M01700
Proceedings of the International Conference
on Science and Science Education
Copyright © November 2015 by Satya Wacana University Press, Jl. Diponegoro 52–60
Salatiga 50711, Indonesia
Telephone: (+62) 298 321212
All Rights Reserved.
No part of this publication may be reproduced in any form or by any electronic or mechanical
means, including photocopying, recording, or any information storage and retrieval system,
without permission in writing from the publisher.
International Standard Book Number: 978-602-1047-21-7
SWUP
iii
Editorial Board
Proceedings of the International Conference on Science and Science Education
(IConSSE 2015)
Secretariat
Telephone
Email
Website
: Faculty of Science and Science Education, Satya Wacana Christian University
Jl. Diponegoro 52–60 Salatiga 50711, Indonesia
: (+62) 298 321212 ext. 238
: [email protected]
: http://fsm.uksw.edu/semnas/iconsse
Steering Committee
Prof. Dr. Ferdy S. Rondonuwu, S.Pd., M.Sc.
Prof. Dr. Eko Sediyono, M.Kom.
Dr. Suryasatria Trihandaru, M.Sc.nat.
Organizing Committee
Chairman
Secretary
Treasurer
: Dr. Adi Setiawan, M.Sc.
: Tundjung Mahatma, Dip.Comp., S.Pd., M.Kom.
: Dra. Lilik Linawati, M.Kom.
SWUP
iv
Proceedings Team
Reviewer
Prof. Dr. Ferdy S. Rondonuwu, S.Pd., M.Sc. (Satya Wacana Christian University, Indonesia)
Prof. Dr. Eko Sediyono, M.Kom. (Satya Wacana Christian University, Indonesia)
Prof. Dr. Sri Wahyuni (Gadjah Mada University, Indonesia)
Prof. Dr. Widowati (Diponegoro University, Indonesia)
Prof. Dr. K.H. Timotius (Krida Wacana Christian University, Indonesia)
Prof. Dr. Edy Cahyono, M.Si. (Semarang State University, Indonesia)
Prof. Dr. Wiyanto, M.Si. (Semarang State University, Indonesia)
Prof. Dr. J. Sardjono (BATAN - National Atomic Energy Agency, Indonesia)
Prof. Dr. Slamin, M.Comp.Sc. (Jember University, Indonesia)
Prof. Ravi Prakash Vyas (Indian Institutes of Information Technology, India)
Prof. Dr. P. Filzmoser (Vienna University of Technology, Austria)
Prof. Dr.rer.nat. Nuryono, MS (Gadjah Mada University, Indonesia)
Prof. Dr. Purwantiningsih (Bogor Agriculture University, Indonesia)
Dr. Ed. Van den Berg (Vrije Universiteit, The Netherlands)
Dr. Colleen Valle (University of Deakin, Australia)
Dr. Suryasatriya Trihandaru, M.Sc.nat. (Satya Wacana Christian University, Indonesia)
Dr. Hanna Arini Parhusip, M.Sc.nat. (Satya Wacana Christian University, Indonesia)
Dr. Adi Setiawan, M.Sc. (Satya Wacana Christian University, Indonesia)
Dr. A. Ign. Kristijanto, MS (Satya Wacana Christian University, Indonesia)
Dr. Lydia Ninan Lestario (Satya Wacana Christian University, Indonesia)
Dr. Siana Halim (Petra Christian University, Indonesia)
Dr. (Candt.) Yohanes Martono, S.Si., M.Sc. (Satya Wacana Christian University, Indonesia)
Alvama Pattiserlihun, S.Si., M.Ps.Ed. (Satya Wacana Christian University, Indonesia)
Editor
Prof. Dr. Ferdy S. Rondonuwu, S.Pd., M.Sc.
Dr. Adi Setiawan, M.Sc.
Dr. Lydia Ninan Lestario
Dr. Hanna Arini Parhusip, M.Sc.nat.
Tundjung Mahatma, Dip.Comp., S.Pd., M.Kom.
Didit Budi Nugroho, D.Sc.
Layout & Cover
Didit Budi Nugroho, D.Sc.
SWUP
v
Welcoming Address
Welcome to the 2015 IConSSE – The International Conference on Science and Science Education!
This conference, which is organized by the Faculty of Science and Mathematics, Satya Wacana Christian
University Salatiga, is held at Laras Asri Resort and Spa Salatiga.
Arts, science and technology are crucial components in the advancement of human civilization. There is art in the
creation of technology, and science provides strong bases for the technological development. We are proud to
inherit the temple of Borobudur which is a proof that Indonesian’s ancient arts and technology are so advanced
that not only is the masterpiece beautiful, but also technologically rich.
This International Conference on Science and Science Education is attended by more than 160 participants. There
are more than 67 papers is presented orally covering wide-variety subjects of science and science education. We
thank you all for your participation.
We thank the Organizing Committee, Reviewers, and Steering Committee for having been working hard. Finally,
we would also like to thank the Rector of Satya Wacana Christian University, and Dean of Faculty of Science and
Mathematics for their support for this conference.
We hope you will enjoy our togetherness. Thank you.
Salatiga, November 30th , 2015
Dr. Adi Setiawan
Chairman
SWUP
vi
Contents
Editorial Team ……………………………………………………………………………………………………..
Proceedings Team ………………………………………………………………………………………………..
Welcoming Address ………………………………………………………………………………………………
Contents …………………………………………………………………………………………………………….
Lessons from the 20th century for 21st century science education
[Berg] ………………………………………………………………………………………………………….
Excited state dynamics of carotenoids free and bound to pigment-protein complexes
[Rondonuwu–Koyama] ………………………………………………………………………………………
Problem solving and reasoning in the learning of mathematics
[Vale] ………………………………………………………………………………………………………….
iii
iv
v
vi
AZ.1
AZ.12
AZ.23
Penalized spline estimator in nonparametric regression
[Andriani–Wibowo–Rahayu] ………………………………………………………………………………..
MA.1
Estimation of parameter in spatial probit regression model
[Fahmi–Ratnasari–Rahayu] ………………………………………………………………………………...
MA.5
Parameter estimation of kernel logistic regression
[Fa’rifah–Suhartono–Rahayu] ……………………………………….……………………………………..
MA.8
Geographically weighted multinomial logistic regression model (Case study: Human development index
value and healths status areas of districts/cities 2013 in Sumatera)
[Fibriyani–Latra–Purhadi] ……………………………………………..……………………………………. MA.13
Comparison of ε-insentive support vector regression and ν-support vector regression in nonlinear
regression problem
[Hustianda–Purnami–Sutikno]……………………………………………………………………………… MA.20
Random forest of modified risk factor on ischemic and hemorrhagic (Case study: Medicum Clinic, Tallinn,
Estonia)
[Karisma–Kormiltsõn–Kuswanto] ………………………..………………………………………………… MA.26
Bivariate generalized pareto distribution to predict the return level of extreme rainfall data (Case: Applied
in Ajung and Ledokombo Stations)
[Lestari–Sutikno–Purhadi] ………………………………………………………………………………….. MA.42
Box–Cox realized asymmetric stochastic volatility model
[Nugroho–Morimoto] ………………………………………………………………………………………… MA.48
Inflow and outflow forecasting of currency using multi-input transfer function
[Reganata–Suhartono]………………………………………………..…………………………………….. MA.53
Classifying the poor household using neural network
[Ruslau–Ulama] ……………………………………………………………………………………………… MA.66
Path analysis model estimates using generalized method of moment (Case study: Maternal mortality in
the Province of East Java)
[Sari–Otok] …………………………………………………………………………………………………… MA.71
Simulation study of reliability coefficient and discrimination index
[Setiawan–Weku] ……………………………………………………………………………………………. MA.79
The effect of enviromental attributes, facilities, and demographic profile on travelled option
[Subanti] …………………………….…………………………………..……………………………………. MA.86
The determinant of traveled expenditure and the number of visitors in Semarang District
[Subanti–Mulyanto–Kurdi]………………………………………………………..…………………………. MA.90
Combination of volatility and Markov-switching models for financial crisis in Indonesia based on real exchange rate
indicators
[Sugiyanto–Zukhronah] …………………………………………………………………………………….. MA.93
Inflow and outflow of currency forecasting using calendar variation model based on time series regression
[Urusyiyah–Suharsono–Suhartono] ………………………………………………………………………. MA.98
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vii
Performance of neural network model in forecasting Indonesian inflation
[Warsito–Suparti–Mukid] …………………………………………………………………………………… MA.103
Financial crisis model in Indonesia using combined of volatility and Markov-switching models based on
international reserve ratio to M2 indicators
[Zukhronah–Susanti–Sugiyanto] ……….………………………………………………………………….. MA.109
Appendix A. (Co-)Presenters Attendance List (Parallel Session)
Appendix B. Question and Answer
SWUP
Proceedings of the IConSSE FSM SWCU (2015), pp. MA.48–52
ISBN: 978-602-1047-21-7
MA.48
Box–Cox realized asymmetric stochastic volatility model
Didit B. Nugrohoa and Takayuki Morimotob
a
Department of Mathematics, Satya Wacana Christian University
Department of Mathematical Sciences, Kwansei Gakuin University
b
Abstract
This study proposes a class of non-linear realized stochastic volatility model by applying
the Box–Cox (BC) transformation, instead of the logarithmic transformation, to the
realized estimator. The proposed models are fitted to daily returns and realized kernel
of six stocks: SP500, FTSE100, Nikkei225, Nasdaq100, DAX, and DJIA using an Markov
Chain Monte Carlo (MCMC) Bayesian method, in which the Hamiltonian Monte Carlo
(HMC) algorithm updates BC parameter and the Riemann manifold HMC (RMHMC)
algorithm updates latent variables and other parameters that are unable to be sampled
directly. Empirical studies provide evidence against log and raw versions of realized
stochastic volatility model.
Keywords Box–Cox transformation, HMC, MCMC, realized stochastic volatility
1. Introduction
Volatility of financial asset returns, defined as the standard deviation of log returns,
has played a major role in many financial applications such as option pricing, portfolio
allocation, and value-at-risk models. In the context of SV model, very closely related studies
of joint models has been proposed by Dobrev & Szerszen (2010), Koopman & M. Scharth
(2013), and Takahashi et al. (2009). Their model is known as the realized stochastic volatility
(RSV) model.
Recently, the Takahashi et al. (2009)'s model has been extended by Takahashi et al.
(2014) by applying a general non-linear bias correction in the realized variance (RV) measure.
This study extends the asymmetric version of Takahashi et al. (2014)'s models, known as the
realized asymmetric SV (R-ASV) model, by applying the BC transformation to the realized
measure. Here we focus on the realized kernel (RK) measure that has some robustness to
market microstructure noise. The realized kernel data behave very well and better than any
available realized variance statistic Goncalves and Meddahi (2011).
Adding an innovation to obtain an RSV model substantially increase the difficulty in
parameter estimation. Nugroho & Morimoto (2015) provided some comparison of
estimation results between HMC-based samplers and multi-move Metropolis--Hastings
sampler provided by Takahashi et al. (2019) and Takahashi et al. (2014), where the RMHMC
sampler give the best performance in terms of inefficiency factor. Therefore, this study
employs HMC-based samplers methods to estimate the parameters and latent variables in
our proposed model when draws cannot be directly sampled.
2. Box-Cox R-ASV model
The basic discrete-time RSV model includes three stochastic processes describing the
dynamics of returns, logarithmic RV, and logarithmic squared volatility. In this framework,
the conditional volatility of returns not only depends on the returns but also on the realized
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D.B. Nugroho, T. Morimoto
MA.49
measure of variance. The logarithmic transformation of RV is known to have better finite
sample properties than RV. Goncalves and Meddahi (2011) provided a short overview of this
transformation and suggested that the log transformation can be improved upon by choosing
values of BC parameter other than zero (corresponding to the log transformation). Motivated
by this result, we apply the BC transformation to the RV measure to obtain a class of R-ASV
model called the BCR-ASV model that takes the following form:
ü = exp -›”ℎ .Y
P
7 = ¼+ ℎ + …
K
(1)
ℎ " =m+† ℎ −m + × " ,
O
”
Û[
K
ℎ ~ •m, o—
”–
N
where corr Y , × " = , represents normal distribution, and 7 is the BC transformation
for realized RV defined as
7 = 7 ü ,G = ß
$\] o
À
, if G ≠ 0,
(2)
log ü
, if G = 0.
Notice that this transformation contains the log transformation for RV (when G = 0) and the
raw statistic (when G = 1) as special cases.
As in previous studies, in order to adopt a Gaussian nonlinear state space form where
the error terms in both return and volatility equations are uncorrelated, we introduce a
transformation
× " = Y + Ý1 − ^ " ,
where ^ " ~ 0,1 and corr Y , ^ " = 0. A reparameterization of the model (1) yields
ℎ " = m¼ + † ℎ − m¼ + Æü exp-−›”ℎ . + T^ " ,
where Æ =
ℎ ~ •m¼ ,
Û[”
–,
o—”
and T = 1 −
.
3. MCMC simulation in the BCR-ASV model
Let
= )ü +/# , ½ = )ü +/# , _ = )ℎ +/# , & = -G, ¼ , , … . , and & =
m, †, Æ, T . By Bayes' theorem, the joint posterior distribution of &, _ given R and V is
& , & , _| , ½ = & , & ×
|_ × ½|& , _ × _|& , ,
(3)
where & , & is a joint prior distribution on parameter & , & .
The MCMC method simulates a new value for each parameter in turn from its
conditional posterior distribution assuming that the current values for the other parameters
are true values. We employ the MCMC scheme as follows:
0) Initialize & , & , _ .
1) Given the current values, draw ¼ , , … , m, Æ, and T from their conditional posteriors
directly.
2) Given ¼ , , … , and ½, draw G by HMC.
3) Given m, Æ, T, _, and , draw † by RMHMC.
4) Given & , & , , and ½, draw _ by RMHMC.
For steps (1), (3), and (4), we implement the same sampling scheme proposed in Nugroho &
Morimoto (2014, 2015). In the following, we study the sampling scheme in step (2) only.
As far as the power parameter G ≠ 0 is only concerned to be sampled and by taking
the normal distribution ŽÀ , À for the prior of G, the logarithm of conditional posterior
distribution for G on the basis of Eq. (3) has the following expression:
SWUP
Box–Cox realized asymmetric stochastic volatility model
< G ∝−
∑/# È
Û”
MA.50
$\] o
À
−
¼
−
ℎÉ −
Ào•] ”
,
$]
which is not of standard form, and therefore we cannot sample G from it directly. In this case,
we implement the HMC algorithm for sampling G because the metric tensor required to
implement the RMHMC sampling scheme cannot be explicitly derived from the above
distribution.
B
4. Empirical results on real data sets
In this section, the BCR-ASV model and MCMC algorithm discussed in the previous
section are applied to the daily returns and RK data for six different international stock
indices: DAX, DJIA, FTSE100, Nasdaq100, Nikkei225, and SP500. These data sets were
downloaded from Oxford-Man Institute ``realised library" and range from January 2000 to
December 2013. Analyses are presented for the sampling efficiency, key parameters that
build the extension models.
We run the MCMC algorithm for 15,000 iterations but discard the first 5,000 draws.
From the resulting 10,000 draws which have passed the Geweke (1992)'s convergence test
for each parameter, we calculate the posterior mean, standard deviation (SD), and 95%
highest posterior density (HPD) interval. Summary of the posterior simulation results for G
are presented in Table 1.
Table 1. Summary of the posterior sample of parameter G in the BCR-ASV model for six
data sets from January 2000 to December 2013.
Statistic
DAX
DJIA
FTSE100
Nasdaq100 Nikkei225
SP500
Mean
–0.0406
0.1226
0.1572
0.0420
0.0503
0.1149
SD
0.0104
0.0099
0.0096
0.0096
0.0128
0.0094
LB
–0.0609
0.1022
0.1385
0.0242
0.0241
0.0968
UB
–0.0202
0.1409
0.1765
0.0617
0.0741
0.1340
Note: LB and UB denote lower and upper bounds of 95% HPD interval, respectively.
The posterior means of G are positive for DJIA, FTSE100, Nasdaq100, Nikkei225, and
SP500 and negative for DAX. In all cases, the 95% HPD interval of G exclude 0 (the log
transformation) or 1 (the raw version). Although not reported, we find that even 99% HPD
interval of G exclude 0 or 1, providing significant evidence to transform the RV series using
the BC transformation against both the logarithmic transformation and no transformation
cases.
To understand the effect of BC transformation, we present the marginal densities of
the transformed RK implied by G = 0 and the estimated G for each stock index in Figure 1.
The marginal density of the BC RV is obviously different from that of the log RV. When the
estimated G is a positive value, the left tail of the former is lighter than that of the latter,
while the right tail of former is heavier, and vice versa when the estimated G is a negative
value. Moreover the marginal density of the former has a heavier right tail than left tail (as
that of the latter) for both positive and negative values of G. Furthermore, the marginal
density of the former has a higher peak than, and a different location from, that of the latter.
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D.B. Nugroho, T. Morimoto
MA.51
Figure 1. Marginal densities of the log RV and BC-RV for six different international stock
indices.
5. Conclusions and extensions
This study presented an extension to the R-ASV models, in which the Box-Cox
transformation is applied to realized measure. The HMC and RMHMC algorithms were
proposed to implement the MCMC method for updating several parameters and the latent
variables in the proposed model, taking advantage of updating the entire latent volatility at
once. The model and sampling algorithms were applied to the daily returns and realized
kernels of six international stock indices. The estimation results showed very strong evidence
supporting the Box-Cox transformation of realized measure. The model can be extended by
assuming a non-Gaussian density of return errors.
References
Dobrev, D., & Szerszen, P. (2010). The information content of high-frequency data for estimating equity
return models and forecasting risk. Working Paper, Finance and Economics Discussion Series.
Geweke, J. (1992). Evaluating the accuracy of sampling-based approaches to the calculation of
posterior moments. In J. M. Bernardo, J. O. Berger, A. P. Dawid, & A. F. M. Smith (Eds.), Bayesian
Statistics 4 (pp. 169–194 (with discussion)). Clarendon Press, Oxford, UK.
Goncalves, S., & Meddahi, N. (2011). Box-Cox transforms for realized volatility. Journal of
Econometrics, 160, 129–144.
Kim, S., Shephard, N., & Chib, S. (2005). Stochastic volatility: likelihood inference and comparison with
ARCH models. In N. Shephard, ed., Stochastic Volatility: Selected Readings (pp. 283–322). Oxford
University Press, New York.
Koopman, S.J., & Scharth, M. (2013). The analysis of stochastic volatility in the presence of daily
realized measures. Journal of Financial Econometrics, 11(1), 76–115.
Nugroho, D.B., & Morimoto, T. (2014). Realized non-linear stochastic volatility models with
asymmetric effects and generalized Student's t-distributions. Journal of The Japan Statistical
Society, 44, 83–118.
Nugroho, D.B., & Morimoto, T. (2015). Estimation of realized stochastic volatility models using
Hamiltonian Monte Carlo-based methods. Computational Statistics, 30(2), 491–516.
Takahashi, M., Omori, Y., & Watanabe, T. (2009). Estimating stochastic volatility models using daily
returns and realized volatility simultaneously. Computational Statistics and Data Analysis, 53,
2404–2426.
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Box–Cox realized asymmetric stochastic volatility model
MA.52
Takahashi, M., Omori, Y., & Watanabe, T. (2014). Volatility and quantile forecasts by realized
stochastic volatility models with generalized hyperbolic distribution. Working Paper Series
CIRJE-F-921, CIRJE, Faculty of Economics, University of Tokyo.
SWUP
on Science and Science Education
Copyright © November 2015 by Satya Wacana University Press, Jl. Diponegoro 52–60
Salatiga 50711, Indonesia
Telephone: (+62) 298 321212
All Rights Reserved.
No part of this publication may be reproduced in any form or by any electronic or mechanical
means, including photocopying, recording, or any information storage and retrieval system,
without permission in writing from the publisher.
International Standard Book Number: 978-602-1047-21-7
SWUP
iii
Editorial Board
Proceedings of the International Conference on Science and Science Education
(IConSSE 2015)
Secretariat
Telephone
Website
: Faculty of Science and Science Education, Satya Wacana Christian University
Jl. Diponegoro 52–60 Salatiga 50711, Indonesia
: (+62) 298 321212 ext. 238
: [email protected]
: http://fsm.uksw.edu/semnas/iconsse
Steering Committee
Prof. Dr. Ferdy S. Rondonuwu, S.Pd., M.Sc.
Prof. Dr. Eko Sediyono, M.Kom.
Dr. Suryasatria Trihandaru, M.Sc.nat.
Organizing Committee
Chairman
Secretary
Treasurer
: Dr. Adi Setiawan, M.Sc.
: Tundjung Mahatma, Dip.Comp., S.Pd., M.Kom.
: Dra. Lilik Linawati, M.Kom.
SWUP
iv
Proceedings Team
Reviewer
Prof. Dr. Ferdy S. Rondonuwu, S.Pd., M.Sc. (Satya Wacana Christian University, Indonesia)
Prof. Dr. Eko Sediyono, M.Kom. (Satya Wacana Christian University, Indonesia)
Prof. Dr. Sri Wahyuni (Gadjah Mada University, Indonesia)
Prof. Dr. Widowati (Diponegoro University, Indonesia)
Prof. Dr. K.H. Timotius (Krida Wacana Christian University, Indonesia)
Prof. Dr. Edy Cahyono, M.Si. (Semarang State University, Indonesia)
Prof. Dr. Wiyanto, M.Si. (Semarang State University, Indonesia)
Prof. Dr. J. Sardjono (BATAN - National Atomic Energy Agency, Indonesia)
Prof. Dr. Slamin, M.Comp.Sc. (Jember University, Indonesia)
Prof. Ravi Prakash Vyas (Indian Institutes of Information Technology, India)
Prof. Dr. P. Filzmoser (Vienna University of Technology, Austria)
Prof. Dr.rer.nat. Nuryono, MS (Gadjah Mada University, Indonesia)
Prof. Dr. Purwantiningsih (Bogor Agriculture University, Indonesia)
Dr. Ed. Van den Berg (Vrije Universiteit, The Netherlands)
Dr. Colleen Valle (University of Deakin, Australia)
Dr. Suryasatriya Trihandaru, M.Sc.nat. (Satya Wacana Christian University, Indonesia)
Dr. Hanna Arini Parhusip, M.Sc.nat. (Satya Wacana Christian University, Indonesia)
Dr. Adi Setiawan, M.Sc. (Satya Wacana Christian University, Indonesia)
Dr. A. Ign. Kristijanto, MS (Satya Wacana Christian University, Indonesia)
Dr. Lydia Ninan Lestario (Satya Wacana Christian University, Indonesia)
Dr. Siana Halim (Petra Christian University, Indonesia)
Dr. (Candt.) Yohanes Martono, S.Si., M.Sc. (Satya Wacana Christian University, Indonesia)
Alvama Pattiserlihun, S.Si., M.Ps.Ed. (Satya Wacana Christian University, Indonesia)
Editor
Prof. Dr. Ferdy S. Rondonuwu, S.Pd., M.Sc.
Dr. Adi Setiawan, M.Sc.
Dr. Lydia Ninan Lestario
Dr. Hanna Arini Parhusip, M.Sc.nat.
Tundjung Mahatma, Dip.Comp., S.Pd., M.Kom.
Didit Budi Nugroho, D.Sc.
Layout & Cover
Didit Budi Nugroho, D.Sc.
SWUP
v
Welcoming Address
Welcome to the 2015 IConSSE – The International Conference on Science and Science Education!
This conference, which is organized by the Faculty of Science and Mathematics, Satya Wacana Christian
University Salatiga, is held at Laras Asri Resort and Spa Salatiga.
Arts, science and technology are crucial components in the advancement of human civilization. There is art in the
creation of technology, and science provides strong bases for the technological development. We are proud to
inherit the temple of Borobudur which is a proof that Indonesian’s ancient arts and technology are so advanced
that not only is the masterpiece beautiful, but also technologically rich.
This International Conference on Science and Science Education is attended by more than 160 participants. There
are more than 67 papers is presented orally covering wide-variety subjects of science and science education. We
thank you all for your participation.
We thank the Organizing Committee, Reviewers, and Steering Committee for having been working hard. Finally,
we would also like to thank the Rector of Satya Wacana Christian University, and Dean of Faculty of Science and
Mathematics for their support for this conference.
We hope you will enjoy our togetherness. Thank you.
Salatiga, November 30th , 2015
Dr. Adi Setiawan
Chairman
SWUP
vi
Contents
Editorial Team ……………………………………………………………………………………………………..
Proceedings Team ………………………………………………………………………………………………..
Welcoming Address ………………………………………………………………………………………………
Contents …………………………………………………………………………………………………………….
Lessons from the 20th century for 21st century science education
[Berg] ………………………………………………………………………………………………………….
Excited state dynamics of carotenoids free and bound to pigment-protein complexes
[Rondonuwu–Koyama] ………………………………………………………………………………………
Problem solving and reasoning in the learning of mathematics
[Vale] ………………………………………………………………………………………………………….
iii
iv
v
vi
AZ.1
AZ.12
AZ.23
Penalized spline estimator in nonparametric regression
[Andriani–Wibowo–Rahayu] ………………………………………………………………………………..
MA.1
Estimation of parameter in spatial probit regression model
[Fahmi–Ratnasari–Rahayu] ………………………………………………………………………………...
MA.5
Parameter estimation of kernel logistic regression
[Fa’rifah–Suhartono–Rahayu] ……………………………………….……………………………………..
MA.8
Geographically weighted multinomial logistic regression model (Case study: Human development index
value and healths status areas of districts/cities 2013 in Sumatera)
[Fibriyani–Latra–Purhadi] ……………………………………………..……………………………………. MA.13
Comparison of ε-insentive support vector regression and ν-support vector regression in nonlinear
regression problem
[Hustianda–Purnami–Sutikno]……………………………………………………………………………… MA.20
Random forest of modified risk factor on ischemic and hemorrhagic (Case study: Medicum Clinic, Tallinn,
Estonia)
[Karisma–Kormiltsõn–Kuswanto] ………………………..………………………………………………… MA.26
Bivariate generalized pareto distribution to predict the return level of extreme rainfall data (Case: Applied
in Ajung and Ledokombo Stations)
[Lestari–Sutikno–Purhadi] ………………………………………………………………………………….. MA.42
Box–Cox realized asymmetric stochastic volatility model
[Nugroho–Morimoto] ………………………………………………………………………………………… MA.48
Inflow and outflow forecasting of currency using multi-input transfer function
[Reganata–Suhartono]………………………………………………..…………………………………….. MA.53
Classifying the poor household using neural network
[Ruslau–Ulama] ……………………………………………………………………………………………… MA.66
Path analysis model estimates using generalized method of moment (Case study: Maternal mortality in
the Province of East Java)
[Sari–Otok] …………………………………………………………………………………………………… MA.71
Simulation study of reliability coefficient and discrimination index
[Setiawan–Weku] ……………………………………………………………………………………………. MA.79
The effect of enviromental attributes, facilities, and demographic profile on travelled option
[Subanti] …………………………….…………………………………..……………………………………. MA.86
The determinant of traveled expenditure and the number of visitors in Semarang District
[Subanti–Mulyanto–Kurdi]………………………………………………………..…………………………. MA.90
Combination of volatility and Markov-switching models for financial crisis in Indonesia based on real exchange rate
indicators
[Sugiyanto–Zukhronah] …………………………………………………………………………………….. MA.93
Inflow and outflow of currency forecasting using calendar variation model based on time series regression
[Urusyiyah–Suharsono–Suhartono] ………………………………………………………………………. MA.98
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vii
Performance of neural network model in forecasting Indonesian inflation
[Warsito–Suparti–Mukid] …………………………………………………………………………………… MA.103
Financial crisis model in Indonesia using combined of volatility and Markov-switching models based on
international reserve ratio to M2 indicators
[Zukhronah–Susanti–Sugiyanto] ……….………………………………………………………………….. MA.109
Appendix A. (Co-)Presenters Attendance List (Parallel Session)
Appendix B. Question and Answer
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Proceedings of the IConSSE FSM SWCU (2015), pp. MA.48–52
ISBN: 978-602-1047-21-7
MA.48
Box–Cox realized asymmetric stochastic volatility model
Didit B. Nugrohoa and Takayuki Morimotob
a
Department of Mathematics, Satya Wacana Christian University
Department of Mathematical Sciences, Kwansei Gakuin University
b
Abstract
This study proposes a class of non-linear realized stochastic volatility model by applying
the Box–Cox (BC) transformation, instead of the logarithmic transformation, to the
realized estimator. The proposed models are fitted to daily returns and realized kernel
of six stocks: SP500, FTSE100, Nikkei225, Nasdaq100, DAX, and DJIA using an Markov
Chain Monte Carlo (MCMC) Bayesian method, in which the Hamiltonian Monte Carlo
(HMC) algorithm updates BC parameter and the Riemann manifold HMC (RMHMC)
algorithm updates latent variables and other parameters that are unable to be sampled
directly. Empirical studies provide evidence against log and raw versions of realized
stochastic volatility model.
Keywords Box–Cox transformation, HMC, MCMC, realized stochastic volatility
1. Introduction
Volatility of financial asset returns, defined as the standard deviation of log returns,
has played a major role in many financial applications such as option pricing, portfolio
allocation, and value-at-risk models. In the context of SV model, very closely related studies
of joint models has been proposed by Dobrev & Szerszen (2010), Koopman & M. Scharth
(2013), and Takahashi et al. (2009). Their model is known as the realized stochastic volatility
(RSV) model.
Recently, the Takahashi et al. (2009)'s model has been extended by Takahashi et al.
(2014) by applying a general non-linear bias correction in the realized variance (RV) measure.
This study extends the asymmetric version of Takahashi et al. (2014)'s models, known as the
realized asymmetric SV (R-ASV) model, by applying the BC transformation to the realized
measure. Here we focus on the realized kernel (RK) measure that has some robustness to
market microstructure noise. The realized kernel data behave very well and better than any
available realized variance statistic Goncalves and Meddahi (2011).
Adding an innovation to obtain an RSV model substantially increase the difficulty in
parameter estimation. Nugroho & Morimoto (2015) provided some comparison of
estimation results between HMC-based samplers and multi-move Metropolis--Hastings
sampler provided by Takahashi et al. (2019) and Takahashi et al. (2014), where the RMHMC
sampler give the best performance in terms of inefficiency factor. Therefore, this study
employs HMC-based samplers methods to estimate the parameters and latent variables in
our proposed model when draws cannot be directly sampled.
2. Box-Cox R-ASV model
The basic discrete-time RSV model includes three stochastic processes describing the
dynamics of returns, logarithmic RV, and logarithmic squared volatility. In this framework,
the conditional volatility of returns not only depends on the returns but also on the realized
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D.B. Nugroho, T. Morimoto
MA.49
measure of variance. The logarithmic transformation of RV is known to have better finite
sample properties than RV. Goncalves and Meddahi (2011) provided a short overview of this
transformation and suggested that the log transformation can be improved upon by choosing
values of BC parameter other than zero (corresponding to the log transformation). Motivated
by this result, we apply the BC transformation to the RV measure to obtain a class of R-ASV
model called the BCR-ASV model that takes the following form:
ü = exp -›”ℎ .Y
P
7 = ¼+ ℎ + …
K
(1)
ℎ " =m+† ℎ −m + × " ,
O
”
Û[
K
ℎ ~ •m, o—
”–
N
where corr Y , × " = , represents normal distribution, and 7 is the BC transformation
for realized RV defined as
7 = 7 ü ,G = ß
$\] o
À
, if G ≠ 0,
(2)
log ü
, if G = 0.
Notice that this transformation contains the log transformation for RV (when G = 0) and the
raw statistic (when G = 1) as special cases.
As in previous studies, in order to adopt a Gaussian nonlinear state space form where
the error terms in both return and volatility equations are uncorrelated, we introduce a
transformation
× " = Y + Ý1 − ^ " ,
where ^ " ~ 0,1 and corr Y , ^ " = 0. A reparameterization of the model (1) yields
ℎ " = m¼ + † ℎ − m¼ + Æü exp-−›”ℎ . + T^ " ,
where Æ =
ℎ ~ •m¼ ,
Û[”
–,
o—”
and T = 1 −
.
3. MCMC simulation in the BCR-ASV model
Let
= )ü +/# , ½ = )ü +/# , _ = )ℎ +/# , & = -G, ¼ , , … . , and & =
m, †, Æ, T . By Bayes' theorem, the joint posterior distribution of &, _ given R and V is
& , & , _| , ½ = & , & ×
|_ × ½|& , _ × _|& , ,
(3)
where & , & is a joint prior distribution on parameter & , & .
The MCMC method simulates a new value for each parameter in turn from its
conditional posterior distribution assuming that the current values for the other parameters
are true values. We employ the MCMC scheme as follows:
0) Initialize & , & , _ .
1) Given the current values, draw ¼ , , … , m, Æ, and T from their conditional posteriors
directly.
2) Given ¼ , , … , and ½, draw G by HMC.
3) Given m, Æ, T, _, and , draw † by RMHMC.
4) Given & , & , , and ½, draw _ by RMHMC.
For steps (1), (3), and (4), we implement the same sampling scheme proposed in Nugroho &
Morimoto (2014, 2015). In the following, we study the sampling scheme in step (2) only.
As far as the power parameter G ≠ 0 is only concerned to be sampled and by taking
the normal distribution ŽÀ , À for the prior of G, the logarithm of conditional posterior
distribution for G on the basis of Eq. (3) has the following expression:
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Box–Cox realized asymmetric stochastic volatility model
< G ∝−
∑/# È
Û”
MA.50
$\] o
À
−
¼
−
ℎÉ −
Ào•] ”
,
$]
which is not of standard form, and therefore we cannot sample G from it directly. In this case,
we implement the HMC algorithm for sampling G because the metric tensor required to
implement the RMHMC sampling scheme cannot be explicitly derived from the above
distribution.
B
4. Empirical results on real data sets
In this section, the BCR-ASV model and MCMC algorithm discussed in the previous
section are applied to the daily returns and RK data for six different international stock
indices: DAX, DJIA, FTSE100, Nasdaq100, Nikkei225, and SP500. These data sets were
downloaded from Oxford-Man Institute ``realised library" and range from January 2000 to
December 2013. Analyses are presented for the sampling efficiency, key parameters that
build the extension models.
We run the MCMC algorithm for 15,000 iterations but discard the first 5,000 draws.
From the resulting 10,000 draws which have passed the Geweke (1992)'s convergence test
for each parameter, we calculate the posterior mean, standard deviation (SD), and 95%
highest posterior density (HPD) interval. Summary of the posterior simulation results for G
are presented in Table 1.
Table 1. Summary of the posterior sample of parameter G in the BCR-ASV model for six
data sets from January 2000 to December 2013.
Statistic
DAX
DJIA
FTSE100
Nasdaq100 Nikkei225
SP500
Mean
–0.0406
0.1226
0.1572
0.0420
0.0503
0.1149
SD
0.0104
0.0099
0.0096
0.0096
0.0128
0.0094
LB
–0.0609
0.1022
0.1385
0.0242
0.0241
0.0968
UB
–0.0202
0.1409
0.1765
0.0617
0.0741
0.1340
Note: LB and UB denote lower and upper bounds of 95% HPD interval, respectively.
The posterior means of G are positive for DJIA, FTSE100, Nasdaq100, Nikkei225, and
SP500 and negative for DAX. In all cases, the 95% HPD interval of G exclude 0 (the log
transformation) or 1 (the raw version). Although not reported, we find that even 99% HPD
interval of G exclude 0 or 1, providing significant evidence to transform the RV series using
the BC transformation against both the logarithmic transformation and no transformation
cases.
To understand the effect of BC transformation, we present the marginal densities of
the transformed RK implied by G = 0 and the estimated G for each stock index in Figure 1.
The marginal density of the BC RV is obviously different from that of the log RV. When the
estimated G is a positive value, the left tail of the former is lighter than that of the latter,
while the right tail of former is heavier, and vice versa when the estimated G is a negative
value. Moreover the marginal density of the former has a heavier right tail than left tail (as
that of the latter) for both positive and negative values of G. Furthermore, the marginal
density of the former has a higher peak than, and a different location from, that of the latter.
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D.B. Nugroho, T. Morimoto
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Figure 1. Marginal densities of the log RV and BC-RV for six different international stock
indices.
5. Conclusions and extensions
This study presented an extension to the R-ASV models, in which the Box-Cox
transformation is applied to realized measure. The HMC and RMHMC algorithms were
proposed to implement the MCMC method for updating several parameters and the latent
variables in the proposed model, taking advantage of updating the entire latent volatility at
once. The model and sampling algorithms were applied to the daily returns and realized
kernels of six international stock indices. The estimation results showed very strong evidence
supporting the Box-Cox transformation of realized measure. The model can be extended by
assuming a non-Gaussian density of return errors.
References
Dobrev, D., & Szerszen, P. (2010). The information content of high-frequency data for estimating equity
return models and forecasting risk. Working Paper, Finance and Economics Discussion Series.
Geweke, J. (1992). Evaluating the accuracy of sampling-based approaches to the calculation of
posterior moments. In J. M. Bernardo, J. O. Berger, A. P. Dawid, & A. F. M. Smith (Eds.), Bayesian
Statistics 4 (pp. 169–194 (with discussion)). Clarendon Press, Oxford, UK.
Goncalves, S., & Meddahi, N. (2011). Box-Cox transforms for realized volatility. Journal of
Econometrics, 160, 129–144.
Kim, S., Shephard, N., & Chib, S. (2005). Stochastic volatility: likelihood inference and comparison with
ARCH models. In N. Shephard, ed., Stochastic Volatility: Selected Readings (pp. 283–322). Oxford
University Press, New York.
Koopman, S.J., & Scharth, M. (2013). The analysis of stochastic volatility in the presence of daily
realized measures. Journal of Financial Econometrics, 11(1), 76–115.
Nugroho, D.B., & Morimoto, T. (2014). Realized non-linear stochastic volatility models with
asymmetric effects and generalized Student's t-distributions. Journal of The Japan Statistical
Society, 44, 83–118.
Nugroho, D.B., & Morimoto, T. (2015). Estimation of realized stochastic volatility models using
Hamiltonian Monte Carlo-based methods. Computational Statistics, 30(2), 491–516.
Takahashi, M., Omori, Y., & Watanabe, T. (2009). Estimating stochastic volatility models using daily
returns and realized volatility simultaneously. Computational Statistics and Data Analysis, 53,
2404–2426.
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MA.52
Takahashi, M., Omori, Y., & Watanabe, T. (2014). Volatility and quantile forecasts by realized
stochastic volatility models with generalized hyperbolic distribution. Working Paper Series
CIRJE-F-921, CIRJE, Faculty of Economics, University of Tokyo.
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