Pseudo Code ARMA p q Family GARCH p
- Slides: 28
Pseudo Code
基因演算法於時間序列的應用 ARMA (p, q) Family � GARCH (p, q) Family � ARCH � GARCH � IGARCH � EGARCH � FIAPARCH �
模式設定 Model Identification Model Estimation Is satisfied model checking? Yes Model Forecasting No
GARCH Family模型參數考量 � Traditional model identification � � GARCH (1, 1), GARCH (1, 2), GARCH (2, 1), GARCH (2, 2), … Local optimization vs. Global optimization? � GARCH (2, 2) � GARCH((2), (2))
全域解的問題 Computational cost � Required time � For a GARCH(p, q) model � � Effectiveness of GAs
基因演算法參數設定 � String representation � � Population initialization � � If the chromosome is represented by (010; 001), the GARCH model should be ARCH((2), (3)) Selected at random Fitness computation AIC � BIC � HQC �… �
Gene Operators � Crossover = two-point � Mutation= random � Pc = 0. 9 � Pm = 0. 01 � Iteration = 100
Empirical studies- Case I Return rates of AT&T � From Jan 1961 to Dec 1967 �
Model Identification � GARCH GA Criteria � (1) (2) (3) (1, 1) (1, 2) (1, 3) (2, 1) (2, 2) (2, 3) (3, 1) (3, 2) (3, 3) ((2), 2) AIC -300. 8 -304. 6 -300. 1 -296. 8 -300. 8 -304. 6 -300. 8 -297. 2 -302. 6 -296. 8 -294. 8 -305. 3 SBC -293. 5 -297. 3 -290. 4 -284. 7 -293. 5 -297. 3 -293. 5 -282. 6 -292. 8 -284. 6 -280. 2 -298. 0 IGARCH GA Criteria (1) (2) (3) (1, 1) (1, 2) (1, 3) (2, 1) (2, 2) (2, 3) (3, 1) (3, 2) (3, 3) ((2), 1) AIC -287. 3 -299. 0 -304. 7 -302. 7 -300. 8 -300. 1 -304. 8 SBC -282. 4 -291. 7 -302. 3 -297. 9 -293. 5 -290. 4 -287. 9 -302. 4
Model Identification (conti. ) � EGARCH Criteria GARCH GA (1) (2) (3) (1, 1) (1, 2) (1, 3) (2, 1) (2, 2) (2, 3) (3, 1) (3, 2) (3, 3) ((3), (2)) AIC -300. 8 -302. 5 -303. 8 -300. 1 -298. 8 -301. 3 -302. 4 -307. 2 -305. 3 -302. 0 -305. 4 -311. 8 -306. 3 SBC -291. 1 -290. 4 -289. 2 -287. 9 -284. 3 -287. 8 -290. 2 -285. 9 -285. 0 -286. 0 -290. 0 -294. 2 Variable Coefficient Std. Error t-value Prob. Intercept 0. 003087 0. 004304 0. 72 0. 4732 ARCH 3 1. 0537 E-8 1. 28 E-11 823. 84 <. 0000 GARDH 2 1. 000000 1. 28 E-11 7. 81 E 10 <. 0000
Q and LM tests Order Q P-value LM P-value 1 0. 0979 0. 7543 0. 0334 0. 8549 2 3. 2911 0. 1929 2. 8256 0. 2435 3 3. 6472 0. 3022 3. 5610 0. 3129 4 4. 2083 0. 3785 3. 6575 0. 4543 5 4. 2396 0. 5155 3. 7784 0. 5817 6 5. 3163 0. 5039 4. 1734 0. 6532 7 7. 2005 0. 4083 5. 3838 0. 6132 8 7. 5628 0. 4773 5. 3874 0. 7155 9 7. 5685 0. 5782 5. 6867 0. 7708 10 8. 2318 0. 6062 6. 3177 0. 7879 11 8. 2619 0. 6897 6. 4197 0. 8439 12 8. 2987 0. 7614 6. 8341 0. 8684
Empirical studies- Case II Shanghai A Shares � From 2002/01/04 to 2008/12/31 �
Model Identification � FIGARCH (1, 0. 47098, 4), AIC=3545. 434, SBC=3555. 257 Coefficient Std. Error t-value Prob. Intercept 0. 01081 0. 01663 0. 6502 0. 5157 ARCH 1 -0. 94513 0. 02283 -41. 4000 0. 0000 GARCH 1 -0. 52623 0. 08249 -6. 3790 0. 0000 GARCH 2 0. 49127 0. 09784 5. 0210 0. 0000 GARCH 3 0. 09356 0. 06797 1. 3770 0. 1688 GARCH 4 -0. 04082 0. 04315 -0. 9460 0. 3443 � FIAPARCH (3, 0. 41212, 1), AIC=3536. 688, SBC=3547. 739 Coefficient Std. Error t-value Intercept 0. 00496 0. 01630 0. 3047 ARCH 1 0. 25737 0. 31417 0. 8192 GARCH 1 0. 62380 0. 30850 2. 0220 GARCH 2 -0. 02063 0. 12184 -0. 1694 GARCH 3 -0. 03648 0. 05274 -0. 6917 Gamma 1 0. 14542 0. 07583 1. 9180 Delta 2. 04210 0. 19048 10. 7200 Prob. 0. 7607 0. 4128 0. 0433 0. 8655 0. 4892 0. 0553 0. 0000
Traditional model identifications of FIGARCH and FIAPARCH FIGARCH Criteria AIC FIAPARCH (1, 0. 5480, 1) (2, 0. 5270, 1) (1, 0. 4926, 2) (2, 0. 4590, 2) (1, d, 1) (2, d, 1) (1, d, 2) 3555. 758 3557. 116 3556. 592 3558. 36 NA NA NA (2, d, 2) NA SBC 3561. 897 3564. 483 3563. 959 3566. 955 NA NA Note: NA denotes no convergence with respect to any d.
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