4.13 Appendix: Tables with out-of-sample
3M 2Y 5Y 10Y 15Y
CIR−2 -28.87 -29.12 -24.06 -30.87 -49.75
( -0.83 ) ( -1.0409 ) ( -1.2122 ) ( -1.8414 ) ( -2.7214 ) AF NS1−L 3.28 -5.29 -3.56 -0.82 -4.23
( 0.0812 ) ( -0.1645 ) ( -0.1536 ) ( -0.043 ) ( -0.2191 ) AF NS1−C -14.66 3.34 -1.3 -11.38 -9.09
( -0.3929 ) ( 0.1157 ) ( -0.0685 ) ( -0.7252 ) ( -0.5434 ) AF NS2−LC 7.98 15.06 13.7 9.48 3.43
( 0.2005 ) ( 0.4632 ) ( 0.5756 ) ( 0.4745 ) ( 0.1703 ) AF NS2−SC 143.44 271.6 279.93 222.21 194.04
( 3.9084 ) ( 8.8893 ) ( 12.5794 ) ( 10.8869 ) ( 9.1715 ) AF NS3 -24.27 -22.84 -24.73 -30.91 -41.28
( -0.6472 ) ( -0.7699 ) ( -1.1962 ) ( -1.7502 ) ( -2.1872 ) AF NS3−CA -25.94 -20.25 -20.28 -29.54 -44.07
( -0.6945 ) ( -0.6743 ) ( -0.9469 ) ( -1.5999 ) ( -2.2393 )
Table 4.7:Mean errors for 1-year point forecasts measured in ba-sis points. t-statistics for zero mean errors are reported in brackets. t-statistics are based on Newey and West (1987) standard errors.
3M 2Y 5Y 10Y 15Y
CIR−2 -134.86 -128.96 -115.21 -119.96 -142.21
( -2.0061 ) ( -2.8772 ) ( -4.4861 ) ( -6.3831 ) ( -6.9637 ) AF NS1−L 57.72 25.75 20.5 20.28 11.72
( 0.8941 ) ( 0.5462 ) ( 0.6497 ) ( 0.7685 ) ( 0.4297 ) AF NS1−C 33.53 46.07 33.44 14.38 11.75
( 0.4312 ) ( 0.7388 ) ( 0.7156 ) ( 0.3764 ) ( 0.3253 ) AF NS2−LC 55.79 49.59 39.46 28.35 15.91
( 1.0067 ) ( 1.3041 ) ( 1.7359 ) ( 1.5804 ) ( 0.8399 ) AF NS2−SC 722.57 838.56 829.8 763.45 734.6
( 12.546 ) ( 16.0571 ) ( 17.4618 ) ( 14.5777 ) ( 12.7829 ) AF NS3 -75.26 -93.43 -102.15 -109.96 -123.24
( -1.3116 ) ( -2.3579 ) ( -4.3854 ) ( -6.4404 ) ( -6.6778 ) AF NS3−CA -87.42 -100.16 -107.89 -119.99 -137.54
( -1.5287 ) ( -2.5662 ) ( -4.8115 ) ( -7.3512 ) ( -7.6402 )
Table 4.8:Mean errors for 5-year point forecasts measured in ba-sis points. t-statistics for zero mean errors are reported in brackets. t-statistics are based on Newey and West (1987) standard errors.
3M 2Y 5Y 10Y 15Y CIR−2 23.17 25.78 23.42 22.24 30.59 AF NS1−L 18.9 19.69 18.5 15.67 16.39 AF NS1−C 18.36 19.18 18.24 16.94 16.5 AF NS2−LC 19.05 19.61 18.34 15.75 16.34 AF NS2−SC 18.15 33.69 29.8 19.72 20.71 AF NS3 18.58 20.73 19.56 18.44 23.02 AF NS3−CA 18.89 20.58 19.36 18.57 24.27
3M 2Y 5Y 10Y 15Y
CIR−2 vs.AF NS1−L 1.685 4.2635 2.567 2.7433 3.1385 CIR−2 vs.AF NS1−C 1.6644 4.498 2.1909 2.0006 3.1673 CIR−2 vs.AF NS2−LC 1.6003 4.314 2.8971 2.7139 3.134 CIR−2 vs.AF NS2−SC 2.0004 -1.8768 -2.8497 0.7577 1.7759 CIR−2 vs.AF NS3 1.5742 2.8889 2.2936 2.1369 2.6163 CIR−2 vs.AF NS3−CA 1.4351 3.1321 2.6369 2.5295 2.0726 AF NS1−Lvs.AF NS1−C 0.9689 0.9366 0.5128 -1.1807 -0.3881 AF NS1−Lvs.AF NS2−LC -0.7973 0.1977 0.5121 -0.5027 0.2569 AF NS1−Lvs.AF NS2−SC 1.3896 -3.3667 -6.9106 -2.9107 -1.898 AF NS1−Lvs.AF NS3 0.5051 -1.5248 -2.2122 -2.0464 -2.674 AF NS1−Lvs.AF NS3−CA 0.0191 -1.3851 -1.3001 -2.1394 -2.8574 AF NS1−Cvs.AF NS2−LC -1.112 -3.7136 -0.1302 1.0217 0.4785 AF NS1−Cvs.AF NS2−SC 0.2535 -3.7658 -5.43 -1.2263 -1.9692 AF NS1−Cvs.AF NS3 -0.474 -1.689 -1.6519 -1.1731 -2.5276 AF NS1−Cvs.AF NS3−CA -1.0286 -1.6187 -1.0486 -1.1269 -2.7335 AF NS2−LCvs.AF NS2−SC 1.3459 -3.6354 -8.2253 -2.9473 -2.0198 AF NS2−LCvs.AF NS3 0.6593 -1.2768 -3.0961 -1.9299 -2.6085 AF NS2−LCvs.AF NS3−CA 0.2085 -1.1975 -2.4129 -2.0235 -2.7891 AF NS2−SCvs.AF NS3 -0.4419 2.8948 6.16 0.4866 -0.5232 AF NS2−SCvs.AF NS3−CA -0.7529 2.9653 7.364 0.4446 -0.7452 AF NS3vs.AF NS3−CA -1.8102 1.4119 0.5083 -0.3649 -2.0927 Table 4.9:Top Panel: Mean absolute errors for 1-month point forecasts.
Bottom Panel:Pairwise comparison of 1-month point forecasts using the Diebold and Mariano (1995) test. The table reportst-tests for differences between models.t-statistics are based on Newey and West (1987) standard errors.
3M 2Y 5Y 10Y 15Y
CIR−2 93.84 80.31 65.03 54.43 62.38
AF NS1−L 105.29 79.58 66.21 57.98 56.36 AF NS1−C 103.22 83.24 67.73 59.48 59.01 AF NS2−LC 104.8 80.58 67.54 59.67 57.54 AF NS2−SC 168.28 271.64 279.93 222.21 194.04 AF NS3 100.32 80.08 66.55 55.5 57.07 AF NS3−CA 101.35 80.92 66.21 56.87 58.83
3M 2Y 5Y 10Y 15Y
CIR−2 vs.AF NS1−L -1.1945 0.0786 -0.1567 -0.4634 0.6365 CIR−2 vs.AF NS1−C -1.404 -0.3995 -0.3784 -0.8251 0.424 CIR−2 vs.AF NS2−LC -1.0808 -0.0209 -0.2275 -0.539 0.4436 CIR−2 vs.AF NS2−SC -2.4958 -5.3415 -9.0112 -5.9977 -4.0191 CIR−2 vs.AF NS3 -0.7496 0.0331 -0.678 -0.4212 1.2258 CIR−2 vs.AF NS3−CA -0.8615 -0.0943 -0.3489 -0.7462 0.8458 AF NS1−Lvs.AF NS1−C 0.2791 -0.6019 -0.3082 -0.2363 -0.428 AF NS1−Lvs.AF NS2−LC 0.2173 -0.1833 -0.2917 -0.5328 -0.4609 AF NS1−Lvs.AF NS2−SC -2.3782 -5.4216 -10.7485 -7.2183 -5.0933 AF NS1−Lvs.AF NS3 0.54 -0.0827 -0.0518 0.3146 -0.0884 AF NS1−Lvs.AF NS3−CA 0.4078 -0.2445 0.0002 0.1543 -0.266 AF NS1−Cvs.AF NS2−LC -0.1795 0.4036 0.0341 -0.0247 0.2058 AF NS1−Cvs.AF NS2−SC -2.387 -6.1462 -11.8557 -6.926 -5.145 AF NS1−Cvs.AF NS3 0.4354 0.394 0.179 0.5185 0.2128 AF NS1−Cvs.AF NS3−CA 0.2859 0.3556 0.3096 0.352 0.0188 AF NS2−LCvs.AF NS2−SC -2.4903 -5.9434 -13.2706 -7.8794 -5.3009 AF NS2−LCvs.AF NS3 0.4412 0.048 0.0955 0.402 0.0465 AF NS2−LCvs.AF NS3−CA 0.3257 -0.0349 0.1497 0.2899 -0.1165 AF NS2−SCvs.AF NS3 2.1517 5.3065 8.9411 5.7529 4.0876 AF NS2−SCvs.AF NS3−CA 2.1286 5.4251 9.3616 5.7002 3.9135 AF NS3vs.AF NS3−CA -1.2831 -0.5823 0.1637 -0.7016 -1.2269 Table 4.10: Top Panel: Mean absolute errors for 1-year point forecasts.
Bottom Panel: Pairwise comparison of 1-year point forecasts using the Diebold and Mariano (1995) test. The table reportst-tests for differences between models.t-statistics are based on Newey and West (1987) standard errors.
3M 2Y 5Y 10Y 15Y CIR−2 184.13 146.45 118.48 119.96 142.21 AF NS1−L 132.86 93.87 63.87 55.94 59.61 AF NS1−C 160.13 138.04 111.71 94.51 89.08 AF NS2−LC 120.81 83.07 61.44 50.29 46.74 AF NS2−SC 722.57 838.56 829.8 763.45 734.6 AF NS3 142.83 116.54 105.09 109.96 123.24 AF NS3−CA 147.17 120.25 109.82 119.99 137.54
3M 2Y 5Y 10Y 15Y
CIR−2 vs.AF NS1−L 0.8124 1.0908 1.6418 2.3192 3.0589 CIR−2 vs.AF NS1−C 0.4422 0.1584 0.1881 0.9441 1.8479 CIR−2 vs.AF NS2−LC 1.065 1.1808 1.7737 3.0022 3.9496 CIR−2 vs.AF NS2−SC -7.6147 -10.9371 -15.6876 -13.9772 -11.4666
CIR−2 vs.AF NS3 1.4283 1.7701 1.3742 1.8582 3.8886
CIR−2 vs.AF NS3−CA 1.367 1.7071 0.9911 -0.0064 0.9711 AF NS1−Lvs.AF NS1−C -2.3985 -3.7605 -4.3816 -6.4203 -8.7866 AF NS1−Lvs.AF NS2−LC 1.7462 0.9935 0.3033 0.6774 1.8278 AF NS1−Lvs.AF NS2−SC -10.6331 -15.0459 -14.0469 -11.7654 -10.5389 AF NS1−Lvs.AF NS3 -0.2028 -0.5501 -1.3959 -2.1464 -2.5987 AF NS1−Lvs.AF NS3−CA -0.2665 -0.611 -1.5525 -2.5987 -3.2188 AF NS1−Cvs.AF NS2−LC 3.2288 5.0872 4.5721 4.8703 4.6388 AF NS1−Cvs.AF NS2−SC -10.7758 -12.8706 -12.7885 -11.2831 -10.0628 AF NS1−Cvs.AF NS3 0.398 0.441 0.1899 -0.6195 -1.2952 AF NS1−Cvs.AF NS3−CA 0.271 0.3523 0.0544 -1.0508 -1.8616 AF NS2−LCvs.AF NS2−SC -11.042 -14.5229 -14.5737 -12.9612 -11.7523 AF NS2−LCvs.AF NS3 -0.4725 -0.697 -1.4743 -2.7439 -3.392 AF NS2−LCvs.AF NS3−CA -0.5173 -0.7473 -1.6387 -3.3244 -4.106 AF NS2−SCvs.AF NS3 8.7173 11.9422 15.8371 13.1773 10.9435 AF NS2−SCvs.AF NS3−CA 8.3437 11.6454 15.6421 13.0456 10.7617 AF NS3vs.AF NS3−CA -0.9146 -1.5049 -3.1973 -7.6749 -11.1326 Table 4.11: Top Panel: Mean absolute errors for 5-year point forecasts.
Bottom Panel: Pairwise comparison of 5-year point forecasts using the Diebold and Mariano (1995) test. The table reportst-tests for differences between models.t-statistics are based on Newey and West (1987) standard errors.
3M 2Y 5Y 10Y 15Y
CIR−2 -0.87 -4.51 0.64 -3.84 -21.6
( -0.1279 ) ( -0.6379 ) ( 0.1189 ) ( -0.7915 ) ( -2.928 ) AF NS1−L 0.94 -2.26 -0.57 1.07 -2.65
( 0.2681 ) ( -0.7225 ) ( -0.2398 ) ( 0.5529 ) ( -1.0008 ) AF NS1−C -3.62 3.06 -1.42 -5.47 -0.32
( -1.2035 ) ( 1.0062 ) ( -0.9715 ) ( -2.4147 ) ( -0.1242 ) AF NS2−LC 0.99 1.17 1.72 2.12 -1.65
( 0.2853 ) ( 0.3447 ) ( 0.6691 ) ( 1.049 ) ( -0.6 ) AF NS2−SC 3.16 31.49 27.74 14.23 14.93 ( 1.2152 ) ( 6.784 ) ( 14.227 ) ( 5.4185 ) ( 5.1105 ) AF NS3 -2.46 -1.02 -0.01 -3.33 -12.99
( -0.6899 ) ( -0.2491 ) ( -0.0046 ) ( -1.0534 ) ( -2.4615 ) AF NS3−CA -2.37 -0.23 2.3 -3.09 -16.13
( -0.6538 ) ( -0.0557 ) ( 0.7961 ) ( -0.9874 ) ( -2.9508 )
Table 4.12:Mean errors for 1-month volatility forecasts measured in basis points.t-statistics for zero mean errors are reported in brackets.
t-statistics are based on Newey and West (1987) standard errors.
3M 2Y 5Y 10Y 15Y
CIR−2 -49.33 -13.48 12.81 20.65 24.56
( -2.9917 ) ( -2.2343 ) ( 2.4998 ) ( 5.2513 ) ( 5.538 ) AF NS1−L 6.34 -11.16 -10.76 -9.93 -8.36
( 0.3651 ) ( -1.3397 ) ( -1.4366 ) ( -1.7233 ) ( -1.2653 ) AF NS1−C -1.73 -29.38 -35.52 -30.27 -25.85
( -0.0877 ) ( -2.2549 ) ( -2.8621 ) ( -2.9855 ) ( -2.5267 ) AF NS2−LC 6.89 -18.38 -16.49 -12.64 -10.01
( 0.3934 ) ( -2.0908 ) ( -2.1388 ) ( -2.1425 ) ( -1.4892 ) AF NS2−SC -7.98 -20.97 -24.69 -28.78 -29.01
( -0.4317 ) ( -2.0598 ) ( -2.5982 ) ( -3.6915 ) ( -3.5362 )
AF NS3 51.66 20.6 21.61 27.54 31.7
( 3.9029 ) ( 3.281 ) ( 4.2437 ) ( 8.4627 ) ( 9.728 ) AF NS3−CA 41.85 11.55 13.79 20.61 25.43
( 3.3766 ) ( 1.7963 ) ( 2.4998 ) ( 5.6274 ) ( 7.3623 ) Table 4.13:Mean errors for 1-year volatility forecasts measured in basis points. t-statistics for zero mean errors are reported in brackets.
t-statistics are based on Newey and West (1987) standard errors.
3M 2Y 5Y 10Y 15Y
CIR−2 -36.69 31.92 66.82 62.77 63.45
( -1.0176 ) ( 2.5187 ) ( 7.8245 ) ( 8.2337 ) ( 7.1063 ) AF NS1−L 21.17 11.77 8.14 -6.42 -8.33
( 0.9248 ) ( 1.3716 ) ( 1.0616 ) ( -1.0238 ) ( -1.1227 ) AF NS1−C -76.63 -101.32 -110.53 -121.05 -122.04
( -2.6755 ) ( -7.3619 ) ( -7.5727 ) ( -8.0712 ) ( -7.3627 ) AF NS2−LC 18.59 0.32 -1.4 -12.9 -14.16
( 0.8811 ) ( 0.0351 ) ( -0.1781 ) ( -2.0432 ) ( -2.1166 ) AF NS2−SC -199.96 -204.57 -211.85 -233.06 -239.72
( -5.4566 ) ( -9.5532 ) ( -9.6411 ) ( -10.3565 ) ( -9.9328 ) AF NS3 120.92 77.13 80.19 81.29 83.78
( 5.3999 ) ( 8.3685 ) ( 12.3702 ) ( 19.3075 ) ( 13.8682 ) AF NS3−CA 96.88 63.27 65.32 63.72 66.83
( 4.32 ) ( 7.367 ) ( 8.184 ) ( 10.1167 ) ( 9.1737 ) Table 4.14:Mean errors for 5-year volatility forecasts measured in basis points. t-statistics for zero mean errors are reported in brackets.
t-statistics are based on Newey and West (1987) standard errors.
3M 2Y 5Y 10Y 15Y CIR−2 32.13 15.97 11.83 9.79 9.72 AF NS1−L 16.58 15.17 14.97 12.6 12.5 AF NS1−C 16.74 15.76 17.35 13.12 12.79 AF NS2−LC 16.66 17.84 16.94 13.49 13.02 AF NS2−SC 15.94 15.17 16.64 13.05 12.63 AF NS3 12.59 11.94 12.03 9.31 8.87 AF NS3−CA 13.12 13.33 13.2 9.71 9.18
3M 2Y 5Y 10Y 15Y
CIR−2 vs.AF NS1−L 4.0665 0.5943 -3.2091 -3.9874 -3.2214 CIR−2 vs.AF NS1−C 4.1781 0.1846 -3.4143 -3.8747 -3.1792 CIR−2 vs.AF NS2−LC 4.0408 -1.5194 -4.7053 -5.1325 -3.8466 CIR−2 vs.AF NS2−SC 4.3657 0.8523 -3.9321 -4.4958 -3.3305 CIR−2 vs.AF NS3 4.5985 4.0707 -0.7097 1.023 1.5551 CIR−2 vs.AF NS3−CA 4.8291 2.7861 -3.4276 0.283 1.5573 AF NS1−Lvs.AF NS1−C -0.1962 -0.5588 -1.954 -0.7133 -0.4144 AF NS1−Lvs.AF NS2−LC -0.9356 -5.1479 -7.4712 -11.3452 -9.3946 AF NS1−Lvs.AF NS2−SC 0.8368 0.0065 -1.7313 -0.6341 -0.1806 AF NS1−Lvs.AF NS3 3.0971 2.9776 2.7257 3.6382 3.0744 AF NS1−Lvs.AF NS3−CA 3.7276 2.0566 1.9461 3.4028 3.0683 AF NS1−Cvs.AF NS2−LC 0.0867 -2.6831 0.3715 -0.5055 -0.3173 AF NS1−Cvs.AF NS2−SC 2.0983 1.8715 1.6669 0.3663 1.2069 AF NS1−Cvs.AF NS3 3.431 2.8813 3.1057 3.1476 2.7091 AF NS1−Cvs.AF NS3−CA 5.3936 2.2072 2.8053 3.077 2.7876 AF NS2−LCvs.AF NS2−SC 0.9574 3.8397 0.357 0.6143 0.5397 AF NS2−LCvs.AF NS3 3.2775 4.6524 4.1105 4.5248 3.5609 AF NS2−LCvs.AF NS3−CA 3.9263 4.3823 3.6655 4.3609 3.579 AF NS2−SCvs.AF NS3 3.9003 3.0314 3.451 3.3774 2.7516 AF NS2−SCvs.AF NS3−CA 8.5896 2.1535 3.0598 3.3768 2.8532 AF NS3vs.AF NS3−CA -0.9161 -3.2542 -2.7995 -1.5879 -1.4881 Table 4.15:Top Panel: Mean absolute errors for 1-month volatility fore-casts.Bottom Panel:Pairwise comparison of 1-month volatility forecasts using the Diebold and Mariano (1995) test. The table reportst-tests for dif-ferences between models.t-statistics are based on Newey and West (1987) standard errors.
3M 2Y 5Y 10Y 15Y CIR−2 64.4 21.66 20.38 24.61 27.87 AF NS1−L 34.73 22.77 22.95 17.75 19.2 AF NS1−C 38.24 41.24 43.49 35.21 32.7 AF NS2−LC 34.47 28.58 26.06 19.1 19.71 AF NS2−SC 40.98 32.98 34.24 33.29 33.78 AF NS3 52.48 25.79 25.57 28.41 32.01 AF NS3−CA 45.38 23.68 24.23 24.11 27.12
3M 2Y 5Y 10Y 15Y
CIR−2 vs.AF NS1−L 2.0112 -0.2429 -0.4941 1.7744 1.5944 CIR−2 vs.AF NS1−C 1.741 -3.7517 -2.5862 -1.3619 -0.5679 CIR−2 vs.AF NS2−LC 1.9874 -1.9139 -1.066 1.348 1.3985 CIR−2 vs.AF NS2−SC 1.7567 -3.7972 -2.5431 -1.6959 -0.8121 CIR−2 vs.AF NS3 0.793 -0.6214 -1.7632 -1.4905 -1.6016 CIR−2 vs.AF NS3−CA 1.3871 -0.4764 -1.6376 0.4531 0.5093 AF NS1−Lvs.AF NS1−C -0.8994 -2.6361 -2.9884 -3.0377 -2.489 AF NS1−Lvs.AF NS2−LC 0.5774 -3.7835 -2.1288 -1.7948 -0.8203 AF NS1−Lvs.AF NS2−SC -2.2944 -3.7053 -4.5132 -4.8371 -4.335 AF NS1−Lvs.AF NS3 -2.3169 -0.5003 -0.4329 -2.3546 -2.3455 AF NS1−Lvs.AF NS3−CA -1.4405 -0.2201 -0.281 -1.4633 -1.5171 AF NS1−Cvs.AF NS2−LC 0.9106 1.9526 2.4222 2.6249 2.2832 AF NS1−Cvs.AF NS2−SC -0.8579 1.7044 1.8094 0.5253 -0.3456 AF NS1−Cvs.AF NS3 -1.7682 1.544 1.7384 0.8263 0.0845 AF NS1−Cvs.AF NS3−CA -0.9266 2.1744 2.2887 1.4398 0.6874 AF NS2−LCvs.AF NS2−SC -2.0964 -1.8671 -3.3142 -4.1284 -3.9 AF NS2−LCvs.AF NS3 -2.3536 0.4625 0.0789 -1.8681 -2.08 AF NS2−LCvs.AF NS3−CA -1.4603 1.3422 0.405 -1.077 -1.3123 AF NS2−SCvs.AF NS3 -1.3979 1.1247 1.3427 0.8029 0.2451 AF NS2−SCvs.AF NS3−CA -0.5883 2.3146 2.2973 1.7598 0.9813 AF NS3vs.AF NS3−CA 3.0646 0.6986 0.5446 2.004 2.455 Table 4.16:Top Panel: Mean absolute errors for 1-year volatility forecasts.
Bottom Panel:Pairwise comparison of 1-year volatility forecasts using the Diebold and Mariano (1995) test. The table reportst-tests for differences between models.t-statistics are based on Newey and West (1987) standard errors.
3M 2Y 5Y 10Y 15Y
CIR−2 80.82 36.07 66.82 62.77 63.45
AF NS1−L 44.3 21.46 19.18 17.72 19.05 AF NS1−C 102.02 103.76 111.93 121.61 122.74 AF NS2−LC 42.77 19.94 18.85 19.74 20.56 AF NS2−SC 202.79 204.57 211.85 233.06 239.72 AF NS3 120.92 77.13 80.19 81.29 83.78 AF NS3−CA 96.88 63.28 65.37 63.72 66.83
3M 2Y 5Y 10Y 15Y
CIR−2 vs.AF NS1−L 2.2802 1.3761 5.2256 0.0045 5.0882 CIR−2 vs.AF NS1−C -1.4412 -3.2208 -2.0978 -0.0059 -2.3946 CIR−2 vs.AF NS2−LC 2.4066 1.675 5.3097 0.0043 4.5126 CIR−2 vs.AF NS2−SC -3.1699 -5.4425 -5.0027 -0.017 -5.455 CIR−2 vs.AF NS3 -1.9924 -3.5793 -1.6747 -0.0019 -6.3537 CIR−2 vs.AF NS3−CA -0.8184 -2.8777 0.285 -0.0001 -1.4049 AF NS1−Lvs.AF NS1−C -2.7069 -5.7338 -6.0203 -6.5377 -5.9846 AF NS1−Lvs.AF NS2−LC 0.5108 0.3376 0.0849 -0.6247 -0.4988 AF NS1−Lvs.AF NS2−SC -3.3074 -7.8362 -8.1353 -9.0825 -8.7645 AF NS1−Lvs.AF NS3 -6.4115 -9.4228 -13.0863 -16.1611 -10.1323 AF NS1−Lvs.AF NS3−CA -4.6646 -6.6731 -5.9603 -8.0308 -6.9329 AF NS1−Cvs.AF NS2−LC 2.9888 6.6 6.6818 6.3298 5.9367 AF NS1−Cvs.AF NS2−SC -3.5245 -8.3813 -8.1859 -9.3567 -9.9273 AF NS1−Cvs.AF NS3 -0.6478 1.4735 1.8851 2.2589 1.7947 AF NS1−Cvs.AF NS3−CA 0.1774 2.2026 2.3882 2.8751 2.4281 AF NS2−LCvs.AF NS2−SC -3.4835 -8.3355 -8.5493 -8.7841 -8.6153 AF NS2−LCvs.AF NS3 -5.8932 -5.9519 -8.8425 -10.5259 -8.4354 AF NS2−LCvs.AF NS3−CA -4.198 -4.8453 -5.2455 -6.2874 -5.787 AF NS2−SCvs.AF NS3 5.3172 4.5908 5.2843 6.0118 5.3172 AF NS2−SCvs.AF NS3−CA 5.7217 5.2012 5.5662 6.3276 5.7217 AF NS3vs.AF NS3−CA 12.8575 2.9561 3.2687 5.6332 7.7661 Table 4.17:Top Panel:Mean absolute errors for 5-year volatility forecasts.
Bottom Panel:Pairwise comparison of 5-year volatility forecasts using the Diebold and Mariano (1995) test. The table reportst-tests for differences between models.t-statistics are based on Newey and West (1987) standard errors.
μ ρ σ Pr(H1=H0) ρ2 Pr(H2=H0)
CIR−2 -0.0331 0.6292 0.6404 0.0000 0.6238 0.0000
( -0.2654 ) ( 17.6246 ) ( -5.9048 ) ( 6.6221 )
AF NS1−L -0.0503 0.2272 1.4972 0.0000 0.2288 0.0000
( -0.3311 ) ( 2.7242 ) ( 6.4993 ) ( 4.4775 )
AF NS1−C -0.1315 0.129 1.0783 4.7490 0.1421 13.4383
( -1.3501 ) ( 2.1464 ) ( 1.0038 ) ( 1.9791 )
AF NS2−LC 0.0329 0.1706 1.0616 7.6944 0.1715 51.7550
( 0.3274 ) ( 2.8818 ) ( 0.7959 ) ( 2.3525 )
AF NS2−SC 0.1118 0.1522 1.0942 2.5141 0.1604 12.1432
( 1.1026 ) ( 2.4951 ) ( 1.2108 ) ( 2.2623 )
AF NS3 -0.1686 0.214 1.2514 0.0000 0.2288 0.0019
( -1.3499 ) ( 3.0703 ) ( 3.2777 ) ( 3.7632 )
AF NS3−CA -0.1497 0.2117 1.1369 0.0230 0.2260 1.8315
( -1.3224 ) ( 3.3391 ) ( 1.7826 ) ( 3.3731 )
Table 4.18: Probability Integral transform tests for the 3-month yield, 1 month ahead. The test is based on Berkowitz (2001). In hy-pothesis H0 all parameters are estimated freely. In the hypothesis H1, μ=ρ= 0 andσ= 1. In the hypothesisH2,ρis estimated freely, and μ= 0 andσ= 1. Probabilities from the Likelihoodratio-tests (in percent) and Parameter estimates underH0 andH2along witht-statistics are re-ported. Thet-statistics are based on tests againstH1.t-statistics are based on Newey and West (1987) standard errors.
μ ρ σ Pr(H1=H0) ρ2 Pr(H2=H0)
CIR−2 -0.2099 0.6791 0.6095 0.0000 0.6837 0.0000
( -1.6023 ) ( 19.9735 ) ( -6.6866 ) ( 7.2657 )
AF NS1−L -0.0707 0.347 0.7366 0.0000 0.3489 0.0003 ( -0.8043 ) ( 8.4634 ) ( -3.5643 ) ( 3.4995 )
AF NS1−C 0.0584 0.3274 0.8112 0.0011 0.3305 0.1862
( 0.6206 ) ( 7.2434 ) ( -2.5342 ) ( 3.6199 )
AF NS2−LC 0.0228 0.3597 0.6871 0.0000 0.3584 0.0000
( 0.2731 ) ( 9.3916 ) ( -4.2514 ) ( 3.3684 )
AF NS2−SC 0.9467 0.3145 0.7946 0.0000 0.7072 0.0000 ( 10.4262 ) ( 7.0993 ) ( -2.8176 ) ( 11.5745 )
AF NS3 -0.0644 0.4472 0.9908 0.0000 0.4478 88.6506
( -0.466 ) ( 8.1014 ) ( -0.1301 ) ( 6.2805 )
AF NS3−CA -0.0051 0.4497 0.8773 0.0000 0.4488 7.9479 ( -0.0415 ) ( 9.1963 ) ( -1.7355 ) ( 5.5821 )
Table 4.19:Probability Integral transform tests for the 2-year yield, 1 month ahead. The test is based on Berkowitz (2001). In hypothesis H0 all parameters are estimated freely. In the hypothesisH1,μ=ρ= 0 andσ= 1. In the hypothesisH2,ρis estimated freely, andμ= 0 andσ= 1. Probabilities from the Likelihoodratio-tests (in percent) and Parameter estimates underH0 andH2 along witht-statistics are reported. The t-statistics are based on tests againstH1. t-statistics are based on Newey and West (1987) standard errors.
μ ρ σ Pr(H1=H0) ρ2 Pr(H2=H0)
CIR−2 -0.0314 0.6181 0.7053 0.0000 0.6141 0.0000
( -0.2336 ) ( 15.7277 ) ( -4.7763 ) ( 7.0749 )
AF NS1−L -0.0120 0.2675 0.7528 0.0003 0.2663 0.0020 ( -0.1491 ) ( 6.3842 ) ( -3.2484 ) ( 2.6419 )
AF NS1−C -0.0327 0.2019 0.7339 0.0002 0.2023 0.0003 ( -0.4529 ) ( 4.9364 ) ( -3.4424 ) ( 1.9285 )
AF NS2−LC 0.0532 0.2771 0.7038 0.0000 0.2798 0.0000
( 0.6982 ) ( 7.0689 ) ( -3.9025 ) ( 2.6125 )
AF NS2−SC 0.8712 0.2379 0.7399 0.0000 0.6718 0.0000 ( 11.4331 ) ( 5.7743 ) ( -3.4634 ) ( 10.0119 )
AF NS3 0.0044 0.3555 0.9822 0.0049 0.3555 94.9428
( 0.0371 ) ( 6.4991 ) ( -0.2418 ) ( 4.7463 )
AF NS3−CA 0.0983 0.3856 0.8898 0.0004 0.3925 9.6955
( 0.8746 ) ( 7.7742 ) ( -1.5158 ) ( 4.8457 )
Table 4.20:Probability Integral transform tests for the 5-year yield, 1 month ahead. The test is based on Berkowitz (2001). In hypothesis H0 all parameters are estimated freely. In the hypothesisH1,μ=ρ= 0 andσ= 1. In the hypothesisH2,ρis estimated freely, andμ= 0 andσ= 1. Probabilities from the Likelihoodratio-tests (in percent) and Parameter estimates underH0 andH2 along with t-statistics are reported. The t-statistics are based on tests againstH1. t-statistics are based on Newey and West (1987) standard errors.
μ ρ σ Pr(H1=H0) ρ2 Pr(H2=H0)
CIR−2 -0.0641 0.6611 0.7075 0.0000 0.6617 0.0000
( -0.4334 ) ( 16.7792 ) ( -4.9576 ) ( 8.119 )
AF NS1−L 0.0578 0.1253 0.7592 0.0051 0.1297 0.0029 ( 0.8463 ) ( 2.9622 ) ( -3.0793 ) ( 1.2654 )
AF NS1−C -0.1638 0.1373 0.7495 0.0003 0.1759 0.0003 ( -2.3982 ) ( 3.2847 ) ( -3.2157 ) ( 1.733 )
AF NS2−LC 0.0917 0.1368 0.7240 0.0001 0.1495 0.0001 ( 1.3915 ) ( 3.3945 ) ( -3.5339 ) ( 1.4024 )
AF NS2−SC 0.5635 0.257 0.7741 0.0000 0.5032 0.0000
( 6.9056 ) ( 5.9629 ) ( -2.996 ) ( 6.3058 )
AF NS3 -0.1637 0.4614 1.0454 0.0000 0.4741 38.0497
( -1.0965 ) ( 7.9142 ) ( 0.6532 ) ( 7.2052 )
AF NS3−CA -0.1335 0.5165 0.9249 0.0000 0.5256 27.6644 ( -0.9182 ) ( 10.0291 ) ( -1.1209 ) ( 7.3305 )
Table 4.21: Probability Integral transform tests for the 10-year yield, 1 month ahead. The test is based on Berkowitz (2001). In hy-pothesis H0 all parameters are estimated freely. In the hypothesis H1, μ=ρ= 0 andσ= 1. In the hypothesisH2,ρis estimated freely, and μ= 0 andσ= 1. Probabilities from the Likelihoodratio-tests (in percent) and Parameter estimates underH0andH2along witht-statistics are re-ported. Thet-statistics are based on tests againstH1. t-statistics are based on Newey and West (1987) standard errors.
μ ρ σ Pr(H1=H0) ρ2 Pr(H2=H0)
CIR−2 -0.3742 0.7580 0.7271 0.0000 0.8151 0.0001
( -1.6955 ) ( 18.716 ) ( -4.6412 ) ( 13.6992 )
AF NS1−L -0.0658 0.1750 0.8024 0.0569 0.1790 0.0900 ( -0.8613 ) ( 3.9150 ) ( -2.5398 ) ( 1.8530 )
AF NS1−C 0.0134 0.2032 0.7995 0.0365 0.2029 0.0916
( 0.1703 ) ( 4.5663 ) ( -2.5871 ) ( 2.0982 )
AF NS2−LC -0.0271 0.1962 0.778 0.0093 0.1960 0.0170 ( -0.3566 ) ( 4.5312 ) ( -2.8645 ) ( 1.9718 )
AF NS2−SC 0.5992 0.3139 0.8148 0.0000 0.5436 0.0000
( 6.4569 ) ( 6.9141 ) ( -2.5027 ) ( 7.3065 )
AF NS3 -0.5441 0.6262 1.0869 0.0000 0.6920 1.3538 ( -2.5425 ) ( 10.3333 ) ( 1.4364 ) ( 13.5686 )
AF NS3−CA -0.5966 0.6653 0.9633 0.0000 0.7486 4.8292 ( -2.8329 ) ( 12.3892 ) ( -0.6295 ) ( 14.3136 )
Table 4.22: Probability Integral transform tests for the 15-year yield, 1 month ahead. The test is based on Berkowitz (2001). In hy-pothesis H0 all parameters are estimated freely. In the hypothesis H1, μ=ρ= 0 andσ= 1. In the hypothesisH2,ρis estimated freely, and μ= 0 andσ= 1. Probabilities from the Likelihoodratio-tests (in percent) and Parameter estimates underH0 andH2along witht-statistics are re-ported. Thet-statistics are based on tests againstH1.t-statistics are based on Newey and West (1987) standard errors.