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Unformatted text preview: White Noise Y t = e t e t s are i.i.d. N ( , 2 e ) ACF PACF k = 0, k &gt; 0 kk = 0, k &gt; 0 ===================================================================== AR(1) Y t = 1 Y t 1 + e t ( 1 1 B ) Y t = e t ACF PACF k = 1 k 11 = 1 = 1 kk = 0, k &gt; 1 AR( p ) Y t = 1 Y t 1 + 2 Y t 2 + + p Y t p + e t ( B ) Y t = e t ACF PACF k die out exponentially kk = 0, k &gt; p MA(1) Y t = e t 1 e t 1 Y t = ( 1 1 B ) e t ACF PACF 1 = 2 1 1 1 + k = 0, k &gt; 1 kk = k k 2 1 4 1 2 1 1 ... 1 + + + + = ( ) ( ) 1 2 1 2 1 1 1 1 + k k MA( q ) Y t = e t 1 e t 1 2 e t 2 q e t q Y t = ( B ) e t ACF PACF k = 2 2 1 1 1 ... 1 ... q q k q k k + + + + + + + , k = 1, , q 1 . q = 2 2 1 ... 1 q q + + + , k = 0, k &gt; q kk die out exponentially ARMA( p , q ) ( B ) Y t = ( B ) e t ACF PACF...
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This note was uploaded on 12/17/2010 for the course STAT 420 taught by Professor Stepanov during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Stepanov
 Statistics

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