TUGAS FUNGSI TRANSFER

(1)

Abstrak

Abstrak —Krisis —Krisis ekonomi ekonomi global global memiliki memiliki dampakdampak yang signifikan terhadap perkembangan pasar modal di yang signifikan terhadap perkembangan pasar modal di IIndndoonenessiaia. . InInddoonenesisia a mmererupupakakan an nenegagara ra yayangng diprediksikan akan mengalami kemajuan pesat dalam diprediksikan akan mengalami kemajuan pesat dalam bida

bidang ng perperekonekonomiomian an dundunia. ia. PotPotensensi i besbesar ar ini ini harharusus didukung dengan adanya Indeks harga saham gabungan didukung dengan adanya Indeks harga saham gabungan (I

(IHSGHSG) ) dadalalam m jajangngka ka papanjnjanang. g. InInflaflasi si tidtidak ak akaakann pe

pernrnah ah lelepas pas dadalalam m keketerterkaikaitatannynnya a dedengngan an IHIHSGSG.. Pendekatan untuk mengetahui hubungan antara inlasi Pendekatan untuk mengetahui hubungan antara inlasi dan IHSG metode !I" dan fungsi transfer. "odel dan IHSG metode !I" dan fungsi transfer. "odel a

akkhhiirr trtranansfsfer er fufuncnctiotionn yanyang g dipdiperoeroleh leh memenjelnjelaskaaskann bah

bah#a IHS#a IHSG G memmemilikiliki depeni dependendensi densi dengan tigan tingkangkatt infl

inflasi paasi pada mada masa sesa sebelubelumnymnya. a. "od"odel akhiel akhirr transfertransfer function

function adalahadalah y y_t_t ==99,,405405++ x x_t_t ++[([(11−− B B))aa_t_t]]

Kata Kunci

Kata Kunci —Inflasi$ —Inflasi$ IHSG$ IHSG$ !I"$ %ung!I"$ %ung si &ransfer.si &ransfer.

I.

I. PENDAHULPENDAHULUANUAN

Krisis ekonomi go!" memiiki #"m$"k %"ng signi&ik"n Krisis ekonomi go!" memiiki #"m$"k %"ng signi&ik"n 'er"#"$ $erkem!"ng"n $"s"r mo#" #i In#onesi". D"m$"k 'er"#"$ $erkem!"ng"n $"s"r mo#" #i In#onesi". D"m$"k kri

krisis sis keke"ng"ng"n "n #n#ni" i" "'""'"  e!e!i i #ik#iken" en" #en#eng"n g"n kriskrisisis ek

ekononomomi i ggo!o!" " %"%"ng ng 'e'er*r*"#"#i i #i #i AmAmererik" ik" *e*e""s s s"s"ng"ng"'' !er$eng"r

!er$eng"r 'er"#"$ 'er"#"$ In#onesi". In#onesi". K"ren" K"ren" se!"gi"n se!"gi"n !es"r!es"r eks$or In#onesi" #i"kk"n #i $"s"r Amerik" #"n 'en' s"*" eks$or In#onesi" #i"kk"n #i $"s"r Amerik" #"n 'en' s"*" " i' s"ng"' mem$eng"ri $erekonomi"n #i In#onesi". " i' s"ng"' mem$eng"ri $erekonomi"n #i In#onesi". +"

+"" " s"'s"'  #"m#"m$"k $"k %"%"ng ng $"i$"ing ng !e!er$er$eng"rng"r  #"r#"ri i krikrisissis ekonomi Amerik" "#"" IH+ %"ng sem"kin 'i#"k se"' ekonomi Amerik" "#"" IH+ %"ng sem"kin 'i#"k se"' [1].

[1].

In#eks H"rg" +""m "!ng"n "'" %"ng e!i #iken" In#eks H"rg" +""m "!ng"n "'" %"ng e!i #iken" #eng"n IH+, 'en' men*"#i se!" is'i" %"ng "kr"! #i #eng"n IH+, 'en' men*"#i se!" is'i" %"ng "kr"! #i 'eing" se!"gi"

'eing" se!"gi"n n m"s%m"s%"r"k"'. -ere!i !"gi "r"k"'. -ere!i !"gi $"r" ines'or$"r" ines'or $"s"r

$"s"r s""m. s""m. IH+ IH+ "#"" "#"" in#eks in#eks %"ng %"ng mengkr mengkr "rg""rg" s""m %"ng #i*" #i !rs". +e/"r" g"ris !es"r mer$"k"n s""m %"ng #i*" #i !rs". +e/"r" g"ris !es"r mer$"k"n s"

s"' ' """"' ' kkrin#rin#ik"'ik"'or or #"r#"ri i $er$ergerger"kk""kk"n n "rg"rg""r""rg"g" s""m %"ng #i'r"ns"ksik"n #i s"' !rs" e&ek #""m krn s""m %"ng #i'r"ns"ksik"n #i s"' !rs" e&ek #""m krn 2"k'

2"k'  'er'e'er'en' n' [3]. "gi ines'or[3]. "gi ines'or, , IHIH+ #"$"' + #"$"' #i*"#i#i*"#ik"nk"n s"' $e#om"n

s"' $e#om"n #""m #""m meng"mmeng"m!i !i ke$'ke$'s"n s"n !erin!erines'"es'"sisi n"

n"mmn n inini i 'i'i#"#"k k mm''"k "k ""rrs s #i#iikik''i i k"k"reren" n" #"#"""mm m

meemm''ssk"k"n n nn''k k mememm!!eei i "'"'" " mmeen*n*""  s"s"""mm en#"kn%" !er#"s"rk"n in&orm"si %"ng 'e$"' #"n m"'"ng. en#"kn%" !er#"s"rk"n in&orm"si %"ng 'e$"' #"n m"'"ng. -ingk"' $er'm

-ingk"' $er'm!"n %"ng #i"r"$k"n #"n !"n %"ng #i"r"$k"n #"n *"ngk" 2"k'*"ngk" 2"k' %"ng #i'e'"$k"n [3].

%"ng #i'e'"$k"n [3]. es

es"rn%"rn%" " $eng"r$eng"r  %"n%"ng g #i'im!#i'im!k"n k"n IHIH+ 'er"#"$+ 'er"#"$ $erekonomi"n

$erekonomi"n neg"r", neg"r", m"k" m"k" $er $er #i"kk"n #i"kk"n $er"m""n$er"m""n 'e

'err"#""#"$ $ 'in'ingkgk"' "' IHIH+ + $"$"#" #" m"m"s" s" %%"n"ng g "k"k"n "n #"#"'"n'"ng.g. P

Peneneeii'i'i"n "n inini i mmenenggggnn"k"k"n "n #"#"'" '" //oosse e !!""n"n"nn #ik"

#ik"renren"k"n "k"n n'n'k k menmenge'ge'"i "i $er$ergerger"k"n "k"n ni"ni"i i s"s""m"m se'i"$ !"nn%" seingg" ines'or men*"#i '" !"n "$" se'i"$ !"nn%" seingg" ines'or men*"#i '" !"n "$" s"*

s"*" " %"%"ng ng menmengn'gn'ngkngk"n "n n'n'k k meme"k"kk"n k"n $en$en"2""2"r"nr"n *"

*" !ei !ei #""m #""m !erines'"si. !erines'"si. D"'" D"'" /ose /ose "#"" "#"" "rg""rg" $en'$"n

$en'$"n #i "kir #i "kir sesi #"n #ign"ksesi #"n #ign"k "n "n se!"g"i "/"n n'se!"g"i "/"n n' kk mer

mer"m""m"k"n k"n ni"ni"i i IHIH+ %"ng + %"ng "k""k"n n #i!#i!k" k" $"#$"#" " $er$erio#io#ee se"n*'n%". Per"m""n IH+ 'i#"k #"$"' "n%" #i#"s"rk"n se"n*'n%". Per"m""n IH+ 'i#"k #"$"' "n%" #i#"s"rk"n $"#"

$"#" #"'" #"'" is'oris is'oris 'ingk"' 'ingk"' IH+ IH+ s"*", s"*", n"mn n"mn *g" *g" "rs"rs me

mem$m$ereri'i'ngngk"n k"n &"&"k'k'oror&&"k"k'o'or r %%"ng "ng memem$m$engeng"r"rii &k'"si 'ingk"' IH+ #"n ke*"#i"nke*"#i"n 'er'en' %"ng &k'"si 'ingk"' IH+ #"n ke*"#i"nke*"#i"n 'er'en' %"ng menim

menim!k"n on*"k"n 'ingk"' !k"n on*"k"n 'ingk"' IHIH+, s"" +, s"" s"'n%s"'n%" " "#"""#"" in&"si [1]. In&"si "#"" $roses meningk"'n%" "rg""rg", in&"si [1]. In&"si "#"" $roses meningk"'n%" "rg""rg", #"

#"$"$"' ' **g" g" #i#ik"k"'"k'"k"n "n sese!"!"g"g"i i keken"in"ik"k"n n 'in'ingk"gk"' ' "r"rg"g" ko

konsnsmmen en #"#"nn"'"'" " memennrrnnnn%" %" nini""i i ""ng ng k"k"reren"n" !"n%"kn%"

!"n%"kn%" *m" *m" "ng "ng !ere#"r !ere#"r #i #i m"s%"r"k"'. m"s%"r"k"'. -er#"$"'-er#"$"' #

#" " ''**"n "n $e$err"m"m"""n"n, , %%""i'i'  nn''k k mmenenggerer'i 'i #"#"nn me

memomo#e#ekk"n "n memek"nk"nisisme me s's'okok"s"s'ik 'ik seser'r'" " memer"r"m"m"k"k"nn ke*"#i"n #i m"s" %"ng "k"n #"'"ng !er#"s"rk"n #"'" m"s" ke*"#i"n #i m"s" %"ng "k"n #"'"ng !er#"s"rk"n #"'" m"s" " [].

" []. PePemo#mo#e"e"n n s"s"' ' #"'#"'" " #er#ere' e' 2"2"k' (k' (time seriestime series)) 'i#"k *g" #i$eng"ri oe &"k'or&"k'or eks'ern" k"ren" 'i#"k *g" #i$eng"ri oe &"k'or&"k'or eks'ern" k"ren" si&"' ke'erk"i'"n "n'"r" 2"k' ke 2"k' %"ng #imiiki oe si&"' ke'erk"i'"n "n'"r" 2"k' ke 2"k' %"ng #imiiki oe #"'

#"'" " #er#ere' e' 2"2"k'k', , se#se#"ng"ngk"n k"n 'er'er#"$"#"$"' ' ke*ke*"#i"#i"nk"nke*"e*"#i"n#i"n 'e

'er'r'enen' ' %%"n"ng g !i!is" s" !e!er$r$eneng"g"rr  #"#"""m m kkrrn n 22"k"k'' 'erse

'erse!'. -er#"$"' !"n%"k me'o#e %"ng #"$"' !'. -er#"$"' !"n%"k me'o#e %"ng #"$"' #ign"k"#ign"k"nn n'k memo#ek"n #"'" 'ime series, s"" s"'n%" "#"" n'k memo#ek"n #"'" 'ime series, s"" s"'n%" "#"" me'o#e &ngsi 'r"ns&er. 6e'o#e &ngsi 'r"ns&er "#"" s"' me'o#e &ngsi 'r"ns&er. 6e'o#e &ngsi 'r"ns&er "#"" s"' mo#

mo#e e %"%"ng ng memenggngg"m!"m!"rk"rk"n "n !"!"2" 2" ni"i ni"i $re$re#iks#iksi i m"sm"s"" #e

#e$"$"n n #"#"ri ri ss"'"'  #"#"'"'" time seriestime series ((output series)output series) "#"" "#"" !er#"s"r

!er#"s"r $"#" $"#" ni"inini"ini"i "i m"s" m"s" " " #"ri #"ri 'ime 'ime series series i'i' sen

sen#iri #"n #iri #"n !er!er#"s#"s"rk"rk"n "n $$" " $"#$"#" " s"'s"'  "'""'"  e!e!ii timetime series

series %"ng !er!ng"n ( %"ng !er!ng"n (input seriesinput series) #eng"n o'$' series) #eng"n o'$' series 'erse

'erse!'. Penei'i"n !'. Penei'i"n ini ini !er'!er'*"n n'k *"n n'k memmemo#ek"o#ek"n n IHIH++ #

#eneng"g"n n $r$re#e#ikik'o'or r 'i'ingngk"k"' ' inin&&""si si %%"n"ng g #i#i""kkk"k"nn menggn"k"n me'o#e &ngsi 'r"ns&er.

menggn"k"n me'o#e &ngsi 'r"ns&er. II.

II. -IN7AUAN PU+--IN7AUAN PU+-AKAAKA

A.

A. Analisis Deret Analisis Deret Waktu (Time Series)Waktu (Time Series) Per

Per"m""m""n "n mermer$"$"k"n k"n """"' ' !"n!"n' ' %"%"ng ng $en$en'ing 'ing #"#""m"m $eren/"n""n

$eren/"n""n %"ng e&ek'i& #"n e&isien [4].%"ng e&ek'i& #"n e&isien [4].

L"ngk" $er'"m" #""m me"kk"n "n"isis

L"ngk" $er'"m" #""m me"kk"n "n"isis time seriestime series "#"

"#"" " i#ei#en'i&n'i&ik"sik"si i mo#mo#e e n'n'k k memei"i"' ' $o$o" " #"'"#"'". . H"H" $er'"m" %"ng

$er'"m" %"ng $er #i$er$er #i$er"'ik"n "'ik"n "#"" "#"" !"2" ke!"n%"k"n!"2" ke!"n%"k"n #

#""''"" timtime e seriserieses !ers!ersi&"' nons'"sioi&"' nons'"sioner, ner, se#"se#"ngk"n ngk"n $"#"$"#" "s

"s$e$ekk"s"s$e$ek k A8 A8 #"#"n n 6A 6A #"r#"ri i momo#e#e  A8A8II6A 6A "n"n%"%" !erken""n

!erken""n #eng"n #eng"n #ere' #ere' !erk"" !erk"" %"ng %"ng s'"sioner. s'"sioner. ee k"

k"reren" n" i' *iki' *ik" " ss"'"'  #"#"'"'" time seriestime series $o' menn*kk"n $o' menn*kk"n 'i#"

'i#"k k s'"s'"sionsioner er m"km"k" " $er$er  #is#is'"s'"sioneionerk"rk"n n [4][4]). ). KoKon#in#isisi s'"si

s'"sioner 'er#iri "'"s #" oner 'er#iri "'"s #" " %"i' s'"sion" %"i' s'"sioner #""m r"'"r"'"er #""m r"'"r"'" #"n

#"n s'"s'"siosioner ner #""#""m m "r"ri"nsi"ns[4][4]. . 7ik" 7ik" #"'#"'" " 'i#'i#"k "k s'"s'"siosionerner #

#""""m m ""rri"i"nsns, , mm""k" k" ##""$$""' ' ##iiss'"'"!!iikk""n n ##eengng""nn me

mengnggngn"k""k"n n 'r'r"ns"ns&o&ormrm"s"si i #"#"n n s"s"" " s"s"'n'n%%" " "#"#"""" #eng"n me"kk"n 'r"ns&orm"si o: ;o:.

#eng"n me"kk"n 'r"ns&orm"si o: ;o:. -r"ns&

-r"ns&orm"sorm"si i o:o:;o: ;o: mermer$"k"n $"k"n 'r"ns&'r"ns&orm"sorm"si i $"ngk"'$"ngk"' %"ng #"$"' #in%"'"k"n se!"g"i !erik'<

%"ng #"$"' #in%"'"k"n se!"g"i !erik'<

λ

λ λ λ λ

1

1 ))

((

=

(( ))

=

t t

−

t t t t

Z

T

(1) (1) Ni"i #"ri

Ni"i #"ri = #eng"n = #eng"n 'r"ns&orm"sin%" %"ng sering 'r"ns&orm"sin%" %"ng sering #ign"k"n#ign"k"n "#"" [5].

"#"" [5].

&abel '.

&abel '. -r"ns&orm"si o:;o: -r"ns&orm"si o:;o:

Pemo#e"n IH+

Pemo#e"n IH+ -

-erk"i'

erk"i' In&"si #eng"n

In&"si #eng"n 6e'o#e >ngsi

6e'o#e >ngsi

-r"ns&er

Nur Arifin, Suroyya Yuliana

Nur Arifin, Suroyya Yuliana11_{, Rida Dwi Lestari}_{, Rida Dwi Lestari}11

,,Nuraziza ArfanNuraziza Arfan11 Dr. Irhamah, S.Si, M.Si

Dr. Irhamah, S.Si, M.Si22

1

1_{Mahasiswa Jurusan Statistika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Institut Teknologi Sepuluh}_{Mahasiswa Jurusan Statistika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Institut Teknologi Sepuluh}

Nopember, Sukolilo 60111, Surabaya Nopember, Sukolilo 60111, Surabaya 2

2_{Dosen Data Analisis 2, Jurusan Statistika, Fakultas Matematika dan Ilmu Pengetahuan Alam}_{Dosen Data Analisis 2, Jurusan Statistika, Fakultas Matematika dan Ilmu Pengetahuan Alam} Institut Teknologi Sepuluh Nopember, Sukolilo 60111, Surabaya

Institut Teknologi Sepuluh Nopember, Sukolilo 60111, Surabaya

e-mail

(2)

ilai  (*ambda) &ransformasi 1 1@' 0,5 _1 0 Ln@' 0,5 1 @'

>ngsi A'okore"si "'" Autocorrelation Function (ACF) "#"" ""' %"ng men#e'eksi keer"'"n !ng"n ine"r "n'"r" $eng"m"'"n @' #"n @'  k $"#" #"'" 'ime series

%"ng #i$is"k"n oe 2"k' se!es"r k. 8ms &ngsi "'okore"si "#"" [5].

)

"r(

)

"r(

)

,

/o(

k t t k t t k

Z

+ + = ρ _B 0

γ

_k ()

>ngsi "'okore"si #ii'ng !er#"s"rk"n s"m$e %"ng #ii'ng #eng"n rms se!"g"i !erik' [5].

∑

= − = +

−

=

n t t k n t k t t k

Z

1 3 1

)

(

)

)(

(

C

ρ

(5)

>ngsi "'okore"si $"rsi" "'" Partial Autocorrelation unction (PA;>) "#"" kore"si "n'"r" @' #"n @'k !erni"i

s"m" #eng"n "'okore"si "n'"r" Z t −Z Ct ) #"n (

k t k t Z

Z + − C + ). >ngsi "'okore"si $"rsi" (PA;>) #"$"'

#irmsk"n se!"g"i !erik' [5].

) C ( ) C ( ) C ( ), C [( k t k t t t k t k t t t k Z Z !ar Z Z !ar Z Z Z Z Co" + + + + − − − − = ρ _()

P"#" $eng"m"'"n time series #im"n" s"m$e PA;>

#ino'"sik"n #eng"n

φ

kk #eng"n $eri'ng"n se$er'i %"ng

'e" #i!erik"n oe Dr!in "#"" se!"g"i !erik' [5].

∑

= = − + + + +

−

=

k # # k# k # # k k# k k k 1 1 1 1 1 , 1

1 φ

ρ

φ

ρ

φ

() #"n 1, 1, 1 , 1

ˆ

k j kj k k k k j

φ

₊

=

φ φ φ

−

₊ ₊ ₊ ₋ , #B 1, 3, ..., k

B. $%entiikasi &o%el A'$&A

I#en'i&ik"si mo#e A8I6A #"$"' #i"kk"n #eng"n mei"' $o' #"ri A;> #"n PA;>. e!er"$" mo#e A8I6A #"ri A;> #"n PA;> "#"" [5].

&abel +. K"r"k'eris'ik - eori A;> #"n PA;> n'k Proses +'"sioner

"odel ,% P,%

! (p) -rn se/"r"

eks$onensi" "'" sinso#i"

Cut o se'e" "g p " (-) Cuts o se'e" "g  -rn se/"r"

eks$onensi" "'" sinso#i" !" (p$-) -rn se'e" "g (F$) -rn se'e" "g ($F) ! (p) atau " (-)

Cut o se'e" "g F Cut o se'e" "g $

C. &o%el Autoreressi"e atau A' (p)

6o#e autoreressi"e (A8) !eror#e p men%"'"k"n s"' mo#e #im"n" $eng"m"'"n 2"k' t !erkom!in"si inier #eng"n $eng"m"'"n se!emn%" t-*+ t-,++ t-p. en'k $ers"m""n mo#e A8 ($) "#""< t p t p t t t Z Z Z a Z



=φ ₁



₋₁ +φ ₃



₋₃ +...+φ



₋ + _(G)

Un'k $roses "'oregressie or#e $er'"m" A8 (1) #i'is <

t t

t Z a

Z



=φ ₁



₋₁ + (9)

D.#i Siniikansi &o%el A'$&A

6o#e A8I6A %"ng !"ik "rs memeni "smsi s"" s"'n%" %"i' $en"ksir"n $"r"me'ern%" signi&ik"n. Hi$o'esis %"ng #ign"k"n $"#" $eng*i"n signi&ik"nsi $"r"me'er A8 "#"" []. H0 < φ p =0 H1 < φ p ≠0 +'"'is'ik U*i < ) C ( C P P S/ t φ φ = ₍₁₃₎ D"er" $eno"k"n <

-o"k H0 *ik" ni"i ,( )

3 ( n r t t − > _α _{"'" P} "alue  α

Hi$o'esis n'k $eng*i"n signi&ik"nsi $"r"me'er 6A "#""< H0 < θ ( =0 H1 < θ ( ≠0 +'"'is'ik U*i < ) C ( C ( ( S/ t θ θ = (1) D"er" $eno"k"n <

-o"k H0 *ik" ni"i ,( )

3 ( n r t t − > _α _{"'" P} "alue  α #im"n", n "#"" !"n%"kn%" o!ser"si r "#"" *m" $"r"me'er %"ng #i'"ksir /. Dianostic C0eckin

Asmsi se"n*'n%" $"#" 6o#e A8I6A n'k

men#"$"'k"n mo#e %"ng !"ik %"i' memeni #" "smsi resi#" "n'"r" "in !er#is'ri!si norm" #"n 10ite noise. Hi$o'esis $"#" $eng*i"n "smsi 10ite noise "#"" se!"g"i !erik' [5].

Hi$o'esis <

H0 <

ρ

₁

=

ρ

₃

=

...

=

ρ

₂

=

0

H1 < P"ing 'i#"k "#" ni"i

ρ

k ≠0

+'"'is'ik U*i <

∑

= −

−

+

=

2 k k

k

n

3

1 3 1

_C

)

(

)

3 (

ρ

(14) D"er" $eno"k"n < -o"k H0 *ik" ni"i  J

) , ( 3 m 2 − α

χ

"'" P"alue 

α

#im"n", n B !"n%"kn%" $eng"m"'"n k

ρ C B "'okore"si resi#" $"#" "g kek m B *m" $"r"me'er

(3)

Peng*i"n kenorm""n resi#" #i"kk"n #eng"n *i kolmooro" Smirno" []. Hi$o'esisn%" "#"" se!"g"i !erik' < Hi$o'esis < H0 <

F

(

x

)

=

F

₀

(

x

)

H1<

F

(

x

)

≠

F

0

(

x

)

+'"'is'ik U*i < ) ( ) ( ₀ s$ _S_x _F _x D =_x − (15) D"er" $eno"k"n <

-o"k H0 *ik" ni"i D > D(1−α ,n)

#im"n",

+ (:) < &ngsi $e"ng km"'i& %"ng #ii'ng #"ri #"'" s"m$e

>0(:) < &ngsi #is'ri!si %"ng #ii$o'esisk"n (norm")

>(:) < &ngsi #is'ri!si %"ng !em #ike'"i F. &o%el Transer Function

6o#e transer unction "#"" s"' mo#e time series %"ng mengg"m!"rk"n ni"i $re#iksi m"s" #e$"n #"ri s"'

time series (%"ng #ise!' output series "'"  ) %"ng

#i#"s"rk"n $"#" ni"ini"i m"s" " #"ri time series i' sen#iri #"n $"#" s"' "'" e!i time series %"ng

!er!ng"n (#ise!' input series "'"  ) #eng"n output

series 'erse!'. en'k mm $ers"m""n mo#e transer

unction #eng"n sinle input (  ) #"n sinle output (  )

"#"" se!"g"i !erik' [5].

B ()  

#im"n" <

B #ere' output %"ng s'"'ioner  B #ere' input %"ng s'"'ioner B #ere' noise

#eng"n   B     

+eingg" !is" #ii"' $"#" $ers"m""n !erik' ini. B         "'" B             Dim"n" <    B 0 1  3 3_{    ,}   B11 3 3   ,   B1 1  3 3   , #"n   B1 1  3 3    , 4./stimasi Parameter

-""$ se"n*'n%" e'e" me"kk"n i#en'i&ik"si mo#e "#"" me"kk"n es'im"si 'er"#"$ $"r"me'er #""m mo#e A8I6A. P"#" $enei'i"n ini $en"ksir"n $"r"me'er mo#e menggn"k"n me'o#e Con%itional 5east Suare (;L+). ;L+ mer$"k"n me'o#e 5east Suare #eng"n meng"smsik"n error $eng"m"'"n se!emn%" %"ng 'i#"k #i"m"'i s"m" #eng"n no #"n meminimmk"n *m" k"#r"' #"ri error mo#e ( sum o suare)<

 B 3B1

Un'k mo#e A8 ($), "#"" se!"g"i !erik' <

  , B 3,B1 B    1   1       Un'k mo#e 6A (F), "#"" se!"g"i !erik' <

  , B 3,B1 B 1 1 3 3   

Es'im"si $"r"me'er transer unction menggn"k"n

Con%itional 5east Suare, %"i' M, , , O #eng"n mem!"' error  %"ng 'i#"k #ike'"i #"n s"m" #eng"n no.

( , , ,  )B 3B0 #im"n" 0B m":Q$r1,!$s1R. 6.Pemili0an &o%el Ter7aik

A#"n%" !e!er"$" mo#e %"ng memngkink"n n'k #ign"k"n #""m $roses $er"m""n mem!erik"n s"'

$erm"s"""n !"r #""m menen'k"n mo#e 'er!"ik %"ng ses"i #ign"k"n #""m $roses $er"m""n. Pemii"n mo#e 'er!"ik #"$"' #i"kk"n !er#"s"rk"n error "si r"m""n. D"'" %"ng 'e" #i!"gi men*"#i #" !"gi"n, %"i' #"'" in sample #"n #"'" out sample m"singm"sing #ign"k"n #""m $eni"i"n mo#e. Un'k #"'" in sample #ign"k"n kri'eri" Akaike8s $normation Criterion (AI;) #"n Sc01art98s Bayesian Criterion (+;). +e#"ngk"n n'k #"'" out sample #"$"' #ign"k"n &ean Suare%

/rror (6+E #"n &ean A7solute Percentae /rror

(6APE). A#"$n !er!"g"i kri'eri" $emii"n mo#e 'er!"ik !er#"s"rk"n error "#"" se!"g"i !erik' [5] <

1. AI; ( Akaike8s $normation Criterion )

AI;(6) B n n σ

C

_a3 +

3 &

#im"n" < n B !"n%"kn%" $eng"m"'"n

6 B !"n%"kn%" $"r"me'er #""m mo#e

3

C

_a

σ

B es'im"si "ri"ns resi#"

3. +; (Sc01art98s Bayesian Criterion)

+;(6) B n n

σ

C

_a3

+

&

n n

#im"n" < n B !"n%"kn%" $eng"m"'"n

6 B !"n%"kn%" $"r"me'er #""m mo#e

3

C

_a

σ

B es'im"si "ri"ns resi#"

III. 6E-DE PENELI-IAN A. Sum7er Data %an !aria7el Penelitian

+m!er #"'" %"ng #ign"k"n #""m $enei'i"n ini "#"" #" !" #"'" sekn#er. D"'" $er'"m" mer$"k"n #"'" IH+ %"ng #i$eroe #"ri S"oo >in"n/e #"n #"'" ke#" mer$"k"n #"'" In&"si %"ng #i$eroe #"ri "nk In#onesi". T"ri"!e %"ng "k"n #ign"k"n "#"" IH+ #"n 'ingk"' In&"si se'i"$ !"nn%" #"ri '"n 3001 ingg" '"n 3013.

B. 5anka0-5anka0 Penelitian

6o#e %"ng ingin #i$eroe #"ri $enei'i"n ini "#"" mo#e &ngsi 'r"ns&er IH+ #eng"n $re#ik'or 'ingk"' in&"si. -""$"n'""$"n "n"isis #""m men/"$"i '*"n $enei'i"n ini "#"" se!"g"i !erik'.

&ahap '  Identifikasi /entuk "odel

I#en'i&ik"si mo#e mei$'i '""$"n'""$"n se$er'i !erik'.

1. 6em$ersi"$k"n #ere' input ('ingk"' in&"si) #"n output (IH+) "g"r mem$eroe #ere' input #"n output %"ng s'"'ioner.

3. 6enen'k"n mo#e A8I6A n'k #ere' input #"n me"kk"n pre10itenin $"#" #ere' 'erse!' n'k mem$eroe #ere' %"ng 10ite noise (  ) .

. 6e"kk"n pre10itenin $"#" #ere' output n'k

mem$eroe .

4. 6en#e'eksi Cross Correlation (;;>) #"n "'okore"si n'k #ere' input #"n #ere' output %"ng 'e" menalami

proses pre10itenin .

5. 6ene'"$k"n ni"ini"i (7+ r+ s) %"ng meng!ngk"n #ere' input #"n output .

. Pen"ksir"n mo#e transer unction semen'"r"

!er#"s"rk"n ni"i (7+r+s) %"ng #i'e'"$k"n se!emn%".

. 6e"kk"n $en"ksir"n "2" #ere' noise (  ) #"n

$eri'ng"n "'okore"si ser'" $"rsi" kore"sin%".

G. 6ene'"$k"n ( , ) n'k mo#e A8I6A ( ,0,) #"ri

(4)

&ahap +  Penaksiran Parameter "odel Transfer Function

Pen"ksir"n $"r"me'er #"ri mo#e transer unction #eng"n menggn"k"n me'o#e Con%itional 5east Suare.

&ahap 0  1ji 2iagnostik "odel Transfer Function

Peng*i"n ke!"ik"n #"ri mo#e %"ng #i$eroe $"#" '""$ se!emn%".

&ahap 3  Penggunaan "odel Transfer Function untuk Peramalan

Per"m""n IH+ n'k 13 !"n ke #e$"n #eng"n menggn"k"n mo#e transer unction "kir.

IT. ANALI+I+ DAN PE6AHA+AN

Penei'i"n ini ingin menge'"i "$"k" "#" !ng"n "n'"r" IH+ #"n in&"si #eng"n me'o#e &ngsi 'r"ns&er. A. Pemeriksaan 2estasioneran Data %an $%entiikasi

&o%el

-""$"n "2" %"ng "rs #i"kk"n "#"" i#en'i&ik"si mo#e #eng"n mei"' time series plot .

Gambar '.Time Series Plot D"'" In&"si

"m!"r 1 'eri"' !"2" #"'" in&"si In#onesi" $erio#e 7"n"ri 3001 ingg" Desem!er 3013 memiiki $o" %"ng /en#erng s'"sioner 2""$n "#" s"" s"' #"'" %"ng mem$n%"i ni"i %"ng s"ng"' 'inggi #i!"n#ing #"'" "inn%". Ken"ik"n ni"i in&"si i' kem!"i 'er*"#i $"#" #"'" ke5G 'e$"'n%" $"#" !"n k'o!er 3005. D"'" in&"si 'erse!' "#" in#ik"si s#" s'"'ioner #""m mean. +e!em menge'"i "$"k" #"'" 'erse!' s#" s'"sioner #""m mean 'ere!i #" #i"kk"n $eng*i"n kes'"siner"n #""m "ri"ns #eng"n menggn"k"n 'r"ns&orm"si 7ox-cox.

Gambar +. Box-Cox Plot #"ri D"'" In&"si

er#"s"rk"n Box-Cox plot #"ri #"'" in&"si #i$eroe ni"i lo1er ;L se!es"r 0,1G #"n upper ;L se!es"r 0,4G, ser'" roun%e% "alue se!es"r 0,4. Ini menn*kk"n !"2" #"'" !em s'"sioner #""m "ri"ns. Un'k i' $er #i"kk"n 'r"ns&orm"si #eng"n rms @'0,4.

Gambar 0. Box-Cox Plot #"ri D"'" -r"ns&orm"si

er#"s"rk"n Box-Cox plot #"ri #"'" 'r"sn&orm"si #i$eroe ni"i lo1er ;L se!es"r 0,5 #"n upper ;L se!es"r 1,44 ser'" ni"i roun%e% "alue se!es"r 1. Ini menn*kk"n !"2" #"'" in&"si In#onesi" 'e" s'"sioner #""m "ri"ns.

+e'e" #i"kk"n $eng*i"n kes'"'ioner"n #""m

"ri"ns, m"k" se"n*'n%" #i"kk"n $eng*i"n

kes'"'ioner"n #"'" #""m mean menggn"k"n #"'" "si 'r"ns&orm"si 7ox-cox #eng"n $eng*i"n %ickey uller.

er#"s"rk"n $eng*i"n %ickey uller #i$eroe p"alue se!es"r 0,01 %"ng !er"r'i e!i ke/i #"ri  (5V) seingg" #"$"' #ik"'"k"n !"2" #"'" 'e" s'"sioner #""m mean.

D"'" in&"si In#onesi" $erio#e 7"n"ri 3001 ingg" Desem!er 3013 'e" s'"'ioner #""m "ri"ns #"n mean. L"ngk" se"n*'n%" "#"" me"kk"n i#en'i&ik"si mo#e n'k menge'"i mo#e A8I6A %"ng ses"i $"#" #"'" in&"si In#onesi" $erio#e !"n"n.

Gambar 3. A;> Plot D"'" -r"ns&orm"si

er#"s"rk"n $o' A;> #ike'"i !"2" "#" 3 "g %"ng ke"r #"ri !"'"s %"i' $"#" "g 1 #"n 13.

Gambar 4. PA;> Plot D"'" -r"ns&orm"si

er#"s"rk"n $o' PA;> #ike'"i !"2" "#"  "g %"ng ke"r #"ri !"'"s %"i' $"#" "g 1,G, #"n 1.

B. Penaksiran Parameter &o%el

Pen"ksir"n $"r"me'er mo#e #i$erk"n "g"r "si $er"m""n "i#.

&abel 0. Pen"ksir"n P"r"me'er 6o#e

140 126 112 98 84 70 56 42 28 14 1 9 8 7 6 5 4 3 2 1 0 Index i n f l a s i 3 2 1 0 -1 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 Lambda S t D e v Lo wer CL Upper CL Limit Estimate 0.34 Lower CL 0.18 Upper CL 0.48 Ro u  !e ! "a #u e 0 .3 4 $usi% 95.0& 'o(i!e'e)

Lam*!a 5.0 2.5 0.0 -2.5 -5.0 5 4 3 2 1 0 Lambda S t D e v Lower CL Upper CL Limit Estimate 1.00 Lower CL 0.53 Upper CL 1.44 Rou!e! "a#ue 1.00 $usi% 95.0& 'o(i!e'e)

Lam*!a 35 30 25 20 15 10 5 1 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 Lag A u t o c o r r e l a t i o n 35 30 25 20 15 10 5 1 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 Lag P a r t i a l A u t o c o r r e l a t i o n

(5)

6o#e P"r"me'e r

Es'im"si p-"alue Ke$'s" n A8I6A ([1,G], 0,0) 6U 0,93G 0,0001 signi&ik"n φ1 0,G 0,0001 signi&ik"n φG 0,1599 0,045 signi&ik"n

-"!e  menn*kk"n !"2" mo#e A8I6A ([1,G], 0,0) ses"i n'k #"'" in&"si In#onesi" $erio#e !"n"n k"ren" $"r"me'ern%" signi&ik"n seingg" #i$eroe $ers"m""n

t t

t

t Z Z a

Z



=0,93G +0,DDG



₋₁ + 0,1599



₋_G +

P"r"me'er mo#e #ik"'"k"n signi&ik"n !i" p"alue  .

+e"n*'n%" #i"kk"n $emeriks""n resi#" n'k

menge'"i "$"k" resi#" 'e" 10ite noise #"n !er#is'ri!si norm".

&abel 3. Peng*i"n Asmsi W0ite noise

6o#e L"g P-"alue Kesim$"n

A8I6A ([1,G]0,0)  0,5G "g" 'o"k H0 13 0,10 "g" 'o"k H0 1G 0,13G "g" 'o"k H0 34 0,101 "g" 'o"k H0

-"!e 4 menn*kk"n !"2" resi#" #"ri mo#e A8I6A ([1,G]0,0) 'e" memeni "smsi 10ite noise. H" 'erse!' #i'n*kk"n #eng"n ni"i p"alue J  (0,05) %"ng mem!erik"n kesim$"n !"2" resi#" 'e" in#e$en#en #"n memeni "smsi 10ite noise.

+e'e" resi#" memeni "smsi 10ite noise, m"k" '""$"n !erik'n%" "#"" memeriks" kenorm""n resi#". er#"s"rk"n *i 2olmooro" Smirno" #ike'"i esi#" s#" !er#is'ri!si norm" #eng"n ni"i $"e se!es"r 0,14. 7"#i mo#e A8I6A ([1,G]0,0) "#"" mo#e 'er!"ik #"ri #"'" in&"si !"n"n.

C.$%entiikasi A1al &o%el Funsi Transer

1. Penen'"n Ni"i (!, s, r) 6o#e "2" >ngsi -r"ns&er Pen#g""n ni"i (!,, s, r) n'k mo#e &ngsi 'r"ns&er #i'en'k"n !er#"s"rk"n s"m$e ;;> "n'"r" α t

#"n

β

t .

Gambar 5. Po' ;;> An'"r" In&"si #"n IH+

Po' ;;> 'erse!' #"$"' #ign"k"n se!"g"i $enen'"n or#e 7, s, r . D"ri !e!er"$" kom!in"si, #i$eroe #g""n or#er n'k mo#e &ngsi 'r"ns&er 'er!"ik "#"" 7B0, sBG #"n r B1. H" ini menn*kk"n !"2" in&"si !er$eng"r signi&ik"n 'er"#"$ IH+ $"#" #e"$"n $erio#e se"n*'n%". +emen'"r" r !erni"i 1 men"n#"k"n !"2" $o' mem!en'k s"' $o"

'er'en'. +eingg" #g""n semen'"r" mo#e &ngsi

'r"ns&ern%" "#"" se!"g"i !erik'.

t t t

x

B

y

η

δ

ω

µ

+ + = 1 G G

3. I#en'i&ik"si 6o#e A8I6A n'k Dere' :oise

8esi#" mo#e semen'"r" &ngsi 'r"ns&er !em memeni "smsi 20ite noise %"ng #"$"' #ii"' #"ri '"!e 5 memiiki p-"alue kr"ng #"ri 0,05. H" ini

menn*kk"n !"2" kom$onen error "#""

%epen%ent , seingg" $er #i'"m!"k"n s"' #ere' noise #""m es'im"si $"r"me'er #eng"n menggn"k"n mo#e A8I6A.

&abel 4. Peng*i"n Asmsi W0ite :oise

L"g P-"alue Kesim$"n

 0,0001 -i#"k W0ite :oise

13 0,0001 -i#"k W0ite :oise

1G 0,0001 -i#"k W0ite :oise

34 0,0001 -i#"k W0ite :oise

Penen'"n mo#e A8I6A #i#"s"rk"n $"#" $o' A;> #"n PA;> #"ri resi#" mo#e semen'"r" &ngsi 'r"ns&er. D"ri "si $eng*i"n resi#", #ike'"i $o' A;> 'rn "m!"' #"n $o' PA;> cuts o se'e" "g1, seingg" mo#e A8I6A n'k #ere' :oise "#"" A8(1) #"n sem" ni"i es'im"si $"r"me'er n'k mo#e semen'"r" "#"" signi&ik"n. +e/"r" mm mo#e &ngsi 'r"ns&er %"ng #i$eroe "#"" se!"g"i !erik'.

)

1 (

)

1 (

)

1 (

1 1 G G

B

a

x

B

C

y

t t t

φ

δ

ω

µ

−

+

−

+

=

(

)(

)

(

)(

)

(

)

(

)

_t

(

)

_t t

a

B

x

B

C

B

y

B

1 1 G G 1 1 1 1

1

1 δ

φ

ω

φ

δ

µ

φ

δ

−

+

−

+

−

=

−

. Penen'"n 6o#e >ngsi -r"ns&er "n'"r" In&"si #"n IH+

Asmsi %"ng "rs 'er$eni #""m $enen'"n mo#e &ngsi 'r"ns&er "#"" 10ite noise #"n ni"i es'im"si $"r"me'er signi&ik"n. Pen"m!""n s"' #ere' noise mem!erik"n "si !"2" mo#e "smsi 10ite noise 'e" 'er$eni, 'e'"$i n'k es'im"si $"r"me'er !em signi&ik"n k"ren" p-"alue e!i !es"r #"ri '"r"& sigini&ik"nsi 5V. +eingg" "ngk" %"ng #i"m!i "#"" #eng"n me"kk"n mo#i&ik"si 'er"#"$ or#e 7+ s, #"n r ingg" #i$eroe mo#e 'er!"ik %"i' #eng"n

or#e 7B0, sB0 #"n r B0.

H"si mo#i&ik"si menn*kk"n !"2" "smsi 10ite noise 'e" 'er$eni %"ng #i'n*kk"n $"#" '"!e , #im"n" p-"alue e!i !es"r #"ri '"r"& signi&ik"nsi 5V.

&abel 5. U*i W0ite :oise 6o#e >ngsi -r"ns&er

L"g P-"alue Kesim$"n

 0,131 W0ite :oise

13 0,53 W0ite :oise

1G 0,1 W0ite :oise

34 0,33 W0ite :oise

Peng*i"n signi&ik"nsi $"r"me'er menn*kk"n !"2" sem" $"r"me'er 'e" signi&ik"n k"ren" p-"alue $"r"me'er e!i !es"r #"ri "&" 5V. Ni"i signi&ik"nsi $"r"me'er #i'"m$ik"n $"#" '"!e .

&abel 6. Peng*i"n +igni&ik"nsi P"r"me'er 6o#e >ngsi -r"ns&er

P"r"me'e

(6)

µ

9,405 0,0001 +igni&ik" n 1 C _1,000 _0,0001 +igni&ik" n NU61 0,54G 0,0001 +igni&ik"_n

+e'e" resi#" memeni "smsi 10ite noise, m"k" #i"kk"n $eng*i"n kenorm""n resi#" #eng"n menggn"k"n *i 2olmoor"-Smirno". U*i Komogor +mirno %"ng #i"kk"n mem!erik"n p-"alue se!es"r 0,01 %"ng !er"r'i resi#" 'i#"k !er#is'ri!si norm" k"ren" p-"alue   se!es"r 0,05. Un'k men#"$"'k"n mo#e &ngsi 'r"ns&er %"ng !"ik, se!"ikn%" #i"kk"n s"' #e'eksi outlier n'k meng"'"si ke'i#"k norm""n resi#" mo#e. -e'"$i #""m "n"isis ini 'i#"k #i"kk"n s"' $en#e'eksi"n outlier+ seingg" mo#e &ngsi 'r"ns&er "n'"r" in&"si #"n IH+ "#"" se!"g"i !erik'. ] ) 1 [( 405 , 9 _t _t t x B a y = + + −

T. KE+I6PULAN DAN +A8AN

er#"s"rk"n "n"isis #"n $em!""s"n, mo#e 'r"ns&er %"ng ses"i "n'"r" in&"si #"n IH+ $erio#e 7"n"ri 3001

s"m$"i Desem!er 3013 "#"" ] ) 1 [( 405 , 9 _t _t t x B a

y = + + − _{#eng"n "smsi sem"}

$"r"me'er signi&ik"n #"n resi#" s#" 10ite noise '"$i 'i#"k !er#is'ri!si norm".

+"r"n %"ng #"$"' #i!erik"n n'k $enei'i"n se"n*'n%" "#"" $er "#"n%" #e'eksi outlier n'k meng"'"si m"s"" ke'i#"knorm""n resi#" seingg" n"n'in%" #i$eroe mo#e %"ng !"gs n'k mo#e 'r"ns&er "n'"r" in&"si #"n IH+.

U;APAN -E8I6A KA+IH

Penis meng/"$k"n 'erim" k"si ke$"#" #osen m"'" ki" An"isis D"'" II %"ng 'e" mem!erik"n !im!ing"n #"n m"sk"n #""m men%ees"ik"n "$or"n ini.

DA>-A8 PU+-AKA

[1] 6"i"no, De##% AW"r, XAn"isis >"k'or>"k'or %"ng 6em$eng"ri Perger"k"n In#eks H"rg" +""m "!ng"n (IH+) #i rs" E&ek In#onesi".Y -g"s

Akir 6"n"*emenEkonomi, De$ok< Uniersi'"s

n"#"rm" (3010).

[3] +er"2"'i, XIn#eks H"rg" +""m "!ng"n (IH+).Y

-g"s Ekonomi 6"kro, De$ok< Uniersi'"s

n"#"rm" (3011).

[] ;r%er, 7.D., 19G. Time Series Analysis. os'on < P!ising ;om$"n%.

[4] 6"kri#"kis, +., Zee2rig', +.;., #"n 6/ee, T.E.,

1999. 7ii# 1 E#isi Ke#", -er*em""n Ir. H"ri

+min'o. &eto%e %an Aplikasi Peramalan. 7"k"r'" < in" 8$" Aks"r".

[5] Zei, Z.Z.+., 1990. Time Series ni"ariate an%