library(readxl)
library(rugarch)
## Loading required package: parallel
##
## Attaching package: 'rugarch'
## The following object is masked from 'package:stats':
##
## sigma
data <- read_excel("C:/Users/chaua/OneDrive - UFM/TLHT/Mô hình ngẫu nhiên/data.xlsx")
## New names:
## • `Date` -> `Date...1`
## • `Date` -> `Date...4`
VNts <- ts(data$VNI)
print(VNts)
## Time Series:
## Start = 1
## End = 1360
## Frequency = 1
## [1] 1222.90 1207.67 1197.33 1200.84 1195.90 1190.72 1185.90 1172.81 1172.98
## [10] 1174.09 1173.13 1168.40 1165.42 1154.20 1151.77 1149.02 1138.07 1126.22
## [19] 1134.62 1132.00 1125.50 1120.18 1138.35 1134.33 1132.03 1129.38 1125.30
## [28] 1118.46 1111.72 1105.40 1115.22 1116.97 1117.42 1122.46 1116.02 1107.53
## [37] 1101.32 1109.54 1108.31 1097.82 1078.39 1075.17 1078.05 1074.98 1063.76
## [46] 1064.63 1061.79 1065.85 1070.64 1067.07 1068.31 1060.44 1065.91 1065.71
## [55] 1066.90 1057.12 1058.26 1053.77 1053.44 1040.31 1040.61 1049.12 1039.63
## [64] 1040.80 1034.85 1041.36 1042.91 1049.25 1048.98 1055.02 1053.81 1052.89
## [73] 1064.30 1069.45 1069.46 1065.35 1070.91 1080.86 1078.45 1079.28 1064.64
## [82] 1059.44 1056.33 1054.29 1052.25 1046.79 1045.10 1040.54 1032.43 1023.10
## [91] 1045.14 1047.40 1062.19 1040.13 1052.80 1053.00 1055.95 1049.18 1037.84
## [100] 1027.18 1024.77 1037.61 1040.55 1024.68 1021.25 1039.56 1053.66 1054.28
## [109] 1082.23 1086.69 1059.31 1058.29 1048.20 1038.64 1043.70 1055.30 1064.03
## [118] 1072.22 1065.84 1089.29 1077.15 1077.59 1075.97 1111.18 1102.57 1117.10
## [127] 1108.08 1098.28 1088.29 1066.68 1060.17 1056.39 1055.76 1053.35 1054.21
## [136] 1051.44 1055.82 1046.35 1043.90 1007.09 1009.29 1015.66 1004.57 1020.34
## [145] 1022.61 1018.88 1023.13 1038.40 1052.48 1055.32 1050.43 1047.45 1032.07
## [154] 1051.81 1050.53 1041.02 1048.69 1093.67 1080.01 1036.28 1048.42 1032.16
## [163] 1005.69 971.46 947.71 946.00 952.12 960.65 969.33 969.26 942.90
## [172] 911.90 941.04 954.53 947.24 985.59 981.65 975.19 997.15 1019.81
## [181] 1023.19 1033.75 1027.94 1027.36 1028.01 993.36 997.70 1019.82 1058.45
## [190] 1060.07 1063.66 1051.58 1061.85 1050.99 1034.81 1006.20 1042.48 1035.91
## [199] 1074.52 1104.26 1078.14 1086.44 1132.11 1126.07 1143.62 1166.54 1174.35
## [208] 1203.28 1214.70 1210.55 1218.93 1205.43 1234.03 1245.66 1240.77 1248.40
## [217] 1249.62 1248.78 1234.60 1243.17 1277.40 1277.35 1280.51 1279.39 1270.80
## [226] 1282.57 1288.88 1277.16 1270.81 1260.43 1269.18 1273.66 1275.28 1274.69
## [235] 1274.20 1262.33 1252.07 1256.50 1256.75 1252.74 1254.15 1249.76 1241.62
## [244] 1231.35 1206.33 1208.12 1191.04 1185.07 1188.50 1194.76 1198.47 1194.14
## [253] 1178.33 1176.49 1179.25 1182.17 1173.92 1174.82 1171.31 1166.48 1149.61
## [262] 1181.29 1195.53 1198.90 1197.60 1218.09 1218.10 1202.82 1185.48 1188.88
## [271] 1169.27 1172.47 1180.40 1217.30 1236.63 1213.93 1230.31 1227.04 1284.08
## [280] 1307.80 1307.91 1291.35 1290.01 1287.98 1288.62 1299.52 1292.68 1293.92
## [289] 1285.45 1268.57 1268.43 1233.38 1218.81 1240.71 1241.64 1240.76 1228.37
## [298] 1182.77 1238.84 1301.53 1293.56 1269.62 1329.26 1360.68 1348.68 1366.80
## [307] 1350.99 1353.77 1341.34 1310.92 1379.23 1370.21 1384.72 1406.45 1432.60
## [316] 1458.56 1472.12 1477.20 1455.25 1482.00 1502.35 1522.90 1520.03 1524.70
## [325] 1516.44 1492.15 1490.51 1497.76 1483.18 1498.50 1498.26 1502.34 1503.78
## [334] 1494.95 1469.10 1461.34 1459.33 1452.74 1446.25 1466.54 1479.08 1473.74
## [343] 1473.71 1499.05 1505.33 1505.00 1485.52 1498.78 1490.13 1498.89 1494.85
## [352] 1512.30 1503.47 1510.84 1504.84 1507.99 1492.10 1492.75 1471.96 1501.71
## [361] 1506.79 1505.38 1500.99 1497.66 1478.96 1470.76 1481.58 1479.58 1439.71
## [370] 1472.89 1465.30 1442.79 1438.94 1452.84 1496.02 1496.05 1510.51 1492.31
## [379] 1503.71 1528.48 1528.57 1522.50 1525.58 1498.28 1485.97 1485.82 1494.39
## [388] 1488.88 1477.03 1456.96 1477.67 1478.74 1477.33 1479.79 1476.61 1475.50
## [397] 1476.02 1476.21 1463.54 1467.98 1452.87 1446.77 1413.58 1443.32 1482.05
## [406] 1485.19 1478.44 1484.84 1493.03 1500.81 1488.87 1463.63 1447.25 1452.35
## [415] 1469.83 1475.85 1466.45 1476.57 1473.37 1462.35 1465.02 1461.50 1467.57
## [424] 1456.51 1444.30 1452.46 1438.97 1444.27 1438.01 1423.02 1391.63 1385.40
## [433] 1389.24 1384.77 1393.80 1395.33 1395.53 1392.70 1391.85 1391.91 1394.80
## [442] 1394.09 1372.73 1365.99 1362.82 1354.63 1339.54 1334.89 1342.06 1339.21
## [451] 1339.31 1324.99 1351.17 1352.76 1350.68 1339.84 1350.48 1352.64 1345.87
## [460] 1345.83 1339.70 1341.43 1345.31 1343.98 1333.61 1341.90 1346.39 1334.65
## [469] 1331.47 1328.14 1313.20 1301.12 1309.55 1298.74 1298.86 1329.43 1374.85
## [478] 1360.94 1363.09 1370.96 1357.05 1353.05 1357.79 1362.43 1341.45 1345.55
## [487] 1334.74 1332.44 1314.22 1310.05 1293.60 1277.07 1276.93 1272.71 1268.83
## [496] 1293.67 1270.79 1243.51 1299.31 1293.92 1279.91 1297.54 1296.30 1347.14
## [505] 1374.68 1388.55 1354.79 1411.13 1420.27 1417.08 1408.55 1410.04 1405.81
## [514] 1390.12 1379.72 1376.87 1379.97 1372.63 1377.77 1359.92 1356.52 1367.36
## [523] 1361.72 1351.74 1323.58 1332.90 1319.88 1358.78 1374.05 1364.28 1340.78
## [532] 1337.78 1328.05 1320.46 1303.57 1308.58 1297.98 1283.93 1278.22 1262.49
## [541] 1252.68 1258.70 1266.36 1269.09 1256.04 1259.58 1241.81 1250.57 1256.43
## [550] 1242.20 1239.39 1229.55 1219.75 1215.77 1248.53 1227.82 1268.28 1260.58
## [559] 1238.71 1247.25 1255.87 1248.33 1252.45 1231.66 1234.89 1242.38 1239.96
## [568] 1236.05 1216.10 1191.44 1186.36 1175.68 1162.21 1163.10 1161.81 1183.45
## [577] 1194.43 1194.05 1200.94 1186.09 1179.90 1184.56 1181.56 1181.73 1170.08
## [586] 1161.97 1168.27 1168.69 1168.52 1186.95 1186.61 1186.17 1168.47 1165.43
## [595] 1162.01 1177.64 1175.04 1173.50 1174.38 1155.78 1114.93 1083.18 1126.91
## [604] 1112.19 1111.29 1075.53 1035.51 1056.61 1023.94 1097.17 1136.12 1166.05
## [613] 1166.78 1164.21 1134.68 1131.00 1191.94 1194.20 1187.40 1186.05 1192.28
## [622] 1184.89 1167.69 1156.49 1143.21 1132.55 1120.47 1103.87 1097.54 1099.49
## [631] 1091.33 1067.52 1078.90 1083.45 1081.08 1067.46 1051.77 1066.99 1055.27
## [640] 1064.09 1045.96 1030.91 1039.13 1029.26 1029.98 1021.49 1019.80 1014.32
## [649] 1008.87 1003.08 1010.22 1005.97 999.94 995.76 994.19 990.00 983.26
## [658] 973.53 968.90 950.79 966.29 959.28 952.22 951.90 951.99 938.29
## [667] 937.75 939.76 935.41 933.68 925.47 919.08 921.05 946.47 950.80
## [676] 961.26 949.90 939.03 944.42 943.69 943.30 942.76 940.18 929.86
## [685] 925.83 924.00 918.84 919.72 915.67 914.68 909.91 914.09 905.21
## [694] 903.98 912.50 908.27 908.58 912.50 906.19 907.94 900.95 894.04
## [703] 897.47 896.26 894.57 888.97 888.82 889.32 890.14 888.25 901.54
## [712] 903.97 891.73 881.65 878.98 874.71 873.47 874.12 868.68 854.78
## [721] 848.21 851.21 846.43 850.15 850.74 855.05 846.92 843.08 841.46
## [730] 840.04 837.80 827.57 814.65 801.13 790.84 813.36 785.17 829.16
## [739] 856.75 855.08 861.69 861.40 872.02 876.83 869.91 868.11 868.72
## [748] 876.46 864.50 863.42 861.16 847.61 842.38 843.49 825.11 829.36
## [757] 851.98 854.59 859.71 868.20 871.28 868.56 855.27 854.44 856.13
## [766] 832.47 863.52 867.37 900.00 899.43 899.92 886.22 883.90 881.17
## [775] 874.80 878.67 864.47 861.39 857.48 869.13 852.74 862.73 852.91
## [784] 845.92 837.01 827.03 832.40 834.21 835.32 828.33 813.73 782.59
## [793] 764.16 762.47 769.11 767.21 770.77 776.66 773.91 768.92 766.84
## [802] 794.97 789.60 780.70 777.22 767.41 765.79 757.94 760.33 748.02
## [811] 746.69 736.75 701.80 680.23 662.53 662.26 696.06 694.21 690.25
## [820] 659.21 666.59 709.73 725.94 747.66 745.78 747.86 761.78 769.25
## [829] 811.35 837.50 835.49 891.44 893.31 889.37 890.61 884.43 882.19
## [838] 898.44 895.97 909.67 903.34 933.09 938.13 928.76 927.93 934.77
## [847] 937.45 938.24 937.68 934.67 930.73 940.75 938.54 925.91 929.09
## [856] 928.14 936.62 959.58 991.46 986.37 978.63 978.96 974.31 967.56
## [865] 967.00 965.84 968.54 960.15 948.98 958.88 955.79 965.14 966.67
## [874] 960.99 965.03 963.51 958.59 958.88 959.43 956.41 952.26 951.13
## [883] 954.03 961.47 966.18 968.17 961.78 960.30 966.06 963.56 963.27
## [892] 965.90 953.43 959.31 970.75 970.39 978.17 976.79 976.35 977.78
## [901] 987.89 1000.56 1008.35 1002.91 1010.03 1012.30 1012.77 1018.33 1016.75
## [910] 1022.49 1024.03 1024.91 1024.34 1022.43 1015.59 998.82 1000.89 995.87
## [919] 996.57 993.60 987.79 987.19 983.56 989.20 989.82 994.46 993.05
## [928] 993.57 991.84 987.38 987.83 988.22 983.09 987.59 989.67 991.19
## [937] 999.59 996.56 997.84 990.75 987.30 988.13 985.75 990.36 997.10
## [946] 995.15 996.74 989.86 987.22 976.07 969.31 970.26 974.12 974.08
## [955] 976.79 977.63 979.36 984.06 978.59 977.26 976.79 982.88 992.45
## [964] 997.26 994.38 984.67 981.03 980.00 979.38 968.91 966.83 975.24
## [973] 965.93 964.61 973.15 991.10 997.39 991.66 986.02 997.94 993.35
## [982] 994.95 988.41 989.46 982.04 982.34 976.05 982.57 982.11 972.53
## [991] 975.40 978.63 973.65 969.05 966.35 975.34 973.04 960.39 961.98
## [1000] 965.61 949.94 943.11 959.13 960.13 962.85 959.20 959.18 949.69
## [1009] 944.01 946.95 953.61 950.08 954.17 962.07 962.90 958.28 948.21
## [1018] 951.16 946.47 959.88 969.34 971.54 972.00 975.14 970.03 982.71
## [1027] 983.78 986.29 976.48 975.69 975.64 965.34 958.54 952.55 947.01
## [1036] 951.22 957.56 957.97 974.14 978.50 979.64 974.13 976.92 968.00
## [1045] 965.86 966.21 962.30 972.10 977.17 982.90 985.95 981.91 988.48
## [1054] 997.56 989.26 986.91 984.46 985.81 988.53 980.76 982.98 975.91
## [1063] 969.79 970.07 988.71 981.78 1002.30 1006.59 1011.86 1004.12 1008.44
## [1072] 1005.41 1001.32 984.60 985.25 994.03 994.49 992.45 993.99 979.63
## [1081] 965.47 990.27 987.06 994.43 988.91 987.57 970.58 964.35 961.30
## [1090] 950.89 952.34 945.25 937.54 926.10 908.67 910.65 915.84 915.93
## [1099] 912.18 908.88 908.79 908.18 906.55 911.05 902.30 901.89 908.70
## [1108] 909.68 901.80 902.71 898.30 896.99 887.44 889.64 880.90 878.22
## [1117] 891.75 892.54 900.81 891.75 897.94 908.56 912.26 918.24 919.24
## [1126] 927.25 933.65 952.04 960.25 961.28 954.58 955.89 958.59 954.82
## [1135] 957.14 958.84 951.59 926.54 926.79 930.20 923.12 921.03 917.97
## [1144] 924.42 922.56 919.02 916.06 898.19 897.15 900.93 905.38 918.12
## [1153] 914.29 926.28 922.16 925.53 924.86 907.96 914.76 888.69 888.82
## [1162] 900.82 910.17 922.73 939.68 953.51 958.36 963.47 971.60 963.37
## [1171] 951.64 970.08 945.89 993.96 996.19 996.12 1008.39 1023.62 1020.40
## [1180] 1018.79 1012.88 1017.13 1015.37 1009.61 1010.74 1011.29 1002.97 1004.74
## [1189] 995.54 993.49 987.61 991.34 987.95 987.01 985.06 970.34 968.90
## [1198] 958.19 968.44 975.94 989.54 998.07 988.17 995.19 991.92 987.05
## [1207] 987.36 979.21 969.62 968.88 964.28 961.37 978.27 978.04 968.47
## [1216] 966.27 956.79 960.23 959.60 953.55 952.77 956.39 949.73 935.52
## [1225] 930.16 927.58 934.08 936.74 933.39 943.97 942.39 921.27 911.11
## [1234] 909.72 898.51 893.16 911.12 915.12 917.51 899.40 914.99 906.01
## [1243] 947.15 960.78 957.35 968.91 983.02 990.52 983.17 969.40 980.95
## [1252] 962.16 987.34 1015.72 1030.53 1020.76 1039.02 1039.01 1036.69 1034.50
## [1261] 1022.74 1013.78 992.87 971.25 948.50 931.75 963.90 985.92 988.94
## [1270] 985.91 1014.98 1040.54 1030.64 1054.62 1073.50 1066.98 1044.85 1028.87
## [1279] 1056.97 1060.45 1062.26 1026.80 1026.46 1029.08 1050.26 1044.86 1080.74
## [1288] 1076.78 1119.86 1094.63 1138.53 1153.28 1148.49 1157.14 1173.02 1167.11
## [1297] 1198.12 1204.33 1199.96 1193.17 1191.54 1188.29 1196.61 1167.03 1172.24
## [1306] 1171.73 1171.22 1153.59 1172.36 1169.36 1159.39 1159.22 1150.19 1138.76
## [1315] 1138.09 1133.31 1126.29 1123.41 1124.15 1112.26 1120.29 1093.48 1121.21
## [1324] 1115.79 1121.54 1119.61 1114.53 1102.85 1076.03 1087.15 1059.73 1041.79
## [1333] 1003.94 1023.25 1040.55 1011.60 1048.71 1105.04 1099.67 1110.36 1110.56
## [1342] 1109.80 1115.64 1104.57 1087.42 1087.42 1062.07 1050.25 1034.69 1062.96
## [1351] 1063.47 1050.11 1048.17 1038.11 1033.56 1022.90 1012.65 1019.75 1005.67
## [1360] 995.77
# Ước lượng mô hình GARCH(1,1) theo phân phối chuẩn
VNspec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(0, 0)))
VNfit <- ugarchfit(VNspec, VNts)
print(VNfit)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(0,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 980.474064 1.850202 529.92813 0.000000
## omega 54.411797 14.101991 3.85845 0.000114
## alpha1 0.876518 0.084797 10.33667 0.000000
## beta1 0.126729 0.071712 1.76720 0.077195
## gamma1 -0.008495 0.077363 -0.10981 0.912563
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 980.474064 10.432802 93.97993 0.000000
## omega 54.411797 29.314175 1.85616 0.063431
## alpha1 0.876518 0.084994 10.31273 0.000000
## beta1 0.126729 0.094421 1.34217 0.179539
## gamma1 -0.008495 0.038935 -0.21819 0.827284
##
## LogLikelihood : -7993.338
##
## Information Criteria
## ------------------------------------
##
## Akaike 11.762
## Bayes 11.781
## Shibata 11.762
## Hannan-Quinn 11.769
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1133 0
## Lag[2*(p+q)+(p+q)-1][2] 1648 0
## Lag[4*(p+q)+(p+q)-1][5] 3062 0
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 21.77 3.070e-06
## Lag[2*(p+q)+(p+q)-1][5] 22.52 3.898e-06
## Lag[4*(p+q)+(p+q)-1][9] 28.72 9.773e-07
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.001665 0.500 2.000 0.9675
## ARCH Lag[5] 0.633910 1.440 1.667 0.8435
## ARCH Lag[7] 6.304484 2.315 1.543 0.1220
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 4.6695
## Individual Statistics:
## mu 2.6985
## omega 0.3900
## alpha1 0.7609
## beta1 0.3443
## gamma1 0.2760
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.28 1.47 1.88
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.008212 0.9934
## Negative Sign Bias 0.260371 0.7946
## Positive Sign Bias 0.491363 0.6232
## Joint Effect 0.329763 0.9543
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 4310 0
## 2 30 4714 0
## 3 40 6374 0
## 4 50 5591 0
##
##
## Elapsed time : 1.096115
# Phân phối Student (std)
vnst.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std")
vnst<- ugarchfit(vnst.spec,VNts)
print(vnst)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : std
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 1.2210e+03 2.769989 440.7966 0.000000
## ar1 6.0808e-02 0.018050 3.3688 0.000755
## ar2 9.4431e-01 0.018061 52.2844 0.000000
## ma1 1.0132e+00 0.003605 281.0598 0.000000
## ma2 7.5935e-02 0.017240 4.4045 0.000011
## omega 4.4139e+00 1.832829 2.4082 0.016030
## alpha1 5.1430e-02 0.021734 2.3663 0.017965
## beta1 8.3257e-01 0.033087 25.1630 0.000000
## gamma1 2.3000e-01 0.048538 4.7385 0.000002
## shape 5.1130e+00 0.744753 6.8654 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 1.2210e+03 1.398784 872.9023 0.000000
## ar1 6.0808e-02 0.007261 8.3742 0.000000
## ar2 9.4431e-01 0.007421 127.2511 0.000000
## ma1 1.0132e+00 0.011060 91.6120 0.000000
## ma2 7.5935e-02 0.009198 8.2555 0.000000
## omega 4.4139e+00 1.995575 2.2118 0.026979
## alpha1 5.1430e-02 0.021463 2.3962 0.016566
## beta1 8.3257e-01 0.038499 21.6258 0.000000
## gamma1 2.3000e-01 0.054470 4.2225 0.000024
## shape 5.1130e+00 0.655481 7.8004 0.000000
##
## LogLikelihood : -5258.488
##
## Information Criteria
## ------------------------------------
##
## Akaike 7.7478
## Bayes 7.7861
## Shibata 7.7477
## Hannan-Quinn 7.7621
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.3725 0.5417
## Lag[2*(p+q)+(p+q)-1][11] 2.8964 1.0000
## Lag[4*(p+q)+(p+q)-1][19] 4.3369 0.9986
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.015 0.3138
## Lag[2*(p+q)+(p+q)-1][5] 3.928 0.2632
## Lag[4*(p+q)+(p+q)-1][9] 6.098 0.2871
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.1408 0.500 2.000 0.7074
## ARCH Lag[5] 1.5852 1.440 1.667 0.5702
## ARCH Lag[7] 3.4625 2.315 1.543 0.4307
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 2.1508
## Individual Statistics:
## mu 0.0049
## ar1 0.1587
## ar2 0.1409
## ma1 0.3647
## ma2 0.3551
## omega 0.1569
## alpha1 0.3433
## beta1 0.2609
## gamma1 0.2300
## shape 0.1825
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.29 2.54 3.05
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.2788 0.78046
## Negative Sign Bias 2.2601 0.02397 **
## Positive Sign Bias 0.2622 0.79323
## Joint Effect 7.2302 0.06491 *
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 38.85 0.004615
## 2 30 50.26 0.008456
## 3 40 58.65 0.022444
## 4 50 69.34 0.029430
##
##
## Elapsed time : 2.882457
# Phân phối Student đối xứng (sstd)
vnsst.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd")
vnsst<- ugarchfit(vnsst.spec,VNts)
print(vnsst)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : sstd
##
## Convergence Problem:
## Solver Message:
# Phân phối Generalized Error Distribution(ged)
vnged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
vnged <- ugarchfit(vnged.spec,VNts)
print(vnged)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : ged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 1217.270778 1.967152 618.7984 0.000000
## ar1 1.969013 0.000105 18730.9286 0.000000
## ar2 -0.968941 0.000044 -22059.3201 0.000000
## ma1 -0.913624 0.000915 -997.9893 0.000000
## ma2 -0.048288 0.001382 -34.9294 0.000000
## omega 3.891791 1.614855 2.4100 0.015953
## alpha1 0.050332 0.004696 10.7178 0.000000
## beta1 0.836148 0.029879 27.9847 0.000000
## gamma1 0.225041 0.039583 5.6853 0.000000
## shape 1.187773 0.063801 18.6167 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 1217.270778 1.025936 1186.49831 0.000000
## ar1 1.969013 0.000366 5386.15548 0.000000
## ar2 -0.968941 0.000629 -1541.12079 0.000000
## ma1 -0.913624 0.001255 -727.71839 0.000000
## ma2 -0.048288 0.004248 -11.36641 0.000000
## omega 3.891791 1.763926 2.20632 0.027361
## alpha1 0.050332 0.128311 0.39226 0.694864
## beta1 0.836148 0.066069 12.65570 0.000000
## gamma1 0.225041 0.153583 1.46528 0.142845
## shape 1.187773 0.061812 19.21588 0.000000
##
## LogLikelihood : -5241.864
##
## Information Criteria
## ------------------------------------
##
## Akaike 7.7233
## Bayes 7.7617
## Shibata 7.7232
## Hannan-Quinn 7.7377
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.01878 0.8910
## Lag[2*(p+q)+(p+q)-1][11] 3.88166 1.0000
## Lag[4*(p+q)+(p+q)-1][19] 5.60784 0.9834
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.7739 0.3790
## Lag[2*(p+q)+(p+q)-1][5] 3.0179 0.4038
## Lag[4*(p+q)+(p+q)-1][9] 5.3138 0.3848
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.02288 0.500 2.000 0.8798
## ARCH Lag[5] 1.45249 1.440 1.667 0.6049
## ARCH Lag[7] 3.60439 2.315 1.543 0.4072
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 1.5586
## Individual Statistics:
## mu 0.001262
## ar1 0.196611
## ar2 0.196371
## ma1 0.225795
## ma2 0.227246
## omega 0.182810
## alpha1 0.297877
## beta1 0.287413
## gamma1 0.306785
## shape 0.220637
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.29 2.54 3.05
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.05323 0.95756
## Negative Sign Bias 2.00413 0.04525 **
## Positive Sign Bias 0.20633 0.83656
## Joint Effect 6.84252 0.07709 *
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 26.74 0.1110
## 2 30 38.93 0.1031
## 3 40 46.53 0.1901
## 4 50 55.59 0.2406
##
##
## Elapsed time : 3.811958
# Phân phối Generalized Error Distribution đối xứng ("sged")
vnsged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged")
vnsged <- ugarchfit(vnsged.spec,VNts)
print(vnsged)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : sged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 1218.223524 1.917132 635.4407 0.000000
## ar1 1.972652 0.000097 20297.4328 0.000000
## ar2 -0.972635 0.000038 -25497.5874 0.000000
## ma1 -0.911554 0.001341 -679.9542 0.000000
## ma2 -0.054146 0.002069 -26.1696 0.000000
## omega 3.363148 1.234813 2.7236 0.006457
## alpha1 0.039476 0.005373 7.3467 0.000000
## beta1 0.859645 0.022844 37.6309 0.000000
## gamma1 0.188780 0.029860 6.3221 0.000000
## skew 1.095398 0.024789 44.1889 0.000000
## shape 1.192417 0.064066 18.6123 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 1218.223524 1.045941 1164.71511 0.000000
## ar1 1.972652 0.000405 4876.01747 0.000000
## ar2 -0.972635 0.000627 -1550.39709 0.000000
## ma1 -0.911554 0.002408 -378.62554 0.000000
## ma2 -0.054146 0.006294 -8.60349 0.000000
## omega 3.363148 1.001853 3.35693 0.000788
## alpha1 0.039476 0.098942 0.39898 0.689908
## beta1 0.859645 0.040664 21.14019 0.000000
## gamma1 0.188780 0.138018 1.36779 0.171377
## skew 1.095398 0.042142 25.99291 0.000000
## shape 1.192417 0.063398 18.80846 0.000000
##
## LogLikelihood : -5235.463
##
## Information Criteria
## ------------------------------------
##
## Akaike 7.7154
## Bayes 7.7576
## Shibata 7.7153
## Hannan-Quinn 7.7312
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.2413 0.6232
## Lag[2*(p+q)+(p+q)-1][11] 4.1394 0.9997
## Lag[4*(p+q)+(p+q)-1][19] 5.9724 0.9718
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 2.621 0.1054
## Lag[2*(p+q)+(p+q)-1][5] 5.703 0.1056
## Lag[4*(p+q)+(p+q)-1][9] 7.697 0.1475
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.2033 0.500 2.000 0.6521
## ARCH Lag[5] 1.2318 1.440 1.667 0.6656
## ARCH Lag[7] 3.0147 2.315 1.543 0.5108
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 2.3514
## Individual Statistics:
## mu 0.001933
## ar1 0.106514
## ar2 0.107729
## ma1 0.179592
## ma2 0.177749
## omega 0.228607
## alpha1 0.495925
## beta1 0.397192
## gamma1 0.509875
## skew 0.109547
## shape 0.226181
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.49 2.75 3.27
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.57560 0.564983
## Negative Sign Bias 3.09526 0.002007 ***
## Positive Sign Bias 0.01883 0.984977
## Joint Effect 11.65637 0.008658 ***
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 22.29 0.26986
## 2 30 47.22 0.01768
## 3 40 44.35 0.25619
## 4 50 60.07 0.13346
##
##
## Elapsed time : 24.01746
SGts <- ts(data$WTI)
print(SGts)
## Time Series:
## Start = 1
## End = 1360
## Frequency = 1
## [1] 9.71 9.72 9.68 9.58 9.57 9.50 9.55 9.48 9.44 9.37 9.47 9.57
## [13] 9.57 9.39 9.34 9.32 9.28 9.28 9.32 9.36 9.40 9.61 9.55 9.58
## [25] 9.56 9.58 9.58 9.46 9.55 9.54 9.62 9.66 9.70 9.62 9.59 9.60
## [37] 9.50 9.49 9.50 9.37 9.38 9.28 9.25 9.30 9.29 9.24 9.41 9.37
## [49] 9.32 9.30 9.24 9.23 9.46 9.52 9.46 9.46 9.49 9.55 9.49 9.54
## [61] 9.59 9.57 9.57 9.57 9.60 9.57 9.66 9.56 9.51 9.53 9.52 9.48
## [73] 9.54 9.52 9.42 9.51 9.53 9.58 9.43 9.36 9.40 9.34 9.24 9.16
## [85] 9.13 9.08 8.93 8.83 8.77 8.81 8.91 8.71 8.68 8.71 8.63 8.81
## [97] 8.95 8.99 9.00 8.94 8.77 8.66 8.66 8.71 8.79 8.87 8.80 8.85
## [109] 8.92 8.89 8.97 8.99 9.10 9.18 9.14 9.19 9.16 9.15 9.16 9.16
## [121] 9.21 9.14 9.14 9.22 9.33 9.31 9.22 9.21 9.11 9.09 9.09 9.13
## [133] 9.08 8.97 9.05 8.90 8.91 8.80 8.87 8.95 8.93 8.95 8.99 8.98
## [145] 9.05 8.93 8.90 8.98 8.93 9.05 9.08 9.13 9.12 9.21 9.15 9.08
## [157] 9.24 9.15 9.13 9.16 9.05 9.14 9.16 9.12 9.17 9.14 9.11 9.20
## [169] 9.39 9.25 9.08 9.16 9.11 9.09 8.83 8.61 8.49 8.46 8.44 8.45
## [181] 8.45 8.57 8.42 8.42 8.45 8.49 8.35 8.20 8.33 8.47 8.51 8.53
## [193] 8.60 8.73 9.16 9.27 9.30 9.42 9.46 9.49 9.52 9.41 9.46 9.35
## [205] 9.40 9.44 9.47 9.50 9.56 9.55 9.53 9.52 9.60 9.55 9.65 9.73
## [217] 9.65 9.57 9.47 9.45 9.45 9.45 9.49 9.45 9.50 9.64 9.69 9.72
## [229] 9.77 9.91 10.01 10.00 9.94 9.89 9.89 9.80 9.85 9.85 9.85 9.90
## [241] 9.93 9.89 9.96 9.91 9.90 9.86 9.69 9.68 9.80 9.77 9.78 9.85
## [253] 9.80 9.78 9.78 9.73 9.66 9.64 9.60 9.49 9.46 9.42 9.47 9.40
## [265] 9.46 9.54 9.64 9.55 9.47 9.40 9.39 9.47 9.50 9.49 9.49 9.73
## [277] 9.64 9.58 9.67 9.72 9.73 9.73 9.70 9.73 9.75 9.72 9.53 9.84
## [289] 9.85 9.80 9.76 9.80 9.92 9.87 9.67 9.74 9.66 9.67 9.50 9.39
## [301] 9.43 9.53 9.62 9.81 9.81 9.79 9.73 9.74 9.76 9.85 9.90 9.90
## [313] 9.94 9.92 9.86 9.99 9.98 9.90 9.92 9.98 9.98 10.04 10.10 10.02
## [325] 9.99 9.97 9.89 9.82 9.79 9.84 9.82 9.81 9.78 9.80 9.73 9.68
## [337] 9.63 9.43 9.47 9.54 9.45 9.35 9.40 9.42 9.50 9.47 9.48 9.39
## [349] 9.34 9.43 9.37 9.51 9.51 9.59 9.62 9.65 9.79 9.82 9.74 9.75
## [361] 9.89 9.88 9.88 9.86 9.34 9.46 9.55 9.40 9.51 9.56 9.57 9.57
## [373] 9.54 9.63 9.69 9.65 9.64 9.60 9.65 9.62 9.51 9.49 9.33 9.30
## [385] 9.33 9.36 9.38 9.30 9.21 9.19 9.18 9.12 9.10 9.22 9.35 9.37
## [397] 9.39 9.39 9.44 9.45 9.38 9.47 9.39 9.29 9.07 9.01 8.93 9.23
## [409] 9.18 9.25 9.29 9.33 9.35 9.39 9.41 9.49 9.47 9.52 9.53 9.51
## [421] 9.53 9.55 9.60 9.55 9.59 9.76 9.82 9.68 9.66 9.71 9.73 9.66
## [433] 9.64 9.54 9.63 9.65 9.55 9.62 9.60 9.75 9.61 9.47 9.53 9.53
## [445] 9.57 9.51 9.80 9.81 9.98 9.91 9.98 10.10 10.04 10.07 10.00 10.05
## [457] 10.04 10.08 10.05 10.06 10.05 10.03 10.23 10.17 10.12 10.23 10.27 10.04
## [469] 9.90 10.09 10.11 10.21 10.26 10.24 10.29 10.76 10.77 10.84 10.62 10.82
## [481] 10.81 10.90 11.00 11.04 11.00 11.33 12.05 11.93 11.90 11.88 11.94 11.81
## [493] 11.76 11.90 11.80 11.79 11.60 11.39 11.37 11.27 11.30 11.40 11.22 11.16
## [505] 11.07 11.11 11.18 11.08 11.08 11.09 11.18 10.96 11.13 11.11 11.07 11.14
## [517] 11.02 11.01 11.00 10.88 10.89 10.98 10.71 10.55 10.43 10.47 10.50 10.44
## [529] 10.37 10.39 10.34 10.38 10.33 10.39 10.54 10.37 10.43 10.38 10.29 10.23
## [541] 10.30 10.10 10.11 10.06 10.04 10.26 10.35 10.21 10.24 10.43 10.54 10.55
## [553] 10.60 10.58 10.60 10.53 10.47 10.59 10.35 10.26 10.30 10.16 9.96 10.04
## [565] 10.03 9.96 9.93 9.99 9.96 9.97 9.95 9.96 9.91 9.93 9.88 9.93
## [577] 9.90 9.94 9.97 9.96 10.00 10.08 10.10 10.15 9.99 9.92 9.99 9.95
## [589] 9.95 10.03 9.93 10.00 9.99 10.07 9.88 9.95 9.92 9.83 9.91 9.95
## [601] 9.86 9.84 9.82 9.85 9.90 9.92 9.92 9.90 9.84 10.05 10.03 10.05
## [613] 10.09 10.24 10.18 10.00 9.86 9.87 9.95 10.02 9.99 10.04 10.00 9.69
## [625] 9.60 9.70 9.70 9.28 9.34 9.25 9.23 9.22 9.30 9.18 9.17 9.22
## [637] 9.28 9.27 9.29 9.35 9.18 9.02 9.07 9.04 9.03 9.12 9.08 9.04
## [649] 9.04 8.89 9.22 9.20 9.20 9.17 9.23 9.13 9.08 9.10 9.05 9.15
## [661] 9.11 9.09 9.11 9.00 9.28 9.11 9.10 8.90 8.82 8.64 8.66 8.75
## [673] 9.00 9.08 9.09 9.06 9.00 9.03 9.15 9.17 9.20 9.12 9.32 9.24
## [685] 9.10 9.07 9.10 9.08 9.12 9.11 9.11 9.15 9.15 9.13 9.20 9.00
## [697] 9.04 8.98 8.90 8.90 9.03 8.59 8.58 8.62 8.52 8.51 8.52 8.60
## [709] 8.55 8.59 8.68 8.70 8.70 8.61 8.71 8.63 8.64 8.63 8.65 8.68
## [721] 8.57 8.65 8.64 8.64 8.71 8.68 8.72 8.64 8.64 8.86 8.76 8.73
## [733] 8.51 8.17 8.22 8.30 8.36 8.32 8.36 8.25 8.44 8.38 8.37 8.29
## [745] 8.32 8.25 8.28 8.35 8.26 8.21 8.31 8.22 8.18 8.19 8.34 8.06
## [757] 8.21 8.04 8.10 8.00 8.12 8.29 8.16 8.17 8.22 8.16 8.25 8.29
## [769] 8.37 8.35 8.39 8.45 8.40 8.28 8.28 8.42 8.28 8.15 8.75 9.90
## [781] 9.83 9.88 9.90 9.95 9.91 9.85 9.84 9.89 9.93 9.92 9.81 9.76
## [793] 9.50 9.52 9.65 9.75 9.73 9.77 9.64 10.16 10.39 10.06 9.94 9.83
## [805] 9.76 9.71 9.67 9.84 9.70 9.79 9.58 9.33 9.09 9.13 9.19 8.92
## [817] 9.04 9.00 8.95 8.59 8.12 8.67 8.06 8.35 8.18 8.08 8.47 8.69
## [829] 8.85 9.19 8.64 8.91 9.04 9.05 8.70 8.68 8.49 8.96 8.86 8.98
## [841] 8.93 9.05 9.26 9.38 9.15 9.34 9.22 9.15 9.20 9.05 8.79 8.76
## [853] 8.77 8.64 8.68 8.59 8.70 8.70 8.78 8.71 8.79 8.76 8.78 8.72
## [865] 8.73 8.73 8.79 8.80 8.58 8.67 8.61 8.66 8.86 8.86 8.90 8.96
## [877] 9.04 8.99 9.02 9.05 9.04 8.95 8.98 8.95 9.03 9.15 8.97 8.86
## [889] 8.99 9.00 8.92 8.89 8.88 8.93 8.85 8.85 8.86 8.64 8.94 8.97
## [901] 8.83 8.90 8.86 8.86 8.85 8.84 8.86 8.91 8.90 9.16 9.10 9.03
## [913] 8.97 8.92 9.00 8.94 8.98 9.06 8.85 8.28 8.25 8.32 8.18 8.22
## [925] 8.22 8.26 8.30 8.35 8.40 8.22 8.37 8.40 8.43 8.34 8.41 8.38
## [937] 8.50 8.47 8.49 8.43 8.37 8.47 8.29 8.40 8.50 8.48 8.47 8.53
## [949] 8.54 8.47 8.61 8.47 8.54 8.45 8.50 8.35 8.28 8.20 8.20 8.18
## [961] 8.18 8.23 8.26 8.25 8.30 8.25 8.17 8.18 8.25 8.30 8.21 8.11
## [973] 8.02 7.90 7.89 7.98 7.78 7.92 7.95 7.98 8.02 8.04 8.03 8.00
## [985] 7.96 7.99 7.95 8.02 8.00 7.98 7.99 7.97 7.93 7.95 7.95 7.94
## [997] 7.96 7.94 7.85 7.88 7.92 7.95 7.87 7.85 7.88 7.95 7.79 7.76
## [1009] 7.58 7.55 7.54 7.50 7.46 7.51 7.50 7.49 7.44 7.39 7.37 7.38
## [1021] 7.45 7.47 7.42 7.62 7.62 7.46 7.51 7.47 7.41 7.40 7.36 7.33
## [1033] 7.38 7.38 7.38 7.40 7.36 7.24 7.40 7.42 7.40 7.26 7.28 7.25
## [1045] 7.28 7.33 7.26 7.25 7.30 7.39 7.37 7.38 7.44 7.39 7.44 7.42
## [1057] 7.40 7.31 7.32 7.31 7.30 7.29 7.26 7.29 7.32 7.41 7.33 7.35
## [1069] 7.31 7.33 7.31 7.26 7.35 7.47 7.76 7.92 8.02 8.00 8.00 7.89
## [1081] 7.84 7.85 7.82 7.90 7.87 7.82 7.86 7.77 7.79 7.79 7.72 7.68
## [1093] 7.58 7.58 7.59 7.64 7.65 7.62 7.60 7.57 7.50 7.41 7.43 7.44
## [1105] 7.42 7.45 7.42 7.30 7.26 7.29 7.33 7.33 7.27 7.26 7.19 7.15
## [1117] 7.17 7.15 7.12 7.11 7.06 7.13 7.15 7.09 7.13 7.10 7.24 7.16
## [1129] 7.19 7.15 7.08 7.03 7.15 7.18 7.30 7.30 7.36 7.32 7.28 7.26
## [1141] 7.23 7.24 7.18 7.14 7.21 7.15 7.25 7.26 7.13 7.22 7.19 7.22
## [1153] 7.19 7.26 7.18 7.08 7.18 6.98 6.84 6.73 6.85 6.95 6.96 7.06
## [1165] 7.05 7.08 6.93 6.95 6.87 6.83 6.86 6.90 6.86 7.01 7.08 7.24
## [1177] 7.27 7.32 7.35 7.33 7.34 7.37 7.32 7.35 7.48 7.43 7.46 7.30
## [1189] 7.31 7.27 7.27 7.32 7.29 7.28 7.29 7.30 7.33 7.36 7.38 7.40
## [1201] 7.41 7.41 7.43 7.40 7.38 7.35 7.39 7.36 7.36 7.41 7.34 7.43
## [1213] 7.36 7.32 7.38 7.43 7.42 7.38 7.36 7.38 7.43 7.44 7.41 7.57
## [1225] 7.58 7.52 7.50 7.48 7.49 7.48 7.48 7.45 7.44 7.49 7.44 7.39
## [1237] 7.34 7.30 7.05 7.12 7.12 7.16 7.14 7.17 7.08 7.16 7.13 7.10
## [1249] 7.17 7.25 7.19 7.15 7.19 7.21 7.24 7.25 7.25 7.25 7.26 7.28
## [1261] 7.28 7.26 7.23 7.24 7.25 7.37 7.39 7.51 7.39 7.48 7.64 7.65
## [1273] 7.66 7.61 7.67 7.69 7.71 7.67 7.72 7.66 7.66 7.61 7.73 7.70
## [1285] 7.70 7.63 7.69 7.70 7.56 7.59 7.53 7.44 7.44 7.46 7.37 7.44
## [1297] 7.36 7.28 7.31 7.26 7.13 7.33 7.34 7.37 7.34 7.41 7.38 7.37
## [1309] 7.47 7.50 7.49 7.46 7.50 7.54 7.62 7.56 7.58 7.50 7.47 7.44
## [1321] 7.48 7.47 7.48 7.54 7.55 7.65 7.61 7.53 7.48 7.59 7.30 7.31
## [1333] 7.89 8.01 8.01 7.88 8.04 8.16 8.23 8.20 8.20 8.28 8.23 8.17
## [1345] 8.49 8.35 7.98 7.86 7.78 7.57 7.57 7.55 7.56 7.63 7.62 7.59
## [1357] 7.57 7.57 7.50 7.47
# Ước lượng mô hình GARCH(1,1) theo phân phối chuẩn
SGspec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(0, 0)))
SGfit <- ugarchfit(SGspec, VNts)
print(SGfit)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(0,0,0)
## Distribution : norm
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 980.474064 1.850202 529.92813 0.000000
## omega 54.411797 14.101991 3.85845 0.000114
## alpha1 0.876518 0.084797 10.33667 0.000000
## beta1 0.126729 0.071712 1.76720 0.077195
## gamma1 -0.008495 0.077363 -0.10981 0.912563
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 980.474064 10.432802 93.97993 0.000000
## omega 54.411797 29.314175 1.85616 0.063431
## alpha1 0.876518 0.084994 10.31273 0.000000
## beta1 0.126729 0.094421 1.34217 0.179539
## gamma1 -0.008495 0.038935 -0.21819 0.827284
##
## LogLikelihood : -7993.338
##
## Information Criteria
## ------------------------------------
##
## Akaike 11.762
## Bayes 11.781
## Shibata 11.762
## Hannan-Quinn 11.769
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1133 0
## Lag[2*(p+q)+(p+q)-1][2] 1648 0
## Lag[4*(p+q)+(p+q)-1][5] 3062 0
## d.o.f=0
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 21.77 3.070e-06
## Lag[2*(p+q)+(p+q)-1][5] 22.52 3.898e-06
## Lag[4*(p+q)+(p+q)-1][9] 28.72 9.773e-07
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.001665 0.500 2.000 0.9675
## ARCH Lag[5] 0.633910 1.440 1.667 0.8435
## ARCH Lag[7] 6.304484 2.315 1.543 0.1220
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 4.6695
## Individual Statistics:
## mu 2.6985
## omega 0.3900
## alpha1 0.7609
## beta1 0.3443
## gamma1 0.2760
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 1.28 1.47 1.88
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.008212 0.9934
## Negative Sign Bias 0.260371 0.7946
## Positive Sign Bias 0.491363 0.6232
## Joint Effect 0.329763 0.9543
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 4310 0
## 2 30 4714 0
## 3 40 6374 0
## 4 50 5591 0
##
##
## Elapsed time : 0.6835511
# Phân phối Student (std)
sgst.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "std")
sgst<- ugarchfit(sgst.spec,VNts)
print(sgst)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : std
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 1.2210e+03 2.769989 440.7966 0.000000
## ar1 6.0808e-02 0.018050 3.3688 0.000755
## ar2 9.4431e-01 0.018061 52.2844 0.000000
## ma1 1.0132e+00 0.003605 281.0598 0.000000
## ma2 7.5935e-02 0.017240 4.4045 0.000011
## omega 4.4139e+00 1.832829 2.4082 0.016030
## alpha1 5.1430e-02 0.021734 2.3663 0.017965
## beta1 8.3257e-01 0.033087 25.1630 0.000000
## gamma1 2.3000e-01 0.048538 4.7385 0.000002
## shape 5.1130e+00 0.744753 6.8654 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 1.2210e+03 1.398784 872.9023 0.000000
## ar1 6.0808e-02 0.007261 8.3742 0.000000
## ar2 9.4431e-01 0.007421 127.2511 0.000000
## ma1 1.0132e+00 0.011060 91.6120 0.000000
## ma2 7.5935e-02 0.009198 8.2555 0.000000
## omega 4.4139e+00 1.995575 2.2118 0.026979
## alpha1 5.1430e-02 0.021463 2.3962 0.016566
## beta1 8.3257e-01 0.038499 21.6258 0.000000
## gamma1 2.3000e-01 0.054470 4.2225 0.000024
## shape 5.1130e+00 0.655481 7.8004 0.000000
##
## LogLikelihood : -5258.488
##
## Information Criteria
## ------------------------------------
##
## Akaike 7.7478
## Bayes 7.7861
## Shibata 7.7477
## Hannan-Quinn 7.7621
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.3725 0.5417
## Lag[2*(p+q)+(p+q)-1][11] 2.8964 1.0000
## Lag[4*(p+q)+(p+q)-1][19] 4.3369 0.9986
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 1.015 0.3138
## Lag[2*(p+q)+(p+q)-1][5] 3.928 0.2632
## Lag[4*(p+q)+(p+q)-1][9] 6.098 0.2871
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.1408 0.500 2.000 0.7074
## ARCH Lag[5] 1.5852 1.440 1.667 0.5702
## ARCH Lag[7] 3.4625 2.315 1.543 0.4307
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 2.1508
## Individual Statistics:
## mu 0.0049
## ar1 0.1587
## ar2 0.1409
## ma1 0.3647
## ma2 0.3551
## omega 0.1569
## alpha1 0.3433
## beta1 0.2609
## gamma1 0.2300
## shape 0.1825
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.29 2.54 3.05
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.2788 0.78046
## Negative Sign Bias 2.2601 0.02397 **
## Positive Sign Bias 0.2622 0.79323
## Joint Effect 7.2302 0.06491 *
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 38.85 0.004615
## 2 30 50.26 0.008456
## 3 40 58.65 0.022444
## 4 50 69.34 0.029430
##
##
## Elapsed time : 2.797715
# Phân phối Student đối xứng (sstd)
sgsst.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sstd")
sgsst<- ugarchfit(sgsst.spec,VNts)
print(sgsst)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : sstd
##
## Convergence Problem:
## Solver Message:
# Phân phối Generalized Error Distribution(ged)
sgged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "ged")
sgged <- ugarchfit(sgged.spec,VNts)
print(sgged)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : ged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 1217.270778 1.967152 618.7984 0.000000
## ar1 1.969013 0.000105 18730.9286 0.000000
## ar2 -0.968941 0.000044 -22059.3201 0.000000
## ma1 -0.913624 0.000915 -997.9893 0.000000
## ma2 -0.048288 0.001382 -34.9294 0.000000
## omega 3.891791 1.614855 2.4100 0.015953
## alpha1 0.050332 0.004696 10.7178 0.000000
## beta1 0.836148 0.029879 27.9847 0.000000
## gamma1 0.225041 0.039583 5.6853 0.000000
## shape 1.187773 0.063801 18.6167 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 1217.270778 1.025936 1186.49831 0.000000
## ar1 1.969013 0.000366 5386.15548 0.000000
## ar2 -0.968941 0.000629 -1541.12079 0.000000
## ma1 -0.913624 0.001255 -727.71839 0.000000
## ma2 -0.048288 0.004248 -11.36641 0.000000
## omega 3.891791 1.763926 2.20632 0.027361
## alpha1 0.050332 0.128311 0.39226 0.694864
## beta1 0.836148 0.066069 12.65570 0.000000
## gamma1 0.225041 0.153583 1.46528 0.142845
## shape 1.187773 0.061812 19.21588 0.000000
##
## LogLikelihood : -5241.864
##
## Information Criteria
## ------------------------------------
##
## Akaike 7.7233
## Bayes 7.7617
## Shibata 7.7232
## Hannan-Quinn 7.7377
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.01878 0.8910
## Lag[2*(p+q)+(p+q)-1][11] 3.88166 1.0000
## Lag[4*(p+q)+(p+q)-1][19] 5.60784 0.9834
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.7739 0.3790
## Lag[2*(p+q)+(p+q)-1][5] 3.0179 0.4038
## Lag[4*(p+q)+(p+q)-1][9] 5.3138 0.3848
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.02288 0.500 2.000 0.8798
## ARCH Lag[5] 1.45249 1.440 1.667 0.6049
## ARCH Lag[7] 3.60439 2.315 1.543 0.4072
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 1.5586
## Individual Statistics:
## mu 0.001262
## ar1 0.196611
## ar2 0.196371
## ma1 0.225795
## ma2 0.227246
## omega 0.182810
## alpha1 0.297877
## beta1 0.287413
## gamma1 0.306785
## shape 0.220637
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.29 2.54 3.05
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.05323 0.95756
## Negative Sign Bias 2.00413 0.04525 **
## Positive Sign Bias 0.20633 0.83656
## Joint Effect 6.84252 0.07709 *
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 26.74 0.1110
## 2 30 38.93 0.1031
## 3 40 46.53 0.1901
## 4 50 55.59 0.2406
##
##
## Elapsed time : 3.530612
# Phân phối Generalized Error Distribution đối xứng ("sged")
sgsged.spec <- ugarchspec(variance.model = list(model = "gjrGARCH", garchOrder = c(1, 1)), mean.model = list(armaOrder = c(2, 2), include.mean = TRUE), distribution.model = "sged")
sgsged <- ugarchfit(sgsged.spec,VNts)
print(sgsged)
##
## *---------------------------------*
## * GARCH Model Fit *
## *---------------------------------*
##
## Conditional Variance Dynamics
## -----------------------------------
## GARCH Model : gjrGARCH(1,1)
## Mean Model : ARFIMA(2,0,2)
## Distribution : sged
##
## Optimal Parameters
## ------------------------------------
## Estimate Std. Error t value Pr(>|t|)
## mu 1218.223524 1.917132 635.4407 0.000000
## ar1 1.972652 0.000097 20297.4328 0.000000
## ar2 -0.972635 0.000038 -25497.5874 0.000000
## ma1 -0.911554 0.001341 -679.9542 0.000000
## ma2 -0.054146 0.002069 -26.1696 0.000000
## omega 3.363148 1.234813 2.7236 0.006457
## alpha1 0.039476 0.005373 7.3467 0.000000
## beta1 0.859645 0.022844 37.6309 0.000000
## gamma1 0.188780 0.029860 6.3221 0.000000
## skew 1.095398 0.024789 44.1889 0.000000
## shape 1.192417 0.064066 18.6123 0.000000
##
## Robust Standard Errors:
## Estimate Std. Error t value Pr(>|t|)
## mu 1218.223524 1.045941 1164.71511 0.000000
## ar1 1.972652 0.000405 4876.01747 0.000000
## ar2 -0.972635 0.000627 -1550.39709 0.000000
## ma1 -0.911554 0.002408 -378.62554 0.000000
## ma2 -0.054146 0.006294 -8.60349 0.000000
## omega 3.363148 1.001853 3.35693 0.000788
## alpha1 0.039476 0.098942 0.39898 0.689908
## beta1 0.859645 0.040664 21.14019 0.000000
## gamma1 0.188780 0.138018 1.36779 0.171377
## skew 1.095398 0.042142 25.99291 0.000000
## shape 1.192417 0.063398 18.80846 0.000000
##
## LogLikelihood : -5235.463
##
## Information Criteria
## ------------------------------------
##
## Akaike 7.7154
## Bayes 7.7576
## Shibata 7.7153
## Hannan-Quinn 7.7312
##
## Weighted Ljung-Box Test on Standardized Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 0.2413 0.6232
## Lag[2*(p+q)+(p+q)-1][11] 4.1394 0.9997
## Lag[4*(p+q)+(p+q)-1][19] 5.9724 0.9718
## d.o.f=4
## H0 : No serial correlation
##
## Weighted Ljung-Box Test on Standardized Squared Residuals
## ------------------------------------
## statistic p-value
## Lag[1] 2.621 0.1054
## Lag[2*(p+q)+(p+q)-1][5] 5.703 0.1056
## Lag[4*(p+q)+(p+q)-1][9] 7.697 0.1475
## d.o.f=2
##
## Weighted ARCH LM Tests
## ------------------------------------
## Statistic Shape Scale P-Value
## ARCH Lag[3] 0.2033 0.500 2.000 0.6521
## ARCH Lag[5] 1.2318 1.440 1.667 0.6656
## ARCH Lag[7] 3.0147 2.315 1.543 0.5108
##
## Nyblom stability test
## ------------------------------------
## Joint Statistic: 2.3514
## Individual Statistics:
## mu 0.001933
## ar1 0.106514
## ar2 0.107729
## ma1 0.179592
## ma2 0.177749
## omega 0.228607
## alpha1 0.495925
## beta1 0.397192
## gamma1 0.509875
## skew 0.109547
## shape 0.226181
##
## Asymptotic Critical Values (10% 5% 1%)
## Joint Statistic: 2.49 2.75 3.27
## Individual Statistic: 0.35 0.47 0.75
##
## Sign Bias Test
## ------------------------------------
## t-value prob sig
## Sign Bias 0.57560 0.564983
## Negative Sign Bias 3.09526 0.002007 ***
## Positive Sign Bias 0.01883 0.984977
## Joint Effect 11.65637 0.008658 ***
##
##
## Adjusted Pearson Goodness-of-Fit Test:
## ------------------------------------
## group statistic p-value(g-1)
## 1 20 22.29 0.26986
## 2 30 47.22 0.01768
## 3 40 44.35 0.25619
## 4 50 60.07 0.13346
##
##
## Elapsed time : 23.63035