( ) 3 N y = E N ( Y N + 3 ) = + 1 ( 2 + N y ) + 2 ( 1 + N y ) Y N + k =...
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This note was uploaded on 04/29/2010 for the course STAT stat 420 taught by Professor Stepanov during the Spring '07 term at University of Illinois at Urbana–Champaign.
 Spring '07
 STEPANOV

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