Joumal ofScience-2016 Vol 10(2). 32-39 PartB: Political Sciences, Economics andLaw
^^% Tap chi Khoa hoc Tru'dng Dai hoc An Giang | r,^
W ^ ISSN 0866 • 8086 ' " ^
DlT BAO G I A V A N G VBET N A M SU* D U N G M O H I N H G A R C H Ngd Van Toin', N g i Q ^ Pfaii Qudc^, Nguyen Huu Thacfa^
'Truang Dgi hgc Himg Vuang
^Truang Dgi hoc Tdi chinh Marketing TPJICM Tlidng tin doing:
Ngdy nhgn bai: 07/12/2015 Ngdy nhdn kit qud binh duyet:
23/12/2015
Ngay chdp nhai dang: 06/2016 Tide:
A forecast on Vietnam goM price by GARCH model Tir khda:
Box—Jenkins A utaregressive Integrated Moving Average (ARIMA). Generalized AuloRegressive Conditional Heteroskedastiaty (GARCH), volatility, gid vang VietNam Keywords:
Box-Jenkins Autoregressive Integrated Moving Average (ARIMA), Generalized Autoregressive Ctmditional Heteroslcedasticity (GARCH), volatility, gold prices of Viet Nam.
A B S T R A C T
TJte purpose ofthe current study is to forecast the gold prices of Viet Nam. Two medtods are considered, which are Box-Jenkins Auta-egressive Integrated Moving Average (ARIMA) and Generalized Autoregressive Conditional Heteroskedasticify (GARCH). Using Akaike's information criterion (AIC) as the goodness of fit measure, the study concludes dial GARCH is a more appropriate model Analysis is carried out by using the Stata 12.0 software.
TOMTAT
Muc dich ciia nghien cuu n^ la de du bdo gtd vdng Vift Nam. Hai phuong phdp dime xem xel, do Id Box-Jenkins Autoregressive Integrated Moving Average (ARIMA) vd Generalized Autoregressive Conditional Heteroskedasttcity (GARCH). Sudungtieu chuanAkaike (Akaike's Information Criterion-AIC) de tim ra mo hmh phit hgp, nghien cuu lUt lugn rdng GARCH (1,1) Id mdi mo hinhdiich hpp han di du bdo. Phdn tich dupc thyrc hien bdng cdch sudymg cdc phdn mim Stata 12.0.
1. G i d l T H I $ U
Myc tieu eua pfaan ticfa cfauoi tiidi gian la d l d u bao cac gia tti tuang lai ciia cfauoi du fapu flidi gian. Trong touong fagp viec du bio vl gia vang i i hihi ich cho myc dicfa diu tu tai Viet Nam. Vang li mpt cdng cy diu bi dac biet quan ttong d cic nudc dang phit ttiln. Lgi bic tu ving v i du doan no la mgt chu dl da va dang tiiu hiit su cfaii y ciia cac nfai diu tu va cd mat do ngMen cuu eao gin d^.
NgMen cuu ciia Miswan, Ping, & Afamad (2013) pfait ttien md Mnh Box-Jenkins Autoregressive Mtegrated Moving Average (ARIMA) dl du bio
gia ving d Malaysia. Biln dgng l i tinh ttang ma pfauang sai dieu kien thay ddi giua togng fliai gia t i rit cao v i t h ^ . Vl mgt ly tfiiQ'lt, kM tilp cin vdi cfaudi du lieu tfadi gian, dieu quan trgng li de dy bio do bien ddng cua chuoi dii Upu hoac tim dugc pfauong sai \hsy doi theo flidi gian.
Md Mnfa ARCH dugc gidi tMpu bdi Engle vao nam 1982 va tdng quit hda bdi Bollerslev nam 1986 l i md hinfa kinfa tl dl md ti cfaudi vdi tinh cfait phuong sai dilu kien t h ^ dli theo thdi gian (Engle, 1982). Cic hg md Mnfa Generafazed faeteroskedasticity (GARCH) dugc pfaat biln dl nim bat bien dgng phan nhdm faogc cic giai dogn
Joumal ofScience - 2016. Vol 10 (2). 32 - 39 bien dgng, v i dy doin sy bien ddng trong tuong lai (Bollerslev, 1986).
Box-Jenkins ARIMA la md Mnfa chuan, ngMen ciiu nay dy bio gii ving Viet Nam su dyng md hinfa GARCH. Bing each sir dyng phin mem Stata 12.0, cac md tiinfa GARCH dugc su dyng de cung cqi mgt thudc do bien dgng pfaan nhdm cua gja vang. Dg phii fagp cua qui trinfa dy bio cie md liinh dugc do bang AIC (Akaike's Infoimation Criterion).
2. CAC NGHIEN CU*U LIEN QUAN NgMen cuu cua Ping, Miswan, & Afamad (2013) nfaim myc dicfa la de dvt bao gia vang tfadi cnia Malf^ia Hai pfaucmg pfa^ dugc xem xet, dd la Box-Jenkins - ARIMA va md faufli GARCH. Su dung tieu cfauan tfadi^ tm Akaike cua (AIC) de jfami md hinfa pfaii pfau hgp, ngMen cuu ket lugn rat^ GARCH la mpt md tiinfa iMcfa fagp hon. Phan tich dugc thyc Men bang each sii dyng cic pfain mem E-views.
NgMen cnhi nay (Sib Roslmdar et al., 2015) li mgt pfaan tich so bd ve gii vang va bien dgng eua nd tap tnmg vio vipc tfayc Men eic md hinh lai Box-Jenkins eung vdi GARCH trong phan tich vi dy bio gii ving. Cdng thiic Box-Cox dugc sii dyng nhu l i phucmg p h ^ cfaiQ^n ddi du heu do CO tiem nang tdt irong dii lipu pfaan pfadi cfauan, tao sy on dinfa pfauang sai va lam giam cac bien ngau nMen su dung dir Ueu 41 nam vl gia vang hing ngiy bat diu tic 02 tfaang 1 nam 1973.
NgMen ciiu niy cM ra ring md tiinfa ket hgp dugc de xuat ARIMA -GARCH cd tfae l i mot cicfa tiep cgn mdi cd tiem ning trong viec dy bio gii ving.
Phit Men nay chiing td siic manh cua md hinh GARCH toong vigc xii Iy bien ddng gii vang cung nhu khac phyc dugc nhung ban che pM tuyen tinh trong md liinh Box-Jenkins.
NgMen eiiu cua Kocak and Un (2014) dg eq) din cac phucmg pfaip khic nhau dang dugc sii dung de dy doan lgi bic ving va Mpu cpii ciia eac pfaucmg p h ^ nay dugc so sanfa. Myc dicfa cua ngMen ciiu nay li de tao m mpt dy doin tgi bic tii ving Sli dyng cac mang tfaan Icmfa nfain tao va
Part B: Political Sciences, Economics and Law GARCH va ea: phii sinh ciia nd, ngMen ciiu sa dyng pfaucmg pfa^ chudi tfadi gian, dua tren so Upu ve ty suit lgi bic tfaeo flidi gian ciia gii vang dugc cung cap bdi San giao dicfa vang ciia Tfad NM Ky tiiugc flidi ky tiiang 2 nam 2014 v i fliang 6 nam 2014.
Ahmad, Pung, Yazir, and Miswan (2014) cic tic gia da trinh bay mgt mo hinfa ket fagp da dugc coi l i mdt cich Mpu qua de cai iMpn dg ctiinfa xic du bao. Bii bao de xuit md hmh kit hgp ciia ARIMA va GARCH vio trong md hinh vi de dy bao gia vang cua Malaysia dugc sii dyng dl trinh biy sy pfaat trien cua cac md fainfa ket fagp. Sy pfau fagp cua md hinfa dugc do bang tieu cM flidng tin Akaike (AIC).
3. PHU'ONG PHAP NGHIEN COtJ Cic phucmg p l i ^ ^ g c su dung toong ngMSn ciiu nay l i Box-JenMns ARIMA va GARCH. Du Upu su dyng cho ngM€n ciiu nay la gia vang Vipt Nam duge thu thgp trong tdioing tiidi gian tu n g ^ 03/01/2000 din ngiy 06/11/2015. Cfaudi dii Ueu Vii^ dugc cung cl^ bdi Thomson Reuters (ht^://thomsonreuters.com). Ty suit lgi bic bang n g ^ eua cM sd Ving dugc tinfa tfaeo cdng tfaiic sau:
F.-P,}
Rr=-E-^Xim
Vdi Pt l i gii Vang tai thdi diem ddng cua ciia ngay giao dicfa tfaii t tucmg iing vi PM la bien tre mdt ngiy cua Vang.
Box-Jenkins ARIMA
Box-Jenldns ARIMA dugc ip dung tren dii Ueu cfaudi tfadi gian dgt tinh diing, chudi tinfa dimg cd dugc bang each 1 ^ sai phan mdt miic do thich hgp. Dieu nay din den mgt md fainfa ARIMA (p.
d. q) trong dd p la bgc ty hdi quy, q li tfaii ty trung bmfa tmgt va d t i fliii bac cua chudi dumg.
Md Mnfa ARIMA(p.i5i',^) cd the vilt nfau sau;
il,,{B){\-BYy,=S+e^(B)u,
Trong do:
Joumal ofScience - 2016. Vol 10 (2). 32 - 39 (jt (B) = l-^B-...^pB''lk qui ttinh ty hoi (juy bac p;
d {B) = l-e[B-...d^BHh qui ttinh tiung binh tmgt bac q;
( 1 - D ) la bgc sai phan bac tini d.
B la toan tii lui ciia bac sai phan.
W, ta nMeu tring.
Mo hinh GARCH
Mo hinh ARCH dgc bipt &rgc xay dyng de tgp md binh vi dy bao ve phuang sai cd dieu kipn.
Md hinh ARCH duge Engle gidi tMeu vao nam 1982 va md hinfa GARCH duge gidi fliipu bdi Bollerslev vio nam 1986. Nhung md fainh nay dugc su dyng rgng rai ttong cic md hinh toan kinh tl, dac biet t i tiong pfaan tiefa chuoi thdi gian tii chinh gidng nfau Bollerslev, Cfaou, Kroner di thye Men vao nam 1992 v i Bolteslev, Engle, Nelson da tien hanh vio nam 1994.
Mo hinfa GARCH (Generafased Autoregressive Conditional Heteroskedasticity) la md hinh tong quit hda cao hem mo hinfa ARCH Mo hinh GARCH (p,q) cd dang sau day:
Trong do:
p: la bac cua md hinh GARCH.
q: la bic cua md hinh ARCH.
Phucmg trinh noi ten ring phuang sai ht bay gid phy fliuoc vio gia tri qua khii ciia nfaiing cii soc, dai dien bdi cac bien ttg ciia hang nhieu bmh phuang, va cac gia toi qua khii ciia ban tiian h dai dien bdi cac biln h^_,. Dang don gian nhat Clia md hinh GARCH la GARCH (1,1), duac bieu dien nhu sau:
PartB: Political Sciences. Economics andLaw
Mpt lgi ich ro rang nhit md hinh GARCH mang Iai so vdi md hinh ARCH Ii ARCH(q) vo tgn bing GARCH (1,1). N I U ARCH co qui nMeu dp tri (q Icm) iM cd tfal se infa hudng den ket qua udc tugng do giam dang ke so bac ty do toong mo hinh, Mdt chuoi du Ueu cang nMeu do tog se co nMeu bien hi mat
Tieu chuan AIC
Akaike (1974) dc xuit beu cfauin AIC la ky fliuat dung d8 lya cfagn md hinh AIC dya tren n§n tang Iy tfauyet flidng tin vi t i mgt tieu cM mi tim kiem mpt md binh phu hgp Md hinh nky dugc chpn bang each giam tfailu kfaoang cacfa Kullback- Leifaler giua md hinh v i do chinh xac.
AIC dugc xic diifli bang cdng thiic sau:
AIC(p,q) =-2}n +2k Trong dd:
l i gii tri tdi da ciia ham Likelihood dugc udc til md hinh;
k l i bac tu do cua md hinh.
Md fainh dugc chgn l i md hinh cd gii tri AIC la gia tn thap nhat
Fhuong phap chuyin dirU^u: Box-Cox Theo Osborne (2010) chuyin ddi du fapu bing Box-Cox tiem nang tot nfaat kM nio muon ehuan hda dii Ueu hoge can bang phuang sai nfau mong mudn, ma Box-Cox duoc hinh dung nhu li mpt logi tiiudc chua bich benfa ciing ddng tfadi dieu chinfa cfauan fada va giam da cdng Myln Phuong pfaip efauyen ddi Box-Cox nhu sau.
jf-i forA*0 y,=\ A
Trong do: J', la dii Ueu thuc tai thdi gian t, J, la du lieu chuyen doi tgi tfadi gian ^ va /I la gia tri
Joumal ofScience - 2016. Vol 10 (2), 32 - 39 trung bmh sai so bmh phucmg cua phan du t l i ^ nfa^ Chuyen du lieu cM sp dung cfao cfauoi dir lieu duong, ^ >• 0.
4. Dtr LIJUVAKfeT QUA NGHIEN CUtJ
PartB: Political Sciences. Economics andLaw So Upu thu thap tii flii tiudng vang, vdi 4145 ky quan s i t Tfaeo xu hudng cfao t h ^ gia vaag Vi^t Nam cd xu huang tang d mgt khoan tiidi gian vi dao dgng manfa.
1000 2000
date
3000
Hmh 1. Gia vang Viet Nam t u Ity quan sat 1 den 414S Ngudn: Kittpidphdn tich sd lieu tieSlata 12.0
Tinfa xu tfae tfae Men tren bieu dd,'dieu niy can tiult phai kfaii tfnfa xu tfae dl dy Ueu cd tinfa diing. Ky tfauat kfaii tinfa xu tfag sit dung la Box-Cox. Sau kM kfaii tinfa xu tfae dii Ueu cd dang nfau sau:
Joumal ofScience-2016 Voi 10(2), 32-39 Part B: Political Sciences, Economics andLaw
1000 2000
date
3000
Hinli 2. Tinh dong cua du* Uen sau khi khv tinh xu the Ngudn: Kel qua phan tich so liiu tit Stata 12.0
Xac dinfa md faufli, faam t y fadi quy (ACF) v i b i fadi quy tiing pfain (PACE) tfae Men tren hinh ve hi dii hpu sau kM da khii tmfa xu tfal.
•If'
Hinh 3. Ham t y hoi quy va tu hoi quy rieng phan NguSn Kit qua phdn tich so liiu tif Slata 12 0
Vi cac gia toi d l u n i m ttong vimg kfadng cd y ngMa, nen ttang b i i ngMgn ciiu se kfadng dimg ARIMA ttong pfauang timfa ttung bmfa cfao Mgu ung A R C H , cM su dung pfauong ttinfa p h u a n g sai.
Joumal ofScience-2016, Vol 10(2). 32-39 Part B: Political Sciences. Economics and Law K l l m t r a hi$u n u g A R C H
LM t e s t f o r a u t o r e g r e s s i v e c o n d i t i o n a l h e t e r o s k e d a s t i c i t y (ARCH) lags(p)
1 2 3 4 5
Chi2
53.812 114.673 132.975 148.710 161.865
df
1 2 3 4 5
Prob > chi2
0.0000 0.0000 0.0000 0.0000 0.0000
HO: n o ARCH e f f e c t s v s . H I : ARCH(p) d i s t u r b a n c e Ng^dn: Kit qud phdn tich so biu tii Stata 12.0
Ket q u i Idem tra Mpu iing A R C H ttt phan men Stata 12.0 tii d u Upu thu tfagp cfao tfaay du Ueu cd Men iing ARCH. B i n g cfaung tfayc ngMpm cho t h i y gia tri P-value deu nhd facm 0.05 tdi dg t i e 5.
2000 date
Hinh 4. Bien dong cua ty suat loi tire cua vang Viet Nam Nguon: Kit qua phdn tich so lieu tit Stata 12.0 Bieu dd cfao tfaiy ty s u i t Igi hie cM so g i i vang
Viet Nam ed tinfa c h i t bien dpng cym {volatility clustering). Nhiing kfaoing tfadi gian tgi tiic vdi bien do dao ddng tdn cd xu faudng pfain bo rai r i c
gan nhau va n g u g c tgi, nhung kfaoang tfadi gian loi tiic vdi dao ddng nhd cd xu faudng pfaan bd rai rac gan nfaau. Vdi tinh chat bien ddng n i y , r i t phu hgp sti dyng md fainh G A R C H d l d u bao.
37
Journal ofScience - 2016, Vol. 10 a), 32 - 39 Port B: Pohlical Sciences. Economics J Kk qui iri^c b'nh ma hinh GARCH cho ket qua nhu- sau:
dgoldprice cons
ARCH L.arch
L.garch
L2.garch
L3.garch
cons
N AIC BIC
(1) dgoldprice
0.00239*
(2.49)
0.0747***
(28.27) 0.932***
(372.60)
0.0000164***
(8.92) 4134 -5102.3 -5077.0
(2) dgoldprice
0.00263*
(2.54)
0.101***
(28.33)
U.911***
(306.14)
0.0000171***
(6.29) 4134 -5027.o -5002.4
(3) dgoldprice
u.00302**
(3.13)
0.145***
(30.07)
0.878***
(234.46) 0..0000405***
(11.59) 4134 -4854.8 -4829.J
• s t a t i s t i c s i n p a r e n t h e s e s p < 0 . 0 5 , ** p < 0 . 0 1 , *** p < 0 . 0 0 1
T4 kit qua tren nhom tac gia chpn mo htah- GARCH (1,1) dung de du bao gia vang VietNam vi mo htah GARCH nay co AIC va BIC la nho nhat.
5. K i T L U ^ N
Doi vm mo hmh ARIMA cho thay khong phu hop voi vice du bao gia vang Viet Nam. Blng chiing nay da dugc chiing mmh tii vice lua chpn dp Oe tii ham tu h6i quy va ham tu h6i quy tiing phan.
M3 htah GARCH la mo hinh c6 kha ning nim bit
Nguon: KSt quaphan tich sd liiu tit Stata 12.0
bien dpng cum hoac cho nhiing thoi ky biln dpng, va du doan s\r bien dpng trong tuong lai. Tii cac gia tn BIC va AIC, mp hinh GARCH (1,1) la mo hmh phd hop nhat vi cac gia tri BIC va AIC la thap nhat. Nhu vzty, dpi voi du bao gia vang o Viet Nam, ket qua nghien ciiu cho thiy chua co the ap dung mo hinh kit hpp ma chi co mo htah GARCH phu hop dl tien hanh du bap.
Joumal ofScience - 2016. Vol 10 (2), 32 - 39 TAI LI|:U THAM KHAO
Ahmad, M. H., Pung, Y. P., Yazu, S. R, &
Miswan, N. H. (2014). A hybrid model for improvmg Malaysian gold forecast accuracy.
Intemational Joumal of Mathematical Analysis, S(28), I377-I387.
Akaike, H. (1974). A new look at flie statistical model identification. Automatic Control, IEEE Transactions on, 19{S), 716-723.
BoUerslev, T. (1986), Generalized autoregressive conditional heteroskedasticity. Joumal of econometi-ics. 57(3), 307-327.
Engle, R F. (1982). An Mtixiduction to tiie Use of A R C H / G A R C H models m AppUed Econometrics. Joumal of Business, New York.
Kocak, H., & Un, T. (2014). Forecasting flie Gold Returns with Artifical Neural Netwoik and Time Series. Intemational Business Research, 7(11), 139.
Part B: Political Sciences, Economics andLaw Miswan, N. H., Ping, P. Y., & Ahmad, M. H.
(2013). On parameter estimation for Malaysian gold prices modelling and forecasting.
Intemational Joumal of Mathematical Analysis, 7(21-24), 1059-1068.
Osborne, J. W. (2010). Improvmg your data transformations: Applymg tiie Box-Cox transformation. Practical Assessment, Research & Evaluation, 75(12), 1-9.
Ping, P. Y., Miswan, N. H , & Ahmad, M. H.
(2013). Forecasting MaMysian Gold Usmg GARCH Model. Applied Mathematical Sciences, 7(58), 2879-2884.
Siti Roslmdar, Y., Noor AzUnna, A., Maiza Hura, A., Roslmazairimah, Z., Agrawat, M., &
Botand, J. (2015). Preliminary Analysis on Hybrid Box-Jenkins-GARCH Modeling In Forecasting Gold Price.
