1. Inisialisasi a0, b0, 0, dan z0. 2. Pembangkitan.

Transkripsi

1 LAMPIRAN 23

2 Lampiran 1. Skema MCMC unuk model ARCH(1) non-cenral Suden- 1. Inisialisasi a0 b0 0 dan z0. 2. Pembangkian. Disribusi poserior bersyara unuk diberikan oleh. Dalam kasus ini bisa dibangkikan secara langsung dari disribusi normal yaiu. dengan dan 3. Pembangkian. Disribusi poserior bersyara unuk diberikan oleh z g( z a b R R ) p( z ) fig 1 24

3 25 dengan ) 2( ) ( 1 2 ) ( T br a br a R a a R b exp 1 ) (1 exp ) ( T z br a R az R b R R b a z g Dalam hal ini poserior z idak mengikui suau disribusi erenu maka parameer z dibangkikan dengan menggunakan meode IC-MH dengan proposalnya yaiu ) ( ~ * IG z dan rasio penerimaannya yaiu: ) ( ) ( 1 1 * * R R b a z g R R b a z g z z r. 4. Pembangkian Disribusi poserior bersyara unuk v diberikan oleh. Diambil logarima disribusi poserior bersyara unuk : Nilai dibangkikan menggunakan meode IC-MH dengan proposal unuk yaiu dan probabilias penerimaannya yaiu. Dicari modus poserior dari arinya bahwa. Dalam kasus ini dan dienukan dengan menggunakan meode yang didasarkan pada ingkah laku disribusi di sekiar modus. Lebih lanju diperoleh bahwa derivaif perama dan kedua dari beruru-uru yaiu:

4 Kemudian dan. Namun bisa bernilai posiif karena iu diambil dengan. 26

5 Lampiran 2. Skema MCMC unuk model ARCH(1) Skewed Suden- 1. Inisialisasi a0 b0 0 dan z0. 2. Membangkikan nilai acak a b kz R. Disribusi poserior bersyara unuk a diberikan oleh Diambil logarima disribusi poserior bersyara unuk a: Nilai a dibangkikan menggunakan meode IC-MH dengan proposal unuk a yaiu dan probabilias penerimaannya yaiu. Dicari modus poserior dari arinya bahwa. Diperoleh bahwa derivaif perama dan kedua dari beruru-uru yaiu 27

6 Kemudian dan. Namun bisa bernilai posiif karena iu diambil dengan. 3. Membangkikan nilai acak b a k Z R Disribusi poserior bersyara unuk a diberikan oleh Diambil logarima disribusi poserior bersyara unuk b: 28

7 Nilai b dibangkikan menggunakan meode IC-MH dengan proposal unuk b yaiu dan probabilias penerimaannya yaiu. Dicari modus poserior dari arinya bahwa. Diperoleh bahwa derivaif perama dan kedua dari beruru-uru yaiu Kemudian dan. Namun bisa bernilai posiif karena iu diambil dengan. 29

8 4. Membangkikan nilai acak k a b Z R Disribusi poserior bersyara unuk k diberikan oleh Diambil logarima disribusi poserior bersyara unuk k: dengan dan. Dalam kasus ini bisa dibangkikan secara langsung dari disribusi normal yaiu dimana: dan 5. Membangkikan nilai-nilai acak a b k R z Disribusi poserior bersyara unuk diberikan oleh dengan =1...T Nilai dibangkikan menggunakan meode IC-MH dengan proposalnya yaiu dan rasio penerimaannya yaiu. 30

9 6. Membangkikan nilai acak k a bz R Disribusi poserior bersyara unuk v diberikan oleh Diambil logarima disribusi poserior bersyara unuk : Nilai dibangkikan menggunakan meode IC-MH dengan proposal unuk yaiu dan probabilias penerimaannya yaiu. 7. Kembali ke langkah 2 31

10 Lampiran 3. Kode Malab unuk Esimasi Model ARCH(1) noncenral Suden- 3.1 Kode Uama funcion hasil=archnc_mcmc(rhp) % Tujuan: Mengesimasi parameer-parameer dalam model ARCH(1) % R_ = sigma_ * z^0.5 * (miu+xhi_) xhi_~n(01) % sigma_^2 = a + b*r_{-1}^2 % % Algorima: MCMC % % Masukan: R = Reurns = 100*[(log(S_)-log(S_{-1}))- 1/T*sum((log(S_)- log(s_{-1}))] % dimana S_ = nilai kurs pada saa % HP = Hyperparameer = [lambda alpha_b bea_b miu_c var_c alpha_nu bea_nu] unuk prior % a ~ exp(lambda) b ~ bea(alpha_bbea_b) % c ~ Normal(miu_cvar_c) % dan nu ~ Gamma(alpha_nu bea_nu) % % Keluaran: hasil.draws = draws % I: Inisialisasi T = lengh(r); R2 = R.^2; % prior unuk a lamd = HP(1); % prior unuk b alp = HP(2); be = HP(3); %prior unuk c muc=hp(4); varc=hp(5); % prior unuk nu alpnu = HP(6); benu = HP(7); % nilai awal a = 0.1; b = 0.1; nu = 20; z = 1./gamrnd(nu/22/nuT1); % banyaknya replikasi Nis = 15000; BI = 5000; N = Nis-BI; % alokasi penyimpanan sampel av = zeros(n1); bv = zeros(n1); cv = zeros(n1); nuv = zeros(n1); zv = zeros(t1); vol = zeros(t1); % Algorima MCMC. Sep 1: Membangkikan Ranai Markov ic for is = 1:Nis % --- pembangkian nilai acak mu Vc = 1/(T+1/varc); Mc = Vc*(R(1)*sqr((1-b)/(a*z(1)))... +sum(r(2:t).*((a+b*r2(1:t-1)).*z(2:t)).^(-0.5))+muc/varc); c = normrnd(mcsqr(vc)11); 32

11 % --- pembangkian nilai acak z alpz = (nu+1)/2; bez1 = 0.5*((1-b)*R(1)^2+a*nu)/a; bez2 = (R2(2:T)+(a+b*R2(1:T-1)).*nu)./(2*(a+b*R2(1:T-1))); bez = [bez1; bez2]; % pembangkian proposal zprop = 1./gamrnd(alpz1./bez); % mengevaluasi probabilias penerimaan gzold1 = (sqr(1-b)*c*r(1)./(a*z(1))^(-0.5)); gzold2 = (c*r(2:t)./(sqr(a+b*r2(1:t... -1).*sqr(z(2:T))))); gzold = [gzold1; gzold2]; gznew1 gznew2 gznew = (sqr(1-b)*c*r(1)*(a*zprop(1))^(-0.5)); = (c*r(2:t)./(sqr(a+b*r2(1:t... -1).*sqr(zprop(2:T))))); = [gznew1; gznew2]; raio = exp(gznew-gzold); % pembaharuan u = rand(t1); minra = min(1raio); ind = find(u<=minra); z(ind) = zprop(ind); % mencari raa-raa dan variansi unuk proposal bersyara hpv = [alpnu benu]; mv = bisecion_nu(hpvz); % raa-raa d2v = 0.5*T/mv-T/4*psi(1mv/2)-(alpnu-1)/mv^2; Dv = min( d2v); s2v = -1/Dv; %variansi % algorima IC-MH % pembangkian proposal nu* pr = runcnormrnd(1mvsqr(s2v)2.140); % mengevaluasi probabilias penerimaan log_pv = 0.5*pr*T*log(pr/2)-T*gammaln(pr/2)-pr/2... *sum(log(z)+1./z)+(alpnu-1)*log(pr)-benu*pr; pos_pr = exp(log_pv); log_pv = 0.5*nu*T*log(nu/2)-T*gammaln(nu/2)-nu/2... *sum(log(z)+1./z)+(alpnu-1)*log(nu)-benu*nu; pos_o = exp(log_pv); raio = pos_pr/pos_o; ap = min(1raio); % pembangkian variabel acak seragam u = rand(1); % pembaruan if u <= ap nu = pr; % --- pembangkian sampel a % mencari raa-raa dan variansi unuk disribusi proposal hp1 = lamd; m_a = bisecion_nc(rr2abchp1z'a'); % raa-raa d2a = 1/(2*m_a^2)+0.5*sum(1./(m_a+b*R2(1:T-1)).^2) *(1-b)*R2(1)/(m_a^3*z(1))-(0.25*c*R(1)*(1... -b)^2./((1-b)/m_a*z(1))^(0.5)*m_a^(4)*z(1)^2)... +c*r(1)*(1-b)./sqr((1-b)./m_a*z(1))*m_a^(3)*z(1)... -sum(r2(2:t)./((m_a+b*r2(1:t-1)).^3.*z(2:t))) *sum(c*R(2:T)./(m_a+b*R(1:T... -1).^(2.5).*sqr(z(2:T)))); Da = min( d2a); s2_a = -1/Da; % variansi % algorima IC-MH % pembagkian proposal a* 33

12 pr = runcnormrnd(1m_asqr(s2_a)1e-41); % mengevaluasi probabilias penerimaan log_pa = -0.5*log(pr)-0.5*sum(log(pr+b*R2(1:T-1))) *(1-b)*R2(1)/(pr*z(1))... +sqr(1-b/pr*z(1)*c*r(1)) *sum((R2(2:T)./((pr+b*R2(1:T-1)).*z(2:T)))... +(c*r(2:t)./(sqr(pr+b*r2(1:t-1)).*sqr(z(2:t)))))... -lamd*pr; % F(pr) pos_pr = exp(log_pa); log_pa = -0.5*log(a)-0.5*sum(log(a+b*R2(1:T-1))) *(1-b)*R2(1)/(a*z(1))-... +sqr(1-b/a*z(1)*c*r(1)) *sum((R2(2:T)./((a+b*R2(1:T-1)).*z(2:T)))... +(c*r(2:t)./(sqr(a+b*r2(1:t-1)).*sqr(z(2:t)))))... -lamd*a; % F(a) pos_o = exp(log_pa); raio = pos_pr/pos_o; ap = min(1raio); % pembangkian variabel acak seragam u = rand(1); % pembaruan if u <= ap a = pr; % --- pembangkian nilai acak b % mencari raa-raa dan variansi unuk disribusi proposal mup = alp; Vp = be; hp1 = [mup Vp]; m_b = bisecion_nc(rr2abchp1z'b'); % raa-raa d2b = -0.5/(1-m_b)^2+0.5*sum((R2(1:T-1).^2)./((a+m_b*R2(1:T... -1)).^2))-0.25*c*R(1)/((1... -m_b/a*z(1)).^(1.5)*a^2*z(1)^2)... -sum(((r2(1:t-1).^2).*(r2(2:t)))..../((a+m_b*r2(1:t-1)).^3.*z(2:t))) *sum(R2(1:T-1).^(2)*c.*R(2:T)./(a+m_b*R(1:T... -1).^(2.5).*sqr(z(2:T))))... -(alp-1)/(m_b^2)-(be-1)/(1-m_b)^2; Db = min( d2b); s2_b = -1/Db; % variansi % algorima IC-MH % pembangkian proposal b* pr = runcnormrnd(1m_bsqr(s2_b)01); % mengevaluasi probabilias penerimaan log_pb = 0.5*log(1-pr)-0.5*sum(log(a+pr*R2(1:T-1))) *(1-pr)*R2(1)/(a*z(1))... +sqr(1-pr/a*z(1))*c*r(1) *sum((R2(2:T)./(a+pr*R2(1:T-1).*z(2:T)))... +c*r(2:t)./sqr(a+pr*r2(1:t-1)).*sqr(z(2:t)))... +(alp-1)*log(pr)+(be-1)*log(1-pr); % F(pr) pos_pr = exp(log_pb); log_pb = 0.5*log(1-b)-0.5*sum(log(a+b*R2(1:T-1))) *(1-b)*R2(1)/(a*z(1))... +sqr(1-b/a*z(1))*c*r(1) *sum((R2(2:T)./(a+b*R2(1:T-1).*z(2:T)))... +c*r(2:t)./sqr(a+b*r2(1:t-1)).*sqr(z(2:t)))... +(alp-1)*log(b)+(be-1)*log(1-b); %F(b) pos_o = exp(log_pb); raio = pos_pr/pos_o; ap = min(1raio); % pembangkian variabel acak seragam u = rand(1); % pembaruan if u <= ap b = pr; 34

13 % pengesimasian sigma vol = [a/(1-b); a+b*r2(1:t-1)]; % simpan a b c dan nu if is > BI av(is-bi1) = a; bv(is-bi1) = b; cv(is-bi1) = c; nuv(is-bi1) = nu; zv = ((is-bi-1)*zv+z)/(is-bi); vol = ((is-bi-1)*vol+vol)/(is-bi); oc % Algorima MCMC. Sep 2: Menghiung raa-raa Mone Carlo draws = [av bv cv nuv]; MP = mean(draws); SP = sd(draws); % ===== Inegraed Auocorrelaion Time (IACT) ============================ % Berapa banyak sampel yang harus dibangkikan unuk mapakan sampel % yang indepen (seberapa cepa konvergensi simulasi) resulsiat = IACT(draws); IAT = [resulsiat.iac]; % ===== Uji Konvergensi Geweke ============================================ idraw1 = round(.1*n); resulcv = momeng(draws(1:idraw1:)); meansa = [resulcv.pmean]; nsea = [resulcv.nse1]; idraw2 = round(.5*n)+1; resulcv = momeng(draws(idraw2:n:)); meansb = [resulcv.pmean]; nseb = [resulcv.nse1]; CD = (meansa - meansb)./sqr(nsea+nseb); oneail = 1-normcdf(abs(CD)01); pv = 2*oneail; % ===== 95% Highes Poserior Densiy (HPD) Inerval ====================== resulshpd = HPD(draws0.05); LB = [resulshpd.lb]; UB = [resulshpd.ub]; % % ===== Numerical Sandard Error (NSE) ==================================== resulsnse = NSE(draws); NSEd = [resulsnse.nse]; %====================== Pengauran Penceakan Hasil ======================= %----- Saisik Parameer in.cnames = char('a''b''c''nu'); in.rnames = char('parameer''mean''sd''lb''ub''iact''nse''g-cd''p- Value'); in.fm = '%16.6f'; mp = [MP; SP; LB; UB; IAT; NSEd; CD; pv]; fprinf(1'esimasi menggunakan MCMC dan Uji Diagnosik\n'); mprin(mpin); hasil.vol hasil.zv hasil.av = vol; = zv; = av; 35

14 hasil.bv = bv; hasil.cv = cv; hasil.nuv = nuv; hasil.draws = draws; %========== Calculae Marginal likelihood by Gelfand-Dey (1994) =========== hea = draws'; [nparndraw] = size(hea); mvn_mean = mean(hea2); mvn_cov = cov(hea'); inv_mvn_cov = inv(mvn_cov); %----- POSTERIOR % domain runcae_val = zeros(1ndraw); for i = 1:ndraw draw_elemen = hea(:i); runcae_val(i) = (draw_elemen-mvn_mean)' * inv_mvn_cov... * (draw_elemen-mvn_mean); criical_value = chi2inv(0.99npar); runcae_index = runcae_val > criical_value; source_pdf_log = mvn_pdf_log(heamvn_mean(:ones(ndraw1))mvn_cov)... - log(0.99); source_pdf_log(runcae_index) = -inf; %----- PRIOR % a prior_pdf_a_log = log(lamd)-lamd*av'; % b prior_pdf_b_log = -bealn(alpbe)+(alp-1).*log(bv')+(be-1).*log(1-bv'); % c prior_pdf_c_log = -1/2*log(2*pi*varc) - 1/2*(cv'-muc).^2/varc; % nu prior_pdf_nu_log = -gammaln(alpnu)+alpnu.*log(benu)+(alpnu-1).*log(nuv')- benu.*nuv'; % LOG TOTALLY PRIOR prior_pdf_log = sum(prior_pdf_a_log) + prior_pdf_b_log... + prior_pdf_c_log + prior_pdf_nu_log; % LIKELIHOOD likelihood_log = zeros(1ndraw); for i = 1:ndraw likelihood_log(i) = ARCHnc_likelihood(Rzdraws(i:)); GD_log = source_pdf_log - prior_pdf_log - likelihood_log; consan = max(gd_log); ML_GD = -consan - log(mean(exp(gd_log - consan))) 3.2 Kode bisecion funcion mv = bisecion_nu(hpvz) % Tujuan : Mencari akar dari F (v)= 0 menggunakan meode bagi dua % % % Masukan : hpv = nilai prior v % z = [z_1 z_2 z_3.z_t] %

15 % keluaran : mv = akar penyelesaian eps_sep = 1e-2; bb = 2.1; ba = 100; if difffnu(hpvzbb) == 0 % derivaif perama mv = bb; reurn; elseif difffnu(hpvzba) == 0 mv = ba; reurn; elseif difffnu(hpvzbb)*difffnu(hpvzba) > 0 error( 'difffnu(a) and difffnu(b) do no have opposie signs' ); while abs(ba - bb) >= eps_sep x = (ba + bb)/2; if difffnu(hpvzx) == 0 mv = x; reurn; elseif difffnu(hpvzx)*difffnu(hpvzba) < 0 bb = x; else ba = x; mv=x; 3.3 Kode bisecion NCT funcion mab = bisecion_nc(rr2abchp1zpar) % Tujuan : Mencari akar dari F (a)=0 aau F (b)=0 menggunakan meode % bagi dua % % % Masukan : R = reurns % R2 = reurns^2 % a = nilai a % b = nilai b % c = nilai miu % hp1 = nilai prior % z = [z_1 z_2 z_3.z_t] % par = 'a' aau 'b' % % keluaran : mab = akar penyelesaian eps_sep = 1e-2; if par == 'a' bb = 1e-5; ba = 1; elseif par == 'b' bb = 0; ba = 1; if diffarch_nc(rr2abchp1zbbpar) == 0 %derivaif perama mab = bb; reurn; elseif diffarch_nc(rr2abchp1zbapar) == 0 mab = ba; reurn; elseif diffarch_nc(rr2abchp1zbapar)*diffarch_nc(rr2abchp1zbbpar) > 0 error( 'diffarch(ba) and diffarch(bb) do no have opposie signs' ); 37

16 while abs(bb - ba) >= eps_sep x = (ba + bb)/2; if diffarch_nc(rr2abchp1zcpar) == 0 mab = x; reurn; elseif diffarch_nc(rr2abchp1zcpar)*diffarch_nc(rr2abchp1zbapar) < 0 bb = x; else ba = x; mab = x; 3.4 Kode unuk urunan perama F() funcion y = difffnu(hpvznu) % Tujuan : Mengiung F (v) % % Masukan : hpv = nilai prior % z = [z_1 z_2 z_3.z_t] % nu = nilai v % % keluaran : y = nilai urunan perama T=lengh(z); %derivaif perama y = T/2*(log(nu/2)+1-psi(nu/2))-0.5*sum(log(z)+1./z)+(hpv(1)-1)/nu-hpv(2); 4.5 Kode unuk urunan perama F(a) dan F(b) funcion Fab = diffarch_nc(rr2abchp1zbspar) % Tujuan : Mengiung F (a) aau F (b) % % Masukan : R = reurns % R2 = reurns^2 % a = nilai a % c = nilai miu % hp1 = nilai prior % z = [z_1 z_2 z_3.z_t] % bs = baas kiri/kanan inerval pada meode bagi dua % par = 'a' aau 'b' % % keluaran : Fab = nilai urunan perama if par =='a'% derivaif perama erhadap a a = bs; lamd = hp1; Fab = -1/(2*a)-0.5*sum(1./(a+b*R2(1:-1))) *(1-b)*R2(1)/(a^2*z(1))... -2*(1-b)^2*R2(1)./(a^3+z(1).^2) *sum(((R2(2:))./((a+b*R2(1:-1)).^2.*z(2:)))... -c*r(2:)./(a+b*r2(1:-1)).^(1.5).*sqr(z(2:)))... -lamd; elseif par == 'b' % derivaif perama erhadap b b = bs; alp = hp1(1); be=hp1(2); Fab = -1/(2*(1-b)) *sum(R2(1:-1)./(a+b*R2(1:-1)))... +R2(1)/(2*a*z(1)) *c*R(1)/sqr(1-b/a*z(1))*a*z(1) *sum(R2(1:-1).*R2(2:)./((a+b*R2(1:... -1)).^2.*z(2:)))-1.5*sum(R2(1:... -1).^2*c.*R(2:)./(a+b*R2(1:-1)).^2.5.*z(2:))... 38

17 +(alp-1)/b-(be-1)/(1-b); 3.6 Kode likelihood NCT funcion [log_likelihood] = ARCHnc_likelihood(Rzdraws) % Tujuan : Mencari log likelihood ARCH(1) NCT % % % Masukan : R = reurns % z = [z_1 z_2 z_3.z_t] % draws = [av bv cv nuv] % % keluaran : log_likelihood T = max(size(r)); sig2 = zeros(t1); sig2(1) = draws(1)/(1-draws(2)); var(1) = sig2(1)*z(1); y2(1) = (R(1)-sqr(var(1))*draws(3))^2; log_likelihood = -0.5*log(2*pi*var(1)) -0.5*y2(1)/var(1); for i=2:t sig2(i) = draws(1) + draws(2)*r(i-1)^2; var(i) = sig2(i)*z(i); y2(i) = (R(i)-sqr(var(i))*draws(3))^2; log_likelihood = log_likelihood -0.5*log(2*pi*var(i)) -0.5*y2(i)/var(i); 3.7 Kode unuk memanggil hasil esimasi clc clear all %daa daa1=csvread('jpy_kursbeli.csv'); daa1 = daa1(-1471:); daa2=csvread('eur_kursbeli.csv'); daa3 = daa3(-1471:); Rjpy=100*price2re(daa1); Rjpy=Rjpy-mean(Rjpy); Reur=100*price2re(daa2); Reur=Reur-mean(Reur); lamd=1; alpb=2.5; beb=3; alpnu=16; benu=0.8; muc=0; varc=1; HP=[lamd alpb beb muc varc alpnu benu]; hasil = archnc_mcmc(rjpyhp); vol = hasil.vol ; zv = hasil.zv; av = hasil.av; bv = hasil.bv; cv = hasil.cv; nuv = hasil.nuv; draws = hasil.draws; % ========== Save daa ==================================================== dlmwrie('f:\nc\hasil\eur_nc_draws.csv'draws'delimier''''precision''%0.16f') 39

18 3.8 Kode Pukung Kode runcnormrnd IACT momeng HPD NSE mprin dan mvn_pdf_log dapa diliha dalam Nugroho (2014). 40

19 Lampiran 4. Kode Malab unuk Esimasi Model ARCH(1) Skewed Suden- 4.1 Kode Uama funcion hasil=archsk_mcmc(rhp) % Tujuan: Mengesimasi parameer-parameer dalam model ARCH(1) % R_ = sigma_*(k*(z-miu_z)+z^0.5*xhi_) xhi_~n(01) % sigma_^2 = a + b*r_{-1}^2 % % Algorima: MCMC % % Masukan: R = Reurns = 100*[(log(S_)-log(S_{-1}))- 1/T*sum((log(S_)- log(s_{-1}))] % dimana S_ = nilai kurs pada saa % HP = Hyperparameer = [lambda alpha_b bea_b miu_k var_k alpha_nu bea_nu] unuk prior % a ~ exp(lambda) b ~ bea(alpha_bbea_b) % k ~ Normal(miu_kvar_k) % dan nu ~ Gamma(alpha_nu bea_nu) % % Keluaran: hasil.draws = draws % I: Inisialisasi T = lengh(r); R2 = R.^2; % prior unuk a lamd = HP(1); % prior unuk b alp = HP(2); be = HP(3); %prior unuk k muk=hp(4); vark=hp(5); % prior unuk nu alpnu = HP(6); benu = HP(7); % nilai awal a = 0.1; b = 0.1; nu = 10; z = 1./gamrnd(nu/22/nuT1); mz=nu/(nu-2); sig2=[a/(1-b); a+b*r2(1:t-1)]; % banyak replikasi Nis = 15000; BI = 5000; N = Nis-BI; % alokasi penyimpanan nilai-nilai acak av = zeros(n1); bv = zeros(n1); kv = zeros(n1); nuv = zeros(n1); zv = zeros(t1); vol = zeros(t1); % Algorima MCMC. Sep 1: Membangkikan Ranai Markov ic for is = 1:Nis % --- pembangkian sampel k A = sig2.^(0.5).*(z-mz); 41

20 B = sig2.*z; sum1 = sum(a.^2./b); sum2 = sum(-1./2*vark); Vk = 1./(sum1+sum2); Mk = Vk*sum(A.*R./B+muk/vark); k = normrnd(mksqr(vk)11); % --- pembangkian sampel z alpz = (nu+1)/2; bez = nu/2+r2/2+k*r.*sig2.^(-0.5)*mz... +k^2.*mz^2/2; % pembangkian proposal zprop = 1./gamrnd(alpz1./bez); % mengevaluasi probabilias penerimaan gzold = k*r.*sig2.^(-0.5)-0.5*k^2*z+k^2*mz*z; gznew = k*r.*sig2.^(-0.5)-0.5*k^2*zprop+k^2*mz*zprop; raio = exp(gznew-gzold); % pembangkian variabel acak seragam u = rand(t1); % pembaharuan minra = min(1raio); ind = find(u<=minra); z(ind) = zprop(ind); % mencari raa-raa dan variansi unuk proposal bersyara hpv = [alpnu benu]; mv = bisecion_nusk(rsig2khpvz); % raa-raa ddv =sum(-4*k./(sig2.^(0.5).*z)*(mv-2)^(-4).*((mv-2)*(rsig2.^(0.5).*k.*z... +sqr(sig2).*k.*(mv/(mv-2))).*sqr(sig2).*k) ); d2v = ddv +0.5*T/mv-T/4*psi(1mv/2)-(alpnu-1)/mv^2; Dv = min( d2v); s2v = -1/Dv; %variansi % algorima IC-MH % pembangkian proposal nu* pr = runcnormrnd(1mvsqr(s2v)2.140); % mengevaluasi probabilias penerimaan log_pv = -0.5*sum((2*R*k.*sig2.^(-0.5)*pr/(pr-2)... +k^2.*(-2.*z*pr/(pr-2)+(pr/(pr-2))^2))./z) *pr*T*log(pr/2)-T*gammaln(pr/2)... -pr/2*sum(log(z)+1./z)+(alpnu-1)*log(pr)-benu*pr; pos_pr = exp(log_pv); log_pv = -0.5*sum((2*R*k.*sig2.^(-0.5)*(nu./(nu-2))... +k^2*(-2*z*(nu/(nu-2))+(nu./(nu-2))^(2)))./z) *nu*T*log(nu/2)-T*gammaln(nu/2)-nu/2... *sum(log(z)+1./z)+(alpnu-1)*log(nu)-benu*nu; pos_o = exp(log_pv); raio = pos_pr/pos_o; ap = min(1raio); % pembangkian variabel acak seragam u = rand(1); % pembaruan if u <= ap nu = pr; mz = nu/(nu-2); % --- pembangkian sampel a % mencari raa-raa dan variansi unuk disribusi proposal hp1 = lamd; m_a = bisecion_sk(rr2abmzkhp1z'a'); % raa-raa d2a = 1/(2*m_a^2)+0.5*sum(1./(m_a+b*R2(1:T-1)).^2) *(1-b)*R2(1)/(m_a^3*z(1))-(0.25*k*R(1)... *(1-b)^2)./(((1-b)/m_a*z(1))^(1.5)*m_a^(4))... +k*r(1)*(1-b)./sqr((1-b)./m_a*m_a^(3)... -(0.75)*k*R(1)*mz)./((m_a/(1-b))^(2.5)*z(1)*(1-b)^(2))... 42

21 -sum(r2(2:t)./((m_a+b*r2(1:t-1)).^3.*z(2:t))) *sum(k*R(2:T)./(m_a+b*R(1:T-1).^(2.5))) *sum((k*R(2:T).*mz)./(m_a... +b*r(1:t-1).^(2.5).*z(2:t)))); Da = min( d2a); s2_a = -1/Da; % variansi % algorima IC-MH % pembagkian proposal a* pr = runcnormrnd(1m_asqr(s2_a)1e-41); % mengevaluasi probabilias penerimaan log_pa = -0.5*log(pr)-0.5*sum(log(pr+b*R2(1:T-1))) *(1-b)*R2(1)/(pr*z(1))-... +sqr((1-b)/pr)*k*r(1)... -(k*r(1)*mz)./(sqr(pr/(1-b)).*z(1)) *sum(R2(2:T)./((pr+b*R2(1:T-1)).*z(2:T))... +(k*r(2:t)./(sqr(pr+b*r2(1:t-1))))... -(k*r(2:t)*mz./(sqr(pr+b*r2(1:t-1))).*z(2:t)))... -lamd*pr; % F(pr) pos_pr = exp(log_pa); log_pa = -0.5*log(a)-0.5*sum(log(a+b*R2(1:T-1))) *(1-b)*R2(1)/(a*z(1))-... +sqr((1-b)/a)*k*r(1)... -(k*r(1)*mz)./(sqr(a/(1-b)).*z(1)) *sum(R2(2:T)./((a+b*R2(1:T-1)).*z(2:T))... +(k*r(2:t)./(sqr(a+b*r2(1:t-1))))... -(k*r(2:t)*mz./(sqr(a+b*r2(1:t-1))).*z(2:t)))... -lamd*a; % F(a) pos_o = exp(log_pa); raio = pos_pr/pos_o; ap = min(1raio); % pembangkian variabel acak seragam u = rand(1); % pembaruan if u <= ap a = pr; % --- pembangkian sampel b % mencari raa-raa dan variansi unuk disribusi proposal mup = alp; Vp = be; hp1 = [mup Vp]; m_b = bisecion_sk(rr2abmzkhp1z'b'); % raa-raa d2b = -0.5/(1-m_b)^2+0.5*sum((R2(1:T-1).^2)./((a+m_b*R2(1:T... -1)).^2))-0.25*k*R(1)/((1-m_b/a).^(1.5)*a^2) *k*R(1)*mz/((1-m_b/a).^(1.5)*a^2.*z(1))... -sum(((r2(1:t-1).^2).*(r2(2:t)))./((a+m_b*r2(1:t... -1)).^3.*z(2:T)))+0.75*sum(R2(1:T... -1).^(2)*k.*R(2:T)./(a+m_b*R(1:T-1).^(2.5))) *sum(R2(1:T-1).^(2)*k.*R(2:T)*mz./(a+m_b*R(1:T... -1).^(2.5).*z(2:T)))-(alp-1)/(m_b^2)-(be-1)/(1-m_b)^2; Db = min( d2b); s2_b = -1/Db; % variansi % algorima IC-MH % pembangkian proposal b* pr = runcnormrnd(1m_bsqr(s2_b)01); % mengevaluasi probabilias penerimaan log_pb =0.5.*log(1-pr)-0.5.*sum(log(a+pr.*R2(1:T-1))) *(1-pr).*R2(1)./(a*z(1))... +sqr((1-pr)/a).*k.*r(1)-k.*r(1).*mz./(sqr(a/(1... -pr)).*z(1))-0.5.*sum(r2(2:t)./(a+pr.*r2(1:t-... 1).*z(2:T))+k.*R(2:T)./sqr(a+pr.*R2(1:T-1))... -k.*r(2:t).*mz./sqr(a+pr.*r2(1:t-1)).*z(2:t))... +(alp-1)*log(pr)+(be-1)*log(1-pr); % F(pr) pos_pr = exp(log_pb); 43

22 log_pb = 0.5.*log(1-b)-0.5.*sum(log(a+b.*R2(1:T-1))) *(1-b).*R2(1)./(a*z(1))... +sqr((1-b)/a).*k.*r(1)-k.*r(1).*mz./(sqr(a/(1... -b)).*z(1))-0.5.*sum(r2(2:t)./(a+b.*r2(1:t... -1).*z(2:T))+k.*R(2:T)./sqr(a+b.*R2(1:T-1))... -k.*r(2:t).*mz./sqr(a+b.*r2(1:t-1)).*z(2:t))... +(alp-1)*log(b)+(be-1)*log(1-b); %F(b) pos_o = exp(log_pb); raio ap = pos_pr/pos_o; = min(1raio); % pembangkian variabel acak seragam u = rand(1); % pembaruan if u <= ap b = pr; % pengesimasian sigma vol = [a/(1-b); a+b*r2(1:t-1)]; sig2 = vol; % simpan a b k dan nu if is > BI av(is-bi1) = a; bv(is-bi1) = b; kv(is-bi1) = k; nuv(is-bi1) = nu; zv = ((is-bi-1)*zv+z)/(is-bi); vol = ((is-bi-1)*vol+vol)/(is-bi); oc % Algorima MCMC. Sep 2: Menghiung raa-raa Mone Carlo draws = [av bv kv nuv]; MP = mean(draws); SP = sd(draws); % ===== Inegraed Auocorrelaion Time (IACT) ============================ % Berapa banyak sampel yang harus dibangkikan unuk mapakan sampel % yang bebas (seberapa cepa konvergensi simulasi) resulsiat = IACT(draws); IAT = [resulsiat.iac]; % ===== Uji Konvergensi Geweke ============================================ idraw1 = round(.1*n); resulcv = momeng(draws(1:idraw1:)); meansa = [resulcv.pmean]; nsea = [resulcv.nse1]; idraw2 = round(.5*n)+1; resulcv = momeng(draws(idraw2:n:)); meansb = [resulcv.pmean]; nseb = [resulcv.nse1]; CD = (meansa - meansb)./sqr(nsea+nseb); oneail = 1-normcdf(abs(CD)01); pv = 2*oneail; % ===== 95% Highes Poserior Densiy (HPD) Inerval ====================== resulshpd = HPD(draws0.05); LB = [resulshpd.lb]; UB = [resulshpd.ub]; % % ===== Numerical Sandard Error (NSE) ==================================== 44

23 resulsnse = NSE(draws); NSEd = [resulsnse.nse]; %====================== Pengauran Penceakan Hasil ======================= %----- Saisik Parameer in.cnames = char('a''b''k''nu'); in.rnames = char('parameer''mean''sd''lb''ub''iact''nse''g-cd''p- Value'); in.fm = '%16.6f'; mp = [MP; SP; LB; UB; IAT; NSEd; CD; pv]; fprinf(1'esimasi menggunakan MCMC dan Uji Diagnosik\n'); mprin(mpin); hasil.vol = vol; hasil.zv = zv; hasil.av = av; hasil.bv = bv; hasil.kv = kv; hasil.nuv = nuv; hasil.draws = draws; 4.2 Kode bisecion funcion mv = bisecion_nusk(rsig2khpvz) % Tujuan : Mencari akar dari F (v)= 0 menggunakan meode bagi dua % % Masukan : R = reurns % Sig2 = sigma_^2 % k = nilai parameer skewness k % hpv = nilai prior v % z = [z_1 z_2 z_3.z_t] % % keluaran : mv = akar penyelesaian eps_sep = 1e-2; bb = 2.1; ba = 100; if difffnusk(rsig2khpvzbb) == 0 % derivaif perama mv = bb; reurn; elseif difffnusk(rsig2khpvzba) == 0 mv = ba; reurn; elseif difffnusk(rsig2khpvzbb).*difffnusk(rsig2khpvzba) > 0 error( 'difffnusk(a) and difffnusk(b) do no have opposie signs' ); while abs(ba - bb) >= eps_sep x = (ba + bb)/2; if difffnusk(rsig2khpvzx) == 0 mv = x; reurn; elseif difffnusk(rsig2khpvzx).*difffnusk(rsig2khpvzba) < 0 bb = x; else ba = x; mv=x; 45

24 4.3 Kode bisecion SKT funcion mab = bisecion_sk(rr2abmzkhp1zpar) % Tujuan : Mencari akar dari F (a)=0 aau F (b)=0 menggunakan meode % bagi dua % % % Masukan : R = reurns % R2 = reurns^2 % a = nilai a % b = nilai b % mz = nilai miu_z % k = nilai parameer skewness k % hp1 = nilai prior % z = [z_1 z_2 z_3.z_t] % par = 'a' aau 'b' % % keluaran : mab = akar penyelesaian eps_sep = 1e-2; if par == 'a' bb = 1e-5; ba = 1; elseif par == 'b' bb = 0; ba = 1; if diffarch_sk(rr2abmzkhp1zbbpar) == 0 %derivaif perama mab = bb; reurn; elseif diffarch_sk(rr2abmzkhp1zbapar) == 0 mab = ba; reurn; elseif diffarch_sk(rr2abmzkhp1zbapar)*diffarch_sk(rr2abmzkhp1zb bpar) > 0 error( 'diffarch(ba) and diffarch(bb) do no have opposie signs' ); while abs(bb - ba) >= eps_sep x = (ba + bb)/2; if diffarch_sk(rr2abmzkhp1zxpar) == 0 mab = x; reurn; elseif diffarch_sk(rr2abmzkhp1zxpar)*diffarch_sk(rr2abmzkhp1zba par) < 0 bb = x; else ba = x; mab = x; 46

25 4.4 Kode unuk urunan perama F() funcion y = difffnusk(rsig2khpvznu) % Tujuan : Mengiung F (v) % % % Masukan : R = reurns % sig2 = sigma_^2 % k = nilai parameer skewness k % hpv = nilai prior % z = [z_1 z_2 z_3.z_t] % nu = nilai v % % keluaran : y = nilai urunan perama T = lengh(z); y = sum(2./(sig2.^(0.5).*z)*k*(nu-2)^(-2).*(r... -sig2.^(0.5)*k.*z+sig2*k*nu/(nu-2)))... +T/2*(log(nu/2)+1-psi(nu/2))-0.5*sum(log(z)+1./z)... +(hpv(1)-1)/nu-hpv(2); 4.5 Kode unuk urunan perama F(a) dan F(b) funcion Fab = diffarch_sk(rr2abmzkhp1zbspar) % Tujuan : Mengiung F (a) aau F (b) % % Masukan : R = reurns % R2 = reurns^2 % a = nilai a % b = nilai b % mz = nilai miu_z % k = nilai parameer skewness k % hp1 = nilai prior % z = [z_1 z_2 z_3.z_t] % bs = baas kiri/kanan inerval pada meode bagi dua % par = 'a' aau 'b' % % keluaran : Fab = nilai urunan perama if par =='a'% derivaif perama erhadap a a = bs; lamd = hp1; Fab = -1/(2*a)-0.5*sum(1./(a+b*R2(1:-1))) *(1-b)*R2(1)/(a^2*z(1)) *k.*(1-b)^2*R(1)./((sqr(1-b)./a).*a.^(2)) *k.*R(1).*mz./sqr(a./(1-b)).*z(1).*(1-b) *sum(((R2(2:))./((a+b*R2(1:-1)).^2.*z(2:))) *k*R(2:)./(a+b*R2(1:-1)).^(1.5) *k.*R(2:).*mz./(a+b*R2(1:... -1)).^(1.5).*z(2:))-lamd; elseif par == 'b' % derivaif perama erhadap b b = bs; alp = hp1(1); be=hp1(2); Fab = -1/(2*(1-b)) *sum(R2(1:-1)./(a+b*R2(1:-1)))... +R2(1)/(2*a*z(1)) *k*R(1)/sqr((1-b)/a).*a *k*R(1).*mz./(sqr((1-b)./a).*a*z(1)) *sum(R2(1:-1).*R2(2:)./((a+b*R2(1:... -1)).^2.*z(2:))) *sum(R2(1:-1)*k.*R(2:)./(a+b*R2(1:-1)).^1.5) *sum(R2(1:-1)*k.*R(2:)./(a+b*R2(1:... -1)).^1.5.*z(2:))+(alp-1)/b-(be-1)/(1-b); 47

26 4.6 Kode unuk memanggil hasil esimasi clc clear all %daa daa1=csvread('jpy_kursbeli.csv'); daa1 = daa1(-1471:); daa2=csvread('eur_kursbeli.csv'); daa3 = daa3(-1471:); Rjpy=100*price2re(daa1); Rjpy=Rjpy-mean(Rjpy); Reur=100*price2re(daa2); Reur=Reur-mean(Reur); lamd=1; alpb=2.5; beb=3; alpnu=16; benu=0.8; muk=0; vark=1; HP=[lamd alpb beb muk vark alpnu benu]; hasil = archsk_mcmc(reurhp); draws = hasil.draws; % ========== Save daa ==================================================== dlmwrie('d:\skripsi\sk\hasil\jpy_sk_draws.csv'draws'delimier''''precis ion''%0.16f') 4.7 Kode Pukung Kode runcnormrnd IACT momeng HPD NSE dan mprin dapa diliha dalam Nugroho (2014). 48

27 Lampiran 5. Serifika Seminar 49

28 50