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!"#$% ’ () *$*+,-. /0. ".1#."
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2)#". 3$)10*+4 5.1) 0.*$ ##6 ".1#."7 Z t 2) #$8)10*/)$ *9):( (;. 8:(:1. ! <+)(31$)103=>44 ! ("?<+)(31$)103=>44 ! ("?<+)(31$)103@>>44 ! ("?<+)(31$)103@>>A0.*$B>A"6B>?@44 ! ("?<+)(31$)103@>>A0.*$B>A"6B=44
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’*$6)0 C*+D Z t E $)#". S n B Z 1 FGF Z n E 1*$6)0 C*+D H(*/)$*1,I J*13 S n 4B n* Z t 4 ! 1C KL M:0":03M3>A"*0<+.3M3L@A@4A @>>>A 1.< B N444 ! <+)(31C4 ! ("?<+)(31C4
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O$ .P*0<+. Q): C*$( () 0)6.+ ,):1 C.#%;( )8 ()6*, X t = c + a 1 *X t-1 + a 2 *X t-2 + a 3 *X t-3 + Z t X t = a 1 *X t-1 + a 2 *X t-2 + a 3 *X t-3 + Z t
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"(*/)$*1, O’3@4 X t = a 1 *X t-1 + Z t X t = 0.2*X t-1 + Z t X t = -0.6*X t-1 + Z t ! "#0?O’@KL*1#0*?"#03+#"(3*1BM3>?R44A $BR>>4 ! <+)(3"#0?O’@4
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OST *$6 OSJT )8 O’3@4 3 a 1 B>?U4
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2)$L"(*/)$*1, O’3@4 X t = 1.2*X t-1 + Z t ! "#0?O’@KL*1#0*?"#03+#"(3*1BM3@?R44A $BR>>4 ! V11)1 #$ *1#0*?"#03+#"(3*1 B M3@?R44A $ B R>>47 W*1W <*1( )8 0)6.+ #" $)( "(*/)$*1,
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N;. $)$L"(*/)$*1, O’3@4
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OST *$6 OSJT )8 O’3@4 3 a 1 B>?XX4
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H(*/)$*1, O’3R4 X t = a 1 *X t-1 + a 2 *X t-2 + Z t X t = 0.4*X t-1 + 0.2*X t-2 + Z t ! "#0?O’RKL*1#0*?"#03+#"(3*1BM3>?UA>?R44A $BR>>4 ! ("?<+)(3"#0?O’@4 Q): M*$ (."( (;. 0)6.+" #$ ,):1 ;C
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OST *$6 OSJT )8 O’3R4 3 a 1 B>?UA a 2 B>?R4
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2)$L"(*/)$*1, O’3R4 X t = 1*X t-1 + 0.2*X t-2 + Z t ! V11)1 #$ *1#0*?"#03+#"(3*1 B M3@A >?R44A $ B @>>>4 7 W*1W <*1( )8 0)6.+ #" $)( "(*/)$*1, X t = -1*X t-1 + 0.2*X t-2 + Z t
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H(*/)$*1, O’3Y4 X t = a 1 *X t-1 + a 2 *X t-2 + a 3 *X t-3 + Z t X t = 0.4*X
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This note was uploaded on 12/06/2011 for the course AMS 316 taught by Professor Xing during the Fall '09 term at SUNY Stony Brook.

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slide_091021 -...

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