S MAT 0800299 Table of content

DAFTAR ISI
ABSTRAK ........................................................................................................ i
KATA PENGANTAR ...................................................................................... iii
UCAPAN TERIMA KASIH ........................................................................... iv
DAFTAR ISI ..................................................................................................... v
DAFTAR TABEL ............................................................................................ viii
DAFTAR GAMBAR ........................................................................................ ix
DAFTAR LAMPIRAN .................................................................................... x
DAFTAR SIMBOL .......................................................................................... xi
BAB 1

PENDAHULUAN .............................................................................. 1
1.1

Latar Belakang ....................................................................... 1

1.2

Rumusan Masalah .................................................................. 3

1.3

Batasan Masalah..................................................................... 3

1.4

Tujuan Penulisan .................................................................... 3

1.5

Manfaat Penulisan .................................................................. 3

BAB 2 LANDASAN TEORI ........................................................................... 4
2.1

Konsep Runtun Waktu ............................................................ 4

2.2

Konsep Stasioneritas ............................................................... 5

2.3

Fungsi Autokerelasi dan Fungsi Autokorelasi Parsial ............ 6
2.3.1

Fungsi Autokorelasi .................................................... 6

2.3.2

Fungsi Autokorelasi Parsial ........................................ 7

2.4

Proses White Noise ................................................................. 8

2.5

Metode Runtun Waktu Box-Jenkins ....................................... 8
2.5.1

Model Runtun Waktu untuk Data Stasioner ............. 9
2.5.1.1 Proses Autoregressive (AR)......................... 9
2.5.1.2 Proses Moving Average (MA) ..................... 14
2.5.1.2 Proses Campuran (ARMA) ......................... 14

2.5.2
2.6

Model Data Nonstasioner.......................................... 15

Pembentukan Model................................................................ 16
2.6.1

Kestasioneran Data ................................................... 16

2.6.2

Identifikasi Model ..................................................... 16

Jaelani Rahman, 2015

MARKOV SWITCHING AUTOREGRESSIVE
Universitas Pendidikan Indonesia | repository.upi.edu | perpustakaan.upi.edu

2.6.3

Estimasi Parameter .................................................... 17

2.6.4

Verifikasi Model ....................................................... 17

2.6.5

Peramalan .................................................................. 18

2.7

Uji Perubahan Struktur............................................................ 19

2.8

Teori Peluang .......................................................................... 20
2.7.1

Ruang Sampel ........................................................... 20

2.7.2

Pengertian Peluang .................................................... 20

2.7.3

Peluang Bersyarat...................................................... 20

2.8

Rantai Markov ......................................................................... 21

2.9

Vektor

2.10

Reducible Rantai Markov ........................................................ 22

2.11

Vektor Eigen ........................................................................... 22

2.12

Rantai Markov Ergodic ........................................................... 23

2.13

Vektor Peluang Steady State ................................................... 23

................................................................................. 21

BAB 3MARKOV SWITCHING AUTOREGRESSIVE .................................... 25
3.1

Model Markov Switching Autoregressive ............................... 25

3.2

Estimasi Parameter .................................................................. 27

3.3

Uji Nonlinearitas ..................................................................... 32

3.5

Peramalan ................................................................................ 33

BAB 4STUDI KASUS ....................................................................................... 35
4.1

Deskripsi Data ......................................................................... 35

4.2

Uji Stasioneritas ...................................................................... 36

4.3

Pembentukan Model Box-Jenkins........................................... 38

4.4

4.3.1

Identifikasi Model ..................................................... 38

4.3.2

Estimasi Parameter .................................................... 39

Pemodelan Markov Switching Autoregressive ........................ 41
4.4.1

Uji Perubahan Struktur.............................................. 41

4.4.2

Uji Bai-Perron ........................................................... 41

4.4.3

Estimasi Parameter .................................................... 43

4.4.4

Uji Nonlinearitas ....................................................... 45

4.4.5

Peramalan .................................................................. 46

Jaelani Rahman, 2015
MARKOV SWITCHING AUTOREGRESSIVE
Universitas Pendidikan Indonesia | repository.upi.edu | perpustakaan.upi.edu

BAB 5 PENUTUP ............................................................................................ 49
5.1

Kesimpulan .............................................................................. 49

5.2

Saran ......................................................................................... 50

DAFTAR PUSTAKA ........................................................................................ 51
LAMPIRAN ....................................................................................................... 53
DAFTAR RIWAYAT HIDUP .......................................................................... 67

Jaelani Rahman, 2015
MARKOV SWITCHING AUTOREGRESSIVE

Universitas Pendidikan Indonesia | repository.upi.edu | perpustakaan.upi.edu

DAFTAR TABEL

Halaman
Tabel 4.1 ADF Nilai Tukar Dollar Terhadap Rupiah ............................................. 36
Tabel 4.2 ADF Data Return ................................................................................... 37
Tabel 4.3 Estimasi Parameter AR(1)...................................................................... 39
Tabel 4.4 Estimasi Parameter MA(1) ..................................................................... 40
Tabel 4.5 Estimasi Parameter ARMA(1,1)............................................................... 40
Tabel 4.6 Uji Perubahan Struktur ........................................................................... 41
Tabel 4.7 Identifikasi Waktu Breaks ...................................................................... 42
Tabel 4.8 Estimasi Parameter ................................................................................. 43
Tabel 4.9 Peluang Transisi ..................................................................................... 44
Tabel 4.10 Nilai Ramalan Return ............................................................................. 46
Tabel 4.11 Nilai Ramalan Nilai Tukar Dollar Terhadap Rupiah ............................. 47

Jaelani Rahman, 2015
MARKOV SWITCHING AUTOREGRESSIVE
Universitas Pendidikan Indonesia | repository.upi.edu | perpustakaan.upi.edu

DAFTAR GAMBAR

Halaman
Gambar 4.1 Plot Nilai Tukar Dollar Terhadap Rupiah .......................................... 35
Gambar 4.2 Plot Return Dollar Terhadap Rupiah .................................................. 37
Gambar 4.3 Plot fak dan fakp data return ............................................................... 38
Gambar 4.4 Plot Bai Perron.................................................................................... 42
Gambar 4.4 Perbandingan nilai estimasi dan nilai sesungguhnya ......................... 45

Jaelani Rahman, 2015
MARKOV SWITCHING AUTOREGRESSIVE
Universitas Pendidikan Indonesia | repository.upi.edu | perpustakaan.upi.edu

DAFTAR LAMPIRAN

Halaman
Lampiran 1 Autokovarian AR(1) ............................................................................ 53
Lampiran 2 Inferensi Peluang Pemulusan Peluang regime ..................................... 55
Lampiran 3 Peluang Transisi m-Periode kedepan Markov 2 state ......................... 56
Lampiran 4 Data Nilai Tukar Dollar Terhadap Rupiah .......................................... 59
Lampiran 5 Data Return Nilai Tukar Dollar Terhadap Rupiah............................... 61
Lampiran 6 Output Oxmetrics ................................................................................. 64
Lampiran 7 Klasifikasi regime ................................................................................ 65
Lampiran 8 Output Peramalan ................................................................................ 66

Jaelani Rahman, 2015
MARKOV SWITCHING AUTOREGRESSIVE
Universitas Pendidikan Indonesia | repository.upi.edu | perpustakaan.upi.edu

DAFTAR SIMBOL

: Mean/ rata-rata
: Langkah ke-k
: White Noise
: Varians dari
: Autokovariansi lag ke-k
: Estimasi autokovariansi lag ke-k
: Autokorelasi lag ke-k
: Estimasi autokorelasi lag ke-k
: Autokorelasi parsial lag ke-k
: Parameter Autoregressive
: Parameter Moving Average
: Operator Backshift
: Operator differensi
: Nilai eigen
: Forecast probabilities
: Inference probabilities
: Smoothed probabilities

Jaelani Rahman, 2015
MARKOV SWITCHING AUTOREGRESSIVE
Universitas Pendidikan Indonesia | repository.upi.edu | perpustakaan.upi.edu