ng dụng mô hình ARIMA – ARCH GARCH để dự báo thanh khoản của 30 cổ phiếu có giá trị vốn hóa và thanh khoản lớn nhất niêm yết trên sở giao dịch chứng khoán thành phố hồ chí minh trong ngắn hạn

Lụứi Caỷm ễn u tiờn, em xin gi li cm n n Thy Cụ trng i hc Kinh t Hu núi chung v Thy Cụ khoa Ti Chớnh Ngõn Hng núi riờng, ó tn tõm ging dy em sut quỏ trỡnh hc v nghiờn cu ti trng c bit, em xin gi li cỏm n chõn thnh nht n Ths on Nh Qunh, ngi ó trc tip hng dn em thc hin ti tt nghip Nh s hng dn v ch bo tn tỡnh ca cụ, em ó cú c nhng kin thc v kinh nghim quý bỏu v cỏch xỏc nh nghiờn cu, phng phỏp nghiờn cu, xỏc nh kt cu cho ti, trỡnh by kt qu v hon thnh ti tt nghip ca mỡnh Cui cựng, em xin by t lũng cm n sõu sc n gia ỡnh v bn bố ó luụn bờn cnh, h tr v ng viờn em hon thnh tt khoỏ lun ca mỡnh Em xin chõn thnh cm n! Hu, thỏng 05/2015 Sinh viờn thc hin Hunh Th Phng i MC LC PHN I: T VN .1 1.Tớnh cp thit ca ti: 2 Mc tiờu nghiờn cu: 2.1.Mc tiờu nghiờn cu .5 3.i t ng, ph m vi: 3.1.i t ng nghiờn cu: 3.2.Ph m vi nghiờn cu: .6 4.Ph ng ph p nghiờn cu 5.Kt cu ti .7 PHN 2: NI DUNG V KT QU NGHIấN CU CHNG 1: Lí LUN THANH KHON V CC Mễ HèNH O LNG, D BO 1.1.Thanh khon: 1.1.1.nh ngha tớnh khon: 1.1.2.Tớnh khon: 1.1.3.Tớnh khon ca c phiu: 1.2.C c yu t nh h ng n khon c phiu: 1.3.o l ng tớnh khon ca c phiu: 10 1.3.1 Ph ng ph p o l ng liờn h sõu: 11 1.3.2 Ph ng ph p o l ng liờn h cht: 13 1.3.3 Ph ng ph p o l ng liờn h thi gian giao dch: .14 1.3.4 Ph ng ph p o l ng liờn h co gión: 14 1.4 D liu nghiờn cu: .16 1.5.Ph ng ph p nghiờn cu: 16 1.5.1 Vn c bn v chui thi gian: 16 1.5.1.1 Chui thi gian l gỡ: 16 1.5.1.2 C c thnh phn ca chui thi gian .16 1.5.2 C c liờn quan n tớnh dng: 17 1.5.2.2 Kh i nim tớnh dng .17 1.5.2.3 Hu qu ca chui khụng dng: 17 1.5.2.4 C ch kim nh tớnh dng ca chui thi gian: .18 ii 1.5.2.4.1 T t 1.5.2.4.3 T t ng quan ACF (Autocorrelation function) .18 ng quan mu PACF (Partial Autocorrelation function): 19 1.5.2.4.4 Kim nh Dickey-Fuller (kim nh nghim n v- Unit root test): 19 1.5.2.4.5 Nhiu trng(white noise): 19 1.5.2.4.6 B c i ngu nhiờn (Random Walk): 20 1.4.1.5 Bin i chui khụng dng thnh chui dng 20 1.4.2 Mụ hỡnh Arima 20 1.4.2.1 C s lý lun 20 1.4.2.2 Qu trỡnh t hi quy (AR Autoregressive Process) 21 1.4.2.3 Qu trỡnh trung bỡnh tr t (MA Moving Average) 21 1.4.2.4 Qu trỡnh trung bỡnh tr t v t hi quy ARMA 22 1.4.2.5 Qu trỡnh trung bỡnh tr t, ng liờn kt, t hi quy ARIMA 22 1.4.2.6 Ph ng ph p Box-Jenkins .23 1.4.3.6.1 nh d ng: 24 1.4.3.6.2 c l ng mụ hỡnh .29 1.4.3.6.3 Kim nh tớnh thớch hp ca mụ hỡnh .29 1.4.3.6.4 D b o 31 1.2.4 Lý thuyt mụ hỡnh ARCH/GARCH .31 1.2.4.1 Mụ hỡnh ARCH: 31 1.2.4.2 L ý thuyt mụ hỡnh GARCH: 34 Ch ng 2: CH S CHNG KHON VN30-INDEX V DIN BIN THANH KHON CA TH TRNG CHNG KHON VIT NAM GIAI ON 2012 2015 36 2.1 Tng quan v ch s chng kho n VN30-Index 36 2.1.1 Ch s VN30 l gỡ .36 2.1.2 í ngha .36 2.1.3 Tiờu chun la chn c phiu vo r VN30 .37 2.1.4 iu kin tham gia ch s VN30: 37 2.1.5 Ph ng ph p tớnh: .38 2.1.5.1 Tiờu tớnh toỏn: 38 2.1.5.2 Cụng thc tớnh VN30: 39 2.1.5.3 Gi tớnh to n ch s 39 2.2 Thanh khon ca th tr ng chng kho n giai o n t nm 2012 n nay: din bin VN-Index, VN30-Index .39 iii 2.2.1 Nm 2012: 40 2.2.2 Nm 2013: hi phc m nh m 43 2.2.3 Nm 2014 n nay: 45 Ch ng 3: D BO THANH KHON CA NHểM 30 C PHIU Cể GI TR VN HểA V KHI LNG GIAO DCH LN NIấM YT TRấN S GIAO DCH CHNG KHON THNH PH H CH MINH 50 3.1 Lý la chn ch s Amivest: 50 3.2 Mu quan s t: .50 3.3 Kt qu nghiờn cu: .51 3.3.1 Thng kờ mụ t s liu: .51 3.3.2 Kim nh tớnh dng ca chui Amivest: 52 3.3.3 Phõn phi x c sut ca chui Amivest: 52 3.3.4 La chn mụ hỡnh ARIMA(p,d,q): 53 3.3.4.1 Mụ hỡnh ARIMA (p,0,q) tt nht d b o: 53 3.3.4.2 D b o th nghim trờn mụ hỡnh ARIMA(1,0,1) : .55 3.3.5 c l ng mụ hỡnh GARCH: 58 3.3.5.1 c l ng mụ hỡnh GARCH(p,q): 58 3.3.5.2 D b o: 59 3.3.5.3 Nhn xột v tho lun: 60 PHN : KấT LUN .62 1.Kt qu t c : 62 H n ch : 63 H ng ph t trin ti : .64 Khuyn ngh: 64 TAI LIU THAM KHO 65 PH LC 67 Ph lc 68 iv DANH MC CC CH CI V Kí HIU VIT TT VN30-INDEX : Ch s chng khoỏn ca 30 doanh nghip cú giỏ tr húa ln nht TTCK : Th tr ng chng khoỏn HOSE NHNN NT DN KLGD DMT : S giao dch chng khoỏn thnh ph H Chớ Minh : Ngõn hng Nh n c : Nh u t : Doanh nghip : Khi l ng giao dch : Danh mc u t CSTT GTVH GTDD CTCP NHTMCP ACF : Chớnh sỏch tin t : Giỏ tr húa : Giỏ tr dao dch : Cụng ty c phn : Ngõn hng th ng m i c phn : Hm t t ng quan PACF AR MA ARIMA : Hm t t ng quan riờng phn : T hi quy (Autoregressive) : Trung bỡnh tr t (Moving Average) : T hi quy tớch hp trung bỡnh tr t (Autogressive Integrated Moving Average) : T hi quy cú iu kin ph ng sai sai s thay i ARCH GARCH PPXS (Autoregressive Conditional Heteroshedasticity) : T hi quy tng qu t cú iu kin ph ng sai sai s thay i (Generalized Autoregressive Conditionnal Heteroshedasticity : Phõn phi xỏc sut v DANH MC BNG BIU Bng 1.1 C c khớa c nh ca khon 10 Bng 1.2 - C c d ng lý thuyt ca ACF v PACF 25 Bng 3.1 Thng kờ mụ t chui Amivest .51 Bng 3.2 La chn mụ hỡnh ARIMA(p,0,q) 54 Bng 3.3 D b o ngoi mu cho giai o n t 06/02/2015 n 27/03/2015 57 Bng 3.4 La chn mụ ARCH/GARCH 58 Bng 3.5: kt qu d b o ch s Amivest theo tun ngy 03/04/2015 n 06/05/2015 .59 vi DANH MC HèNH Hỡnh 1.1 - Quy trỡnh ca ph ng ph p Box-Jenkins 24 Hỡnh 1.2 - Quỏ trỡnh AR(1) .26 Hỡnh 1.3 - Quỏ trỡnh MA(1) 26 Hỡnh 1.4 - Quỏ trỡnh MA(2) 27 Hỡnh 1.5 Quỏ trỡnh ARIMA(1) 28 Hỡnh 2.1 T trng ngnh theo GTVH ca r VN30 .37 (Ngun: HOSE) 37 Hỡnh 2.2 Din bin khon TTCK nm 2012 40 Hỡnh 2.3 Din bin khon TTCK nm 2013 44 Hỡnh 2.4 Tỡnh hỡnh khon TTCK t nm 2014 n 46 Hỡnh 3.1 th PPXS ca chui Amivest .52 Hỡnh 3.2 D b o Amivest giai o n t 10/02/2012 n 30/01/2015 55 Hỡnh 3.3 Phn d , gi tr thc v gi tr c l ng t mụ hỡnh ARIMA(1,0,1) 56 Hỡnh 3.4 Gi tr thc v d b o ch s Amivest 56 Hỡnh 3.5 D b o ph ng sai cho chui Amivest 59 vii viii TểM TT TI Thanh khon c xem l yu t huyt m ch ca th tr ng ti chớnh Vic iu tit phự hp ca nú l rt quan trng cho s hnh tr n tru ca mt nn kinh t Chớnh vỡ vy, vic tin hnh o l ng v d b o gi tr t khon, cng nh ri ro thụng qua bin ng ph ng lai ca ng sai ca ch s khon l iu thc s cn thit vi bt k mt nh u t , mt doanh nghip no nghiờn cu u t vo bt k mt ti sn no, c bit l trờn th tr ng chng khoỏn Tuy nhiờn, tớnh t i thi im hin t i, hu nh ch a cú nghiờn cu n c v o l ng v d b o khon Nm bt c thc t ny, tụi quyt nh la chn ti: : ng dng mụ hỡnh ARIMA ARCH/GARCH d bỏo khon ca 30 c phiu cú giỏ tr húa v khon ln nht niờm yt trờn s giao dch chng khoỏn thnh ph H Chớ Minh ngn hn Mc tiờu quan trng nht m ti h ng n l d b o khon t ng lai gn cho nhúm c phiu r VN30 T ú, giỳp cho nh u t v cỏc nh ho ch nh chớnh s ch nm bt xu th khon v c i nhỡn chun x c h n v tỡnh hỡnh hin t i v t ng lai v tỡnh hỡnh khon ca nhng c phiu Bluechip trờn th tr ng chng kho n Vit Nam thc hin cụng t c d b o, ti ó s dng ch s khon Amivest v tin hnh c l ng v kim nh c c mụ hỡnh ARIMA, ARCH/GARCH Bng ph ng ph p th v sai, thụng qua c c ch tiờu: AIC, SIC, R2, MAE, MAPE, Thiel, Bias,cui cựng mụ hỡnh GARCH(1,2) l mụ hỡnh thớch hp nht c la chn d b o Kt qu d bỏo ca mụ hỡnh c nh gi t ng i sỏt vi giỏ tr thc t, giỏ tr trung bỡnh d bỏo ca ch s AMIVEST tng dn t ng lai T nhng kt qu ny, tụi cng ó a mt s khuyn ngh cho nh u t gúp phn giỳp h cú th a nhng quyt nh ỳng n nht PHN I: T VN 1.Tớnh cp thit ca ti: TTCK úng vai trũ quan trng i vi s ph t trin ca nn kinh t ca mt quc gia Th tr ng ny giỳp NT n gn h n vi DN, qua ú DN cú c hi tip cn vi ngun ln, m rng sn xut kinh doanh, ph t trin bn vng TTCK t i n c bit n l mt kờnh u t v thu hỳt hp dn nhiu quc gia Chớnh kh nng sinh li khng l m th tr ng mang l i ó thu hỳt rt nhiu NT, DN coi TTCK l n i t o ngun thu nhp v huy ng ch yu ca h Gi c chng kho n l hỡnh nh phn chiu nhng c bn ca nn kinh t v mụ, c bit l sc khe ca DN v l mi quan tõm hng u ca NT cng nh nh nghiờn cu Bờn c nh gi c, th tr ng ti chớnh núi chung v TTCK núi riờng, cú mt yu t quan trng khụng th khụng k n ú chớnh l khon Thanh khon c xem l yu t huyt m ch ca th tr ng ti chớnh Trong t c phm nghiờn cu How best to supply liquidity to a securities market (1996), Handa v Schawarts ó a nhn nh: Nh u t mong mun ba iu t th tr ng, ú l: Thanh khon, khon v khon Vic iu tit phự hp ca nú l rt quan trng cho s hnh tr n tru ca mt nn kinh t Khi th tr ng gim tớnh khon l lỳc nhng nh t chc th tr ng phi lo ng i bi khon th hin nim tin ca nh u t , l c s cho c c doanh nghip s dng kờnh th tr ng chng kho n huy ng Thanh khon tt lm cho gi c phn nh thc cht cung cu m khụng b búp mộo bi c c giao dch thao tỳng, lm gi trờn th tr ng c bit, khon rt c chỳ ý TTCK nh mt nhng tiờu quan trng d b o, quyt nh xu h ng th tr ng, ca nhúm c phiu hoc tng c phiu riờng l Mt phn no ú, nú cng phn nh mc ri ro ca c phiu 5.4 c l ng mụ hỡnh ARIMA(0 1) Dependent Variable: AMIVEST Method: Least Squares Date: 05/10/15 Time: 15:35 Sample: 2/10/2012 1/30/2015 Included observations: 156 Convergence achieved after 13 iterations MA Backcast: 2/03/2012 Variable Coefficient Std Error t-Statistic Prob C MA(1) 6561.604 0.231359 981.1692 0.078499 6.687535 2.947277 0.0000 0.0037 R-squared Adjusted R-squared S.E of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) Inverted MA Roots 0.073194 0.067175 9962.644 1.53E+10 -1656.577 12.16199 0.000636 Mean dependent var S.D dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter Durbin-Watson stat 6557.303 10315.13 21.26381 21.30291 21.27969 1.886671 -.23 5.5 c l ng mụ hỡnh ARIMA(0 2): Dependent Variable: AMIVEST Method: Least Squares Date: 05/10/15 Time: 15:36 Sample: 2/10/2012 1/30/2015 Included observations: 156 Convergence achieved after 11 iterations MA Backcast: 1/27/2012 2/03/2012 Variable Coefficient Std Error t-Statistic Prob C MA(2) 6549.669 0.188320 958.7324 0.079203 6.831593 2.377689 0.0000 0.0186 R-squared Adjusted R-squared S.E of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.048381 0.042201 10095.13 1.57E+10 -1658.638 7.829400 0.005797 Mean dependent var S.D dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter Durbin-Watson stat 75 6557.303 10315.13 21.29023 21.32933 21.30611 1.472934 5.6 c l ng mụ hỡnh ARIMA(1 2) Dependent Variable: AMIVEST Method: Least Squares Date: 05/10/15 Time: 15:37 Sample (adjusted): 2/17/2012 1/30/2015 Included observations: 155 after adjustments Convergence achieved after iterations MA Backcast: 2/03/2012 2/10/2012 Variable Coefficient Std Error t-Statistic Prob C AR(1) MA(2) 6607.210 0.282672 0.121509 1225.554 0.080477 0.083400 5.391203 3.512464 1.456946 0.0000 0.0006 0.1472 R-squared Adjusted R-squared S.E of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) Inverted AR Roots 0.118699 0.107102 9771.734 1.45E+10 -1642.444 10.23610 0.000068 Mean dependent var S.D dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter Durbin-Watson stat 6588.460 10341.20 21.23154 21.29045 21.25547 2.024947 28 5.7Mụ hỡnh ARIMA(2,0,0) Dependent Variable: AMIVEST Method: Least Squares Date: 05/18/15 Time: 12:53 Sample (adjusted): 2/24/2012 1/30/2015 Included observations: 154 after adjustments Convergence achieved after iterations Variable Coefficient Std Error t-Statistic Prob C AR(2) 6657.147 0.264419 1098.505 0.078148 6.060186 3.383570 0.0000 0.0009 R-squared Adjusted R-squared S.E of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) Inverted AR Roots 0.070044 0.063926 10026.91 1.53E+10 -1636.316 11.44854 0.000910 Mean dependent var S.D dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter Durbin-Watson stat 51 -.51 76 6627.226 10363.63 21.27683 21.31628 21.29286 1.545606 Kim nh t t ng quan phn d cho mụ hỡnh ARIMA(p,0,q): Kim nh gi thuyt: Ho: phn d t t ng quan H1: phn d khụng t t ng quan 6.1 Mụ hỡnh ARIMA(2,0,2) Breusch-Godfrey Serial Correlation LM Test: F-statistic Obs*R-squared 2.077136 8.238512 Prob F(4,147) Prob Chi-Square(4) 0.0867 0.0832 Test Equation: Dependent Variable: RESID Method: Least Squares Date: 05/14/15 Time: 00:20 Sample: 2/24/2012 1/30/2015 Included observations: 154 Presample missing value lagged residuals set to zero Variable Coefficient Std Error t-Statistic Prob C AR(2) MA(2) RESID(-1) RESID(-2) RESID(-3) RESID(-4) 2013345 0.025065 -0.044430 0.189585 0.010511 -0.029428 0.085215 1877889 0.023342 0.042092 0.082286 0.089917 0.084508 0.088738 1.072132 1.073824 -1.055530 2.303969 0.116901 -0.348228 0.960298 0.2854 0.2847 0.2929 0.0226 0.9071 0.7282 0.3385 R-squared Adjusted R-squared S.E of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.053497 0.014864 9245.185 1.26E+10 -1621.241 1.384752 0.224430 Mean dependent var S.D dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter Durbin-Watson stat 4.191337 9314.671 21.14598 21.28403 21.20206 2.021017 Gi tr P-Value = 0.0867, ch a cú c s b c b gi thit H o Vy phn d mụ hỡnh ARIMA(2,0,2) khụng t t ng quan 77 6.2.Mụ hỡnh ARIMA(1,0,1): Breusch-Godfrey Serial Correlation LM Test: F-statistic Obs*R-squared 0.957673 3.910273 Prob F(4,148) Prob Chi-Square(4) 0.4327 0.4183 Test Equation: Dependent Variable: RESID Method: Least Squares Date: 05/10/15 Time: 15:33 Sample: 2/17/2012 1/30/2015 Included observations: 155 Presample missing value lagged residuals set to zero Variable Coefficient Std Error t-Statistic Prob C AR(1) MA(1) RESID(-1) RESID(-2) RESID(-3) RESID(-4) -626.1150 -0.010694 0.061473 0.002230 -0.050190 -0.167172 0.039309 4217.317 0.048324 0.176637 0.165542 0.134034 0.117223 0.107744 -0.148463 -0.221302 0.348019 0.013471 -0.374459 -1.426103 0.364839 0.8822 0.8252 0.7283 0.9893 0.7086 0.1559 0.7158 R-squared Adjusted R-squared S.E of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.025228 -0.014290 9365.556 1.30E+10 -1633.797 0.638385 0.699352 Mean dependent var S.D dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter Durbin-Watson stat -14.70736 9299.347 21.17157 21.30902 21.22740 2.000707 Gi tr P-Value = 0.4327, ch a cú c s b c b gi thit H o Vy phn d mụ hỡnh ARIMA(1,0,1) khụng t t ng quan 6.3.Mụ hỡnh ARIMA(2,0,0): Breusch-Godfrey Serial Correlation LM Test: F-statistic Obs*R-squared 5.043811 18.47470 Prob F(4,148) Prob Chi-Square(4) Test Equation: Dependent Variable: RESID Method: Least Squares Date: 05/10/15 Time: 15:33 Sample: 2/24/2012 1/30/2015 Included observations: 154 Presample missing value lagged residuals set to zero 78 0.0008 0.0010 Variable Coefficient Std Error t-Statistic Prob C AR(2) RESID(-1) RESID(-2) RESID(-3) RESID(-4) 248.0458 1.687575 0.222788 -1.827487 0.020422 -0.283158 1050.209 0.821170 0.081323 0.835246 0.082827 0.230827 0.236187 2.055085 2.739537 -2.187963 0.246557 -1.226710 0.8136 0.0416 0.0069 0.0302 0.8056 0.2219 R-squared Adjusted R-squared S.E of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.119966 0.090235 9532.524 1.34E+10 -1626.476 4.035049 0.001839 Mean dependent var S.D dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter Durbin-Watson stat 5.69E-06 9994.089 21.20099 21.31931 21.24905 2.042527 Gi tr P-Value = 0.008, ú b c b gi thit Ho Vy phn d mụ hỡnh ARIMA(2,0,0) cú t t ng quan 6.4.Mụ hỡnh ARIMA(1,0,0) Breusch-Godfrey Serial Correlation LM Test: F-statistic Obs*R-squared 2.660621 10.33299 Prob F(4,149) Prob Chi-Square(4) 0.0350 0.0352 Test Equation: Dependent Variable: RESID Method: Least Squares Date: 05/10/15 Time: 15:34 Sample: 2/17/2012 1/30/2015 Included observations: 155 Presample missing value lagged residuals set to zero Variable Coefficient Std Error t-Statistic Prob C AR(1) RESID(-1) RESID(-2) RESID(-3) RESID(-4) 163.7982 2.184295 -2.250378 -0.582766 -0.192203 0.111132 1144.149 1.821870 1.829549 0.591903 0.206123 0.100034 0.143162 1.198930 -1.230018 -0.984563 -0.932468 1.110940 0.8864 0.2325 0.2206 0.3264 0.3526 0.2684 R-squared Adjusted R-squared S.E of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.066664 0.035344 9621.317 1.38E+10 -1638.495 2.128496 0.065105 Mean dependent var S.D dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter Durbin-Watson stat 7.90E-06 9795.991 21.21929 21.33710 21.26714 2.057429 Gi tr P-Value = 0.0350, b c b gi thit Ho Vy phn d mụ hỡnh ARIMA(1,0,0) khụng t t ng quan 79 6.5.Mụ hỡnh ARIMA(2,0,1): Breusch-Godfrey Serial Correlation LM Test: F-statistic Obs*R-squared 1.956926 7.785833 Prob F(4,147) Prob Chi-Square(4) 0.1041 0.0997 Test Equation: Dependent Variable: RESID Method: Least Squares Date: 05/10/15 Time: 15:32 Sample: 2/24/2012 1/30/2015 Included observations: 154 Presample missing value lagged residuals set to zero Variable Coefficient Std Error t-Statistic Prob C AR(2) MA(1) RESID(-1) RESID(-2) RESID(-3) RESID(-4) 309.4455 1.803137 3.146983 -3.183177 -1.010275 -0.235218 -0.250228 1326.043 0.963897 6.084093 6.085466 2.082388 0.456773 0.304633 0.233360 1.870674 0.517248 -0.523079 -0.485152 -0.514957 -0.821409 0.8158 0.0634 0.6058 0.6017 0.6283 0.6074 0.4127 R-squared Adjusted R-squared S.E of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.050557 0.011805 9615.210 1.36E+10 -1627.284 1.304613 0.258619 Mean dependent var S.D dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter Durbin-Watson stat 3.792380 9672.469 21.22447 21.36251 21.28054 2.038375 Gi tr P-Value = 0.1041, chp nhn gi thit Ho Vy phn d mụ hỡnh ARIMA(2,0,1) cú t t ng quan 6.6.Mụ hỡnh ARIMA(0,0,1): Breusch-Godfrey Serial Correlation LM Test: F-statistic Obs*R-squared 4.207037 15.73588 Prob F(4,150) Prob Chi-Square(4) 0.0029 0.0034 Test Equation: Dependent Variable: RESID Method: Least Squares Date: 05/10/15 Time: 15:35 Sample: 2/10/2012 1/30/2015 Included observations: 156 Presample missing value lagged residuals set to zero Variable Coefficient Std Error 80 t-Statistic Prob C MA(1) RESID(-1) RESID(-2) RESID(-3) RESID(-4) 66.76969 4.367019 -4.346984 1.203607 -0.196353 0.247648 R-squared Adjusted R-squared S.E of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.100871 0.070900 9571.947 1.37E+10 -1648.284 3.365624 0.006546 945.5022 6.206742 6.209644 1.438033 0.345280 0.111331 0.070618 0.703593 -0.700038 0.836981 -0.568677 2.224426 Mean dependent var S.D dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter Durbin-Watson stat 0.9438 0.4828 0.4850 0.4039 0.5704 0.0276 4.181838 9930.453 21.20876 21.32607 21.25641 2.064048 Gi tr P-Value = 0.0029, ú b c b gi thit Ho Vy phn d mụ hỡnh ARIMA(0,0,1) khụng t t ng quan 6.7 Mụ hỡnh ARIMA(0,0,2): Breusch-Godfrey Serial Correlation LM Test: F-statistic Obs*R-squared 6.186172 22.09024 Prob F(4,150) Prob Chi-Square(4) 0.0001 0.0002 Test Equation: Dependent Variable: RESID Method: Least Squares Date: 05/10/15 Time: 15:36 Sample: 2/10/2012 1/30/2015 Included observations: 156 Presample missing value lagged residuals set to zero Variable Coefficient Std Error t-Statistic Prob C MA(2) RESID(-1) RESID(-2) RESID(-3) RESID(-4) 103.3800 3.352731 0.230811 -3.413305 0.020758 0.863035 901.3954 1.936550 0.079969 1.949548 0.081521 0.374400 0.114689 1.731290 2.886242 -1.750819 0.254639 2.305118 0.9088 0.0855 0.0045 0.0820 0.7994 0.0225 R-squared Adjusted R-squared S.E of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.141604 0.112991 9476.983 1.35E+10 -1646.728 4.948910 0.000319 Mean dependent var S.D dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter Durbin-Watson stat 8.928144 10062.50 21.18882 21.30612 21.23647 2.061815 Gi tr P-Value = 0.00001, ú chp nhn gi thit Ho Vy phn d mụ hỡnh ARIMA(0,0,2) cú t t ng quan 81 6.8 Mụ hỡnh ARIMA(1,0,2) Breusch-Godfrey Serial Correlation LM Test: F-statistic Obs*R-squared 2.131053 8.441169 Prob F(4,148) Prob Chi-Square(4) 0.0798 0.0767 Test Equation: Dependent Variable: RESID Method: Least Squares Date: 05/10/15 Time: 15:37 Sample: 2/17/2012 1/30/2015 Included observations: 155 Presample missing value lagged residuals set to zero Variable Coefficient Std Error t-Statistic Prob C AR(1) MA(2) RESID(-1) RESID(-2) RESID(-3) RESID(-4) 144.0131 0.043209 7.621494 -0.078025 -7.636260 0.011887 1.115977 1214.780 2.280057 5.499310 2.278657 5.190812 0.199914 0.702619 0.118551 0.018951 1.385900 -0.034241 -1.471111 0.059459 1.588309 0.9058 0.9849 0.1679 0.9727 0.1434 0.9527 0.1144 R-squared Adjusted R-squared S.E of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.054459 0.016126 9629.476 1.37E+10 -1638.105 1.420696 0.210323 Mean dependent var S.D dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter Durbin-Watson stat 4.840499 9708.072 21.22715 21.36460 21.28298 2.069535 Gi tr P-Value = 0.0798, ch a cú c s b c b gi thit H o Vy phn d mụ hỡnh ARIMA(1,0,2) khụng t t ng quan Kim tra hin t ng ph ng sai sai s thay i ca mụ hỡnh ARIMA(1 1) Kim nh gi thit: Ho: mụ hỡnh khụng cú tớnh ARCH ( ph H1: mụ hỡnh cú tớnh ARCH (ph ng sai sai s khụng i) ng sai sai s thay i) Heteroskedasticity Test: ARCH F-statistic Obs*R-squared 38.83881 111.8122 Prob F(12,130) Prob Chi-Square(12) Test Equation: Dependent Variable: RESID^2 Method: Least Squares 82 0.0000 0.0000 Date: 05/18/15 Time: 13:12 Sample (adjusted): 5/11/2012 1/30/2015 Included observations: 143 after adjustments Variable Coefficient Std Error t-Statistic Prob C RESID^2(-1) RESID^2(-2) RESID^2(-3) RESID^2(-4) RESID^2(-5) RESID^2(-6) RESID^2(-7) RESID^2(-8) RESID^2(-9) RESID^2(-10) RESID^2(-11) RESID^2(-12) -6676427 -0.079549 -0.407529 0.014217 0.069560 -0.000762 0.015023 -0.074780 -0.018690 -0.087413 -0.064392 -0.048897 4.013721 25120729 0.041814 0.046751 0.041262 0.041312 0.041286 0.041289 0.041394 0.041259 0.041412 0.042034 0.041547 0.188552 -0.265774 -1.902445 -8.717016 0.344544 1.683767 -0.018446 0.363841 -1.806528 -0.452988 -2.110815 -1.531910 -1.176885 21.28706 0.7908 0.0593 0.0000 0.7310 0.0946 0.9853 0.7166 0.0731 0.6513 0.0367 0.1280 0.2414 0.0000 R-squared Adjusted R-squared S.E of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.781903 0.761771 2.68E+08 9.34E+18 -2971.235 38.83881 0.000000 Mean dependent var S.D dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter Durbin-Watson stat 92605309 5.49E+08 41.73756 42.00691 41.84701 2.067765 Gi tr P-Value = 0.0000, ú b c b gi thit Ho Vy ARIMA(1,0,1) khụng t t ng quan 8.c l ng cỏc mụ hỡnh GARCH(p,q): 8.1 Mụ hỡnh GARCH(1,1) Dependent Variable: AMIVEST Method: ML - ARCH (Marquardt) - Student's t distribution Date: 05/15/15 Time: 20:43 Sample (adjusted): 2/17/2012 1/30/2015 Included observations: 155 after adjustments Convergence achieved after 80 iterations MA Backcast: 2/10/2012 Presample variance: backcast (parameter = 0.7) GARCH = C(4) + C(5)*RESID(-1)^2 + C(6)*GARCH(-1) Variable Coefficient Std Error z-Statistic Prob C AR(1) MA(1) 1145.737 0.880100 -0.766845 335.5553 0.037734 0.049803 3.414450 23.32396 -15.39749 0.0006 0.0000 0.0000 0.013465 -0.013481 140.1681 0.9893 0.9892 0.0000 Variance Equation C RESID(-1)^2 GARCH(-1) 1.06E+08 -13.59319 1.047389 7.89E+09 1008.333 0.007472 83 T-DIST DOF 2.000544 R-squared Adjusted R-squared S.E of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.087267 0.050264 10077.95 1.50E+10 -1498.249 2.358394 0.033240 Inverted AR Roots Inverted MA Roots 88 77 0.040351 49.57811 Mean dependent var S.D dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter Durbin-Watson stat 0.0000 6588.460 10341.20 19.42257 19.56001 19.47839 1.664752 8.2 Mụ hỡnh GARCH(0,1) Dependent Variable: AMIVEST Method: ML - ARCH (Marquardt) - Student's t distribution Date: 05/15/15 Time: 20:48 Sample (adjusted): 2/17/2012 1/30/2015 Included observations: 155 after adjustments Convergence achieved after 160 iterations MA Backcast: 2/10/2012 Presample variance: backcast (parameter = 0.7) GARCH = C(4) + C(5)*GARCH(-1) Variable Coefficient Std Error z-Statistic Prob C AR(1) MA(1) 2917.688 0.970383 -0.941531 723.4531 0.020742 0.030054 4.033002 46.78299 -31.32784 0.0001 0.0000 0.0000 Variance Equation C GARCH(-1) 1.06E+08 -0.970730 1.10E+08 0.020829 0.965502 -46.60374 0.3343 0.0000 T-DIST DOF 2.227189 0.298277 7.466849 0.0000 R-squared Adjusted R-squared S.E of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.073441 0.042348 10119.86 1.53E+10 -1528.101 2.362009 0.042675 Inverted AR Roots Inverted MA Roots 97 94 Mean dependent var S.D dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter Durbin-Watson stat 8.3 Mụ hỡnh GARCH(2,1) Dependent Variable: AMIVEST Method: ML - ARCH (Marquardt) - Student's t distribution Date: 05/15/15 Time: 20:53 Sample (adjusted): 2/17/2012 1/30/2015 Included observations: 155 after adjustments 84 6588.460 10341.20 19.79485 19.91266 19.84270 1.509458 Failure to improve Likelihood after 90 iterations MA Backcast: 2/10/2012 Presample variance: backcast (parameter = 0.7) GARCH = C(4) + C(5)*RESID(-1)^2 + C(6)*RESID(-2)^2 + C(7)*GARCH(-1) Variable Coefficient Std Error z-Statistic Prob C AR(1) MA(1) 2092.834 0.850414 -0.696259 565.0502 0.033060 0.075638 3.703801 25.72316 -9.205185 0.0002 0.0000 0.0000 Variance Equation C RESID(-1)^2 RESID(-2)^2 GARCH(-1) 1.06E+08 2.923129 3.514965 -0.038493 7.99E+08 21.74794 26.52550 0.079763 0.132926 0.134409 0.132513 -0.482587 0.8943 0.8931 0.8946 0.6294 T-DIST DOF 2.049580 0.391326 5.237530 0.0000 R-squared Adjusted R-squared S.E of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.118759 0.076795 9936.189 1.45E+10 -1515.275 2.830033 0.008521 Inverted AR Roots Inverted MA Roots 85 70 Mean dependent var S.D dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter Durbin-Watson stat 6588.460 10341.20 19.65516 19.81224 19.71896 1.794928 8.4 Mụ hỡnh GARCH(1,2) Dependent Variable: AMIVEST Method: ML - ARCH (Marquardt) - Student's t distribution Date: 05/15/15 Time: 20:57 Sample (adjusted): 2/17/2012 1/30/2015 Included observations: 155 after adjustments Convergence achieved after 52 iterations MA Backcast: 2/10/2012 Presample variance: backcast (parameter = 0.7) GARCH = C(4) + C(5)*RESID(-1)^2 + C(6)*GARCH(-1) + C(7)*GARCH(-2) Variable Coefficient Std Error z-Statistic Prob C AR(1) MA(1) 1396.955 0.863657 0.741855 311.0177 0.047553 0.066800 4.491559 18.16202 -11.10564 0.0000 0.0000 0.0000 Variance Equation C RESID(-1)^2 GARCH(-1) GARCH(-2) 1.06E+08 -12.25567 0.573219 0.491480 8.90E+09 1024.088 0.479915 0.490260 0.011938 -0.011967 1.194417 1.002488 0.9905 0.9905 0.2323 0.3161 T-DIST DOF 2.000738 0.061641 32.45798 0.0000 85 R-squared Adjusted R-squared S.E of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.088777 0.045385 10103.80 1.50E+10 -1495.238 2.045943 0.053069 Inverted AR Roots Inverted MA Roots 86 74 Mean dependent var S.D dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter Durbin-Watson stat 6588.460 10341.20 19.39661 19.55369 19.46042 1.681431 8.5 Mụ hỡnh GARCH(2,0) Dependent Variable: AMIVEST Method: ML - ARCH (Marquardt) - Normal distribution Date: 05/10/15 Time: 15:47 Sample (adjusted): 2/17/2012 1/30/2015 Included observations: 155 after adjustments Convergence not achieved after 500 iterations MA Backcast: 2/10/2012 Presample variance: backcast (parameter = 0.7) GARCH = C(4) + C(5)*RESID(-1)^2 Variable Coefficient Std Error z-Statistic Prob C AR(1) MA(1) 4863.967 0.770201 -0.359119 4202.998 0.151948 0.172262 1.157261 5.068845 -2.084722 0.2472 0.0000 0.0371 5.242564 3.771017 0.0000 0.0002 Variance Equation C RESID(-1)^2 R-squared Adjusted R-squared S.E of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) Inverted AR Roots Inverted MA Roots 68914987 0.934024 0.114969 0.091368 9857.457 1.46E+10 -1604.183 4.871379 0.001012 13145282 0.247685 Mean dependent var S.D dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter Durbin-Watson stat 77 36 86 6588.460 10341.20 20.76365 20.86183 20.80353 2.320240 8.6 Mụ hỡnh GARCH(2,2) Dependent Variable: AMIVEST Method: ML - ARCH (Marquardt) - Student's t distribution Date: 05/15/15 Time: 23:24 Sample (adjusted): 2/17/2012 1/30/2015 Included observations: 155 after adjustments Failure to improve Likelihood after 90 iterations MA Backcast: 2/10/2012 Presample variance: backcast (parameter = 0.7) GARCH = C(4) + C(5)*RESID(-1)^2 + C(6)*RESID(-2)^2 + C(7)*GARCH(-1) Variable Coefficient Std Error z-Statistic Prob C AR(1) MA(1) 2092.834 0.850414 -0.696259 565.0502 0.033060 0.075638 3.703801 25.72316 -9.205185 0.0002 0.0000 0.0000 Variance Equation C RESID(-1)^2 RESID(-2)^2 GARCH(-1) 1.06E+08 2.923129 3.514965 -0.038493 7.99E+08 21.74794 26.52550 0.079763 0.132926 0.134409 0.132513 -0.482587 0.8943 0.8931 0.8946 0.6294 T-DIST DOF 2.049580 0.391326 5.237530 0.0000 R-squared Adjusted R-squared S.E of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.118759 0.076795 9936.189 1.45E+10 -1515.275 2.830033 0.008521 Inverted AR Roots Inverted MA Roots 85 70 Mean dependent var S.D dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter Durbin-Watson stat 6588.460 10341.20 19.65516 19.81224 19.71896 1.794928 8.7 Mụ hỡnh GARCH(0,2) Dependent Variable: AMIVEST Method: ML - ARCH (Marquardt) - Student's t distribution Date: 05/18/15 Time: 13:06 Sample (adjusted): 2/17/2012 1/30/2015 Included observations: 155 after adjustments Convergence achieved after 88 iterations MA Backcast: 2/10/2012 Presample variance: backcast (parameter = 0.7) GARCH = C(4) + C(5)*GARCH(-1) + C(6)*GARCH(-2) Variable Coefficient Std Error z-Statistic Prob C AR(1) 1062.038 0.894538 396.9537 0.037843 2.675470 23.63799 0.0075 0.0000 87 MA(1) -0.781461 0.052482 -14.89009 0.0000 Variance Equation C GARCH(-1) GARCH(-2) 1.06E+08 0.019296 1.038855 9.83E+09 0.560307 0.578212 0.010808 0.034439 1.796669 0.9914 0.9725 0.0724 T-DIST DOF 2.000650 0.060015 33.33589 0.0000 R-squared Adjusted R-squared S.E of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) Inverted AR Roots Inverted MA Roots 0.098312 0.061757 10016.79 1.48E+10 -1498.962 2.689428 0.016574 Mean dependent var S.D dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter Durbin-Watson stat 6588.460 10341.20 19.43177 19.56922 19.48760 1.685019 89 78 8.8 Mụ hỡnh GARCH(1,0) Dependent Variable: AMIVEST Method: ML - ARCH (Marquardt) - Student's t distribution Date: 05/15/15 Time: 20:51 Sample (adjusted): 2/17/2012 1/30/2015 Included observations: 155 after adjustments Convergence achieved after 73 iterations MA Backcast: 2/10/2012 Presample variance: backcast (parameter = 0.7) GARCH = C(4) + C(5)*RESID(-1)^2 Variable Coefficient Std Error z-Statistic Prob C AR(1) MA(1) 1365.511 0.936836 -0.793186 1098.759 0.015989 0.031527 1.242776 58.59297 -25.15855 0.2140 0.0000 0.0000 Variance Equation C RESID(-1)^2 1.06E+08 6.236535 6.39E+08 37.31626 0.166341 0.167126 0.8679 0.8673 T-DIST DOF 2.056261 0.355988 5.776216 0.0000 R-squared Adjusted R-squared S.E of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.158244 0.129997 9645.642 1.39E+10 -1524.012 5.602184 0.000092 Inverted AR Roots Inverted MA Roots 94 79 Mean dependent var S.D dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter Durbin-Watson stat 88 6588.460 10341.20 19.74209 19.85990 19.78994 1.860971 Kim tra tớnh ARCH ca mụ hỡnh GARCH(1 2) Heteroskedasticity Test: ARCH F-statistic Obs*R-squared 0.364901 4.659739 Prob F(12,130) Prob Chi-Square(12) 0.9734 0.9684 Test Equation: Dependent Variable: WGT_RESID^2 Method: Least Squares Date: 05/18/15 Time: 13:17 Sample (adjusted): 5/11/2012 1/30/2015 Included observations: 143 after adjustments Variable Coefficient Std Error t-Statistic Prob C WGT_RESID^2(-1) WGT_RESID^2(-2) WGT_RESID^2(-3) WGT_RESID^2(-4) WGT_RESID^2(-5) WGT_RESID^2(-6) WGT_RESID^2(-7) WGT_RESID^2(-8) WGT_RESID^2(-9) WGT_RESID^2(-10) WGT_RESID^2(-11) WGT_RESID^2(-12) 0.002044 0.035913 0.087883 0.006128 -0.011167 0.004526 -0.021698 -0.030012 -0.027599 -0.030055 0.006357 -0.012370 0.058303 0.000855 0.087407 0.060348 0.060734 0.060330 0.060273 0.060218 0.060246 0.060166 0.060213 0.060391 0.060107 0.069492 2.389590 0.410872 1.456257 0.100899 -0.185106 0.075097 -0.360334 -0.498168 -0.458725 -0.499133 0.105265 -0.205793 0.838981 0.0183 0.6818 0.1477 0.9198 0.8534 0.9403 0.7192 0.6192 0.6472 0.6185 0.9163 0.8373 0.4030 R-squared Adjusted R-squared S.E of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.032586 -0.056714 0.007360 0.007042 506.2754 0.364901 0.973377 Mean dependent var S.D dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter Durbin-Watson stat 0.002182 0.007160 -6.898957 -6.629608 -6.789507 1.975479 Gi tr P-Value = 0.9734, ú chp nhn gi thit Ho Vy mụ hỡnh GARCH(1,1) cú ph ng sai sai s khụng i 89