ycextra.RdYield curve or zero-coupon bonds prices curve extrapolation using the Nelson-Siegel, Svensson, Smith-Wilson models.
A vector of non-negative numerical quantities, containing the yield to maturities.
A vector of non-negative numerical quantities, containing the zero-coupon prices.
A vector containing the observed maturities.
the output maturities needed.
A character string giving the type of
method used fo intepolation and extrapolation. method can be either
"NS" for Nelson-Siegel, "SV" for Svensson, or "SW" Smith-Wilson.
A character string, giving the type of return. Either "prices" or "rates".
The ultimate forward rate.
The number of years after which the yield
curve converges to the UFR. T_UFR is used only
when method is "SW".
An S4 Object
This function interpolates between observed points of a yield curve, or zero-coupon prices, and extrapolates the curve using the Nelson-Siegel, Svensson, Smith-Wilson models. The result can be either prices or zero rates. For the purpose of extrapolation, an ultimate forward rate (UFR) to which the yield curve converges must be provided. With the Smith-Wilson method, a period of convergence (number of years) to the ultimate forward rate, after the last liquid point, must be provided.
# Yield to maturities
txZC <- c(0.01422,0.01309,0.01380,0.01549,0.01747,0.01940,0.02104,0.02236,0.02348,
0.02446,0.02535,0.02614,0.02679,0.02727,0.02760,0.02779,0.02787,0.02786,0.02776
,0.02762,0.02745,0.02727,0.02707,0.02686,0.02663,0.02640,0.02618,0.02597,0.02578,0.02563)
# Prices
p <- c(0.9859794,0.9744879,0.9602458,0.9416551,0.9196671,0.8957363,0.8716268,0.8482628,
0.8255457,0.8034710,0.7819525,0.7612204,0.7416912,0.7237042,0.7072136
,0.6922140,0.6785227,0.6660095,0.6546902,0.6441639,0.6343366,0.6250234,0.6162910,0.6080358,
0.6003302,0.5929791,0.5858711,0.5789852,0.5722068,0.5653231)
# Observed maturities
u <- 1:30
# Output maturities
t <- seq(from = 1, to = 60, by = 0.5)
# Svensson extrapolation
(yc <- ycextra(p = p, matsin = u, matsout = t,
method="SV", typeres="prices", UFR = 0.018))
#>
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#> An object of class "ycInterExtra"
#> Slot "matsin":
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
#> [26] 26 27 28 29 30
#>
#> Slot "observedvalues":
#> [1] 0.9859794 0.9744879 0.9602458 0.9416551 0.9196671 0.8957363 0.8716268
#> [8] 0.8482628 0.8255457 0.8034710 0.7819525 0.7612204 0.7416912 0.7237042
#> [15] 0.7072136 0.6922140 0.6785227 0.6660095 0.6546902 0.6441639 0.6343366
#> [22] 0.6250234 0.6162910 0.6080358 0.6003302 0.5929791 0.5858711 0.5789852
#> [29] 0.5722068 0.5653231
#>
#> Slot "method":
#> [1] "SV"
#>
#> Slot "typeres":
#> [1] "prices"
#>
#> Slot "coefficients":
#> [1] 0.0180000000 -0.0005215513 -0.0688081223 0.0788325156 2.7512343646
#> [6] 5.4899523017
#>
#> Slot "matsout":
#> [1] 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
#> [16] 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5
#> [31] 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5 22.0 22.5 23.0
#> [46] 23.5 24.0 24.5 25.0 25.5 26.0 26.5 27.0 27.5 28.0 28.5 29.0 29.5 30.0 30.5
#> [61] 31.0 31.5 32.0 32.5 33.0 33.5 34.0 34.5 35.0 35.5 36.0 36.5 37.0 37.5 38.0
#> [76] 38.5 39.0 39.5 40.0 40.5 41.0 41.5 42.0 42.5 43.0 43.5 44.0 44.5 45.0 45.5
#> [91] 46.0 46.5 47.0 47.5 48.0 48.5 49.0 49.5 50.0 50.5 51.0 51.5 52.0 52.5 53.0
#> [106] 53.5 54.0 54.5 55.0 55.5 56.0 56.5 57.0 57.5 58.0 58.5 59.0 59.5 60.0
#>
#> Slot "fittedvalues":
#> [1] 0.9861187 0.9802368 0.9740973 0.9673145 0.9596865 0.9511445 0.9417120
#> [8] 0.9314739 0.9205512 0.9090831 0.8972126 0.8850780 0.8728061 0.8605093
#> [15] 0.8482841 0.8362109 0.8243547 0.8127665 0.8014847 0.7905370 0.7799420
#> [22] 0.7697103 0.7598465 0.7503500 0.7412164 0.7324379 0.7240046 0.7159048
#> [29] 0.7081258 0.7006537 0.6934747 0.6865746 0.6799392 0.6735546 0.6674072
#> [36] 0.6614840 0.6557723 0.6502600 0.6449356 0.6397881 0.6348071 0.6299830
#> [43] 0.6253064 0.6207686 0.6163616 0.6120778 0.6079098 0.6038511 0.5998955
#> [50] 0.5960370 0.5922702 0.5885900 0.5849918 0.5814711 0.5780237 0.5746459
#> [57] 0.5713341 0.5680850 0.5648954 0.5617624 0.5586835 0.5556561 0.5526778
#> [64] 0.5497466 0.5468603 0.5440170 0.5412151 0.5384529 0.5357288 0.5330414
#> [71] 0.5303894 0.5277715 0.5251865 0.5226333 0.5201110 0.5176185 0.5151548
#> [78] 0.5127193 0.5103110 0.5079292 0.5055732 0.5032423 0.5009358 0.4986532
#> [85] 0.4963940 0.4941574 0.4919432 0.4897506 0.4875794 0.4854290 0.4832990
#> [92] 0.4811890 0.4790987 0.4770276 0.4749755 0.4729419 0.4709265 0.4689291
#> [99] 0.4669494 0.4649869 0.4630416 0.4611130 0.4592010 0.4573052 0.4554255
#> [106] 0.4535616 0.4517133 0.4498803 0.4480624 0.4462594 0.4444712 0.4426975
#> [113] 0.4409381 0.4391928 0.4374615 0.4357440 0.4340400 0.4323494 0.4306721
#>
#> Slot "residuals":
#> [1] -1.393119e-04 3.905907e-04 5.592509e-04 -5.691472e-05 -8.841095e-04
#> [6] -1.476347e-03 -1.179264e-03 -2.131342e-05 1.190985e-03 1.986297e-03
#> [11] 2.010528e-03 1.373918e-03 4.748191e-04 -3.004063e-04 -9.121516e-04
#> [16] -1.260734e-03 -1.416475e-03 -1.397739e-03 -1.082115e-03 -7.716726e-04
#> [21] -4.705337e-04 -2.829671e-04 -7.064712e-05 1.259902e-04 4.347465e-04
#> [26] 7.089211e-04 8.792734e-04 9.614521e-04 8.726731e-04 4.277367e-04
#>
#> Slot "fwdrates":
#> [1] 0.01221729 0.01233909 0.01351961 0.01535605 0.01755138 0.01989051
#> [7] 0.02222138 0.02444003 0.02647885 0.02829748 0.02987556 0.03120728
#> [13] 0.03229704 0.03315622 0.03380072 0.03424909 0.03452118 0.03463714
#> [19] 0.03461673 0.03447884 0.03424117 0.03392006 0.03353040 0.03308558
#> [25] 0.03259756 0.03207688 0.03153278 0.03097328 0.03040528 0.02983466
#> [31] 0.02926636 0.02870454 0.02815259 0.02761329 0.02708885 0.02658097
#> [37] 0.02609096 0.02561973 0.02516790 0.02473581 0.02432361 0.02393121
#> [43] 0.02355842 0.02320489 0.02287019 0.02255379 0.02225511 0.02197353
#> [49] 0.02170838 0.02145899 0.02122466 0.02100469 0.02079839 0.02060508
#> [55] 0.02042408 0.02025472 0.02009638 0.01994843 0.01981028 0.01968135
#> [61] 0.01956109 0.01944898 0.01934452 0.01924722 0.01915665 0.01907238
#> [67] 0.01899398 0.01892109 0.01885335 0.01879040 0.01873194 0.01867765
#> [73] 0.01862726 0.01858050 0.01853713 0.01849690 0.01845960 0.01842502
#> [79] 0.01839298 0.01836330 0.01833580 0.01831033 0.01828676 0.01826493
#> [85] 0.01824473 0.01822604 0.01820874 0.01819275 0.01817796 0.01816428
#> [91] 0.01815163 0.01813994 0.01812914 0.01811915 0.01810993 0.01810141
#> [97] 0.01809354 0.01808627 0.01807955 0.01807336 0.01806763 0.01806235
#> [103] 0.01805748 0.01805298 0.01804883 0.01804500 0.01804147 0.01803821
#> [109] 0.01803520 0.01803243 0.01802987 0.01802752 0.01802534 0.01802334
#> [115] 0.01802149 0.01801979 0.01801822 0.01801678 0.01801545
#>
#> Slot "UFR":
#> [1] 0.018
#>
#> Slot "T_UFR":
#> numeric(0)
#>
#> Slot "extrapvalues":
#> [1] 0.9861187 0.9802368 0.9740973 0.9673145 0.9596865 0.9511445 0.9417120
#> [8] 0.9314739 0.9205512 0.9090831 0.8972126 0.8850780 0.8728061 0.8605093
#> [15] 0.8482841 0.8362109 0.8243547 0.8127665 0.8014847 0.7905370 0.7799420
#> [22] 0.7697103 0.7598465 0.7503500 0.7412164 0.7324379 0.7240046 0.7159048
#> [29] 0.7081258 0.7006537 0.6934747 0.6865746 0.6799392 0.6735546 0.6674072
#> [36] 0.6614840 0.6557723 0.6502600 0.6449356 0.6397881 0.6348071 0.6299830
#> [43] 0.6253064 0.6207686 0.6163616 0.6120778 0.6079098 0.6038511 0.5998955
#> [50] 0.5960370 0.5922702 0.5885900 0.5849918 0.5814711 0.5780237 0.5746459
#> [57] 0.5713341 0.5680850 0.5648954 0.5617624 0.5586835 0.5556561 0.5526778
#> [64] 0.5497466 0.5468603 0.5440170 0.5412151 0.5384529 0.5357288 0.5330414
#> [71] 0.5303894 0.5277715 0.5251865 0.5226333 0.5201110 0.5176185 0.5151548
#> [78] 0.5127193 0.5103110 0.5079292 0.5055732 0.5032423 0.5009358 0.4986532
#> [85] 0.4963940 0.4941574 0.4919432 0.4897506 0.4875794 0.4854290 0.4832990
#> [92] 0.4811890 0.4790987 0.4770276 0.4749755 0.4729419 0.4709265 0.4689291
#> [99] 0.4669494 0.4649869 0.4630416 0.4611130 0.4592010 0.4573052 0.4554255
#> [106] 0.4535616 0.4517133 0.4498803 0.4480624 0.4462594 0.4444712 0.4426975
#> [113] 0.4409381 0.4391928 0.4374615 0.4357440 0.4340400 0.4323494 0.4306721
#>
#Smith-Wilson extrapolation
(yc <- ycextra(p = p, matsin = u, matsout = t,
method="SW", typeres="rates", UFR = 0.019, T_UFR = 20))
#> An object of class "ycInterExtra"
#> Slot "matsin":
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
#> [26] 26 27 28 29 30
#>
#> Slot "observedvalues":
#> [1] 0.9859794 0.9744879 0.9602458 0.9416551 0.9196671 0.8957363 0.8716268
#> [8] 0.8482628 0.8255457 0.8034710 0.7819525 0.7612204 0.7416912 0.7237042
#> [15] 0.7072136 0.6922140 0.6785227 0.6660095 0.6546902 0.6441639 0.6343366
#> [22] 0.6250234 0.6162910 0.6080358 0.6003302 0.5929791 0.5858711 0.5789852
#> [29] 0.5722068 0.5653231
#>
#> Slot "method":
#> [1] "SW"
#>
#> Slot "typeres":
#> [1] "rates"
#>
#> Slot "coefficients":
#> alpha Xhi1 Xhi2 Xhi3 Xhi4 Xhi5
#> 0.13800000 -5.42453600 3.32294038 0.78303576 0.14012771 0.40161214
#> Xhi6 Xhi7 Xhi8 Xhi9 Xhi10 Xhi11
#> -0.44965071 -0.69810401 0.30063796 -0.21920933 0.30069831 0.09682321
#> Xhi12 Xhi13 Xhi14 Xhi15 Xhi16 Xhi17
#> 0.02404538 -0.41865806 0.18910967 -0.25643448 0.01311163 0.31468923
#> Xhi18 Xhi19 Xhi20 Xhi21 Xhi22 Xhi23
#> -0.73719634 0.61735759 -0.42266618 0.53350232 -0.49372835 0.49744112
#> Xhi24 Xhi25 Xhi26 Xhi27 Xhi28 Xhi29
#> -0.57758224 0.21879333 0.11173171 -0.16899163 -0.08575088 -0.22688918
#> Xhi30
#> 0.54874193
#>
#> Slot "matsout":
#> [1] 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
#> [16] 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5
#> [31] 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5 22.0 22.5 23.0
#> [46] 23.5 24.0 24.5 25.0 25.5 26.0 26.5 27.0 27.5 28.0 28.5 29.0 29.5 30.0 30.5
#> [61] 31.0 31.5 32.0 32.5 33.0 33.5 34.0 34.5 35.0 35.5 36.0 36.5 37.0 37.5 38.0
#> [76] 38.5 39.0 39.5 40.0 40.5 41.0 41.5 42.0 42.5 43.0 43.5 44.0 44.5 45.0 45.5
#> [91] 46.0 46.5 47.0 47.5 48.0 48.5 49.0 49.5 50.0 50.5 51.0 51.5 52.0 52.5 53.0
#> [106] 53.5 54.0 54.5 55.0 55.5 56.0 56.5 57.0 57.5 58.0 58.5 59.0 59.5 60.0
#>
#> Slot "fittedvalues":
#> [1] 0.01421997 0.01346633 0.01309000 0.01325966 0.01380001 0.01457817
#> [7] 0.01548999 0.01646887 0.01747000 0.01845969 0.01940000 0.02026282
#> [13] 0.02104000 0.02173254 0.02235999 0.02294028 0.02348000 0.02398368
#> [19] 0.02446000 0.02491572 0.02535001 0.02575976 0.02614000 0.02648531
#> [25] 0.02679000 0.02705033 0.02727000 0.02745312 0.02760000 0.02771092
#> [31] 0.02779000 0.02784175 0.02787000 0.02787694 0.02786000 0.02781813
#> [37] 0.02776000 0.02769399 0.02762000 0.02753726 0.02745001 0.02736182
#> [43] 0.02727000 0.02717184 0.02707000 0.02696698 0.02686000 0.02674661
#> [49] 0.02663000 0.02651396 0.02640000 0.02628881 0.02618000 0.02607335
#> [55] 0.02597000 0.02587150 0.02578000 0.02569811 0.02563000 0.02557910
#> [61] 0.02554482 0.02552573 0.02552053 0.02552807 0.02554730 0.02557726
#> [67] 0.02561711 0.02566608 0.02572346 0.02578861 0.02586097 0.02594000
#> [73] 0.02602524 0.02611625 0.02621263 0.02631402 0.02642010 0.02653057
#> [79] 0.02664515 0.02676359 0.02688567 0.02701119 0.02713993 0.02727175
#> [85] 0.02740647 0.02754395 0.02768405 0.02782666 0.02797167 0.02811896
#> [91] 0.02826846 0.02842007 0.02857372 0.02872933 0.02888685 0.02904621
#> [97] 0.02920736 0.02937025 0.02953483 0.02970108 0.02986894 0.03003839
#> [103] 0.03020940 0.03038194 0.03055600 0.03073153 0.03090854 0.03108700
#> [109] 0.03126690 0.03144822 0.03163096 0.03181510 0.03200065 0.03218758
#> [115] 0.03237589 0.03256559 0.03275667 0.03294913 0.03314297
#>
#> Slot "residuals":
#> [1] -3.252953e-14 -2.264855e-14 7.660539e-15 2.109424e-14 3.430589e-14
#> [6] 4.640732e-14 5.684342e-14 6.394885e-14 7.704948e-14 8.393286e-14
#> [11] 8.104628e-14 7.716050e-14 8.459899e-14 9.492407e-14 1.034728e-13
#> [16] 1.091349e-13 1.154632e-13 1.227907e-13 1.270095e-13 1.310063e-13
#> [21] 1.326717e-13 1.341149e-13 1.351141e-13 1.358913e-13 1.354472e-13
#> [26] 1.348921e-13 1.342260e-13 1.332268e-13 1.320055e-13 1.305622e-13
#>
#> Slot "fwdrates":
#> [1] 0.01179138 0.01172419 0.01358269 0.01597229 0.01848201 0.02081083
#> [7] 0.02288215 0.02465309 0.02607866 0.02700195 0.02742443 0.02751892
#> [13] 0.02739357 0.02731895 0.02733521 0.02732665 0.02728430 0.02729172
#> [19] 0.02734226 0.02732209 0.02719195 0.02691284 0.02646974 0.02584941
#> [25] 0.02508314 0.02432000 0.02357863 0.02278813 0.02195095 0.02115491
#> [31] 0.02041890 0.01973581 0.01907508 0.01832676 0.01752312 0.01690784
#> [37] 0.01648865 0.01606099 0.01560661 0.01525882 0.01500730 0.01468365
#> [43] 0.01428329 0.01395561 0.01369884 0.01336329 0.01295350 0.01263586
#> [49] 0.01243394 0.01228349 0.01215996 0.01203161 0.01190152 0.01181427
#> [55] 0.01178560 0.01183678 0.01198682 0.01229265 0.01273393 0.01317513
#> [61] 0.01358458 0.01396473 0.01431779 0.01464581 0.01495066 0.01523406
#> [67] 0.01549759 0.01574270 0.01597074 0.01618294 0.01638044 0.01656430
#> [73] 0.01673548 0.01689489 0.01704336 0.01718166 0.01731050 0.01743055
#> [79] 0.01754241 0.01764666 0.01774383 0.01783440 0.01791883 0.01799755
#> [85] 0.01807094 0.01813936 0.01820317 0.01826267 0.01831817 0.01836992
#> [91] 0.01841819 0.01846321 0.01850521 0.01854438 0.01858092 0.01861501
#> [97] 0.01864682 0.01867649 0.01870417 0.01872999 0.01875409 0.01877657
#> [103] 0.01879754 0.01881711 0.01883538 0.01885242 0.01886832 0.01888316
#> [109] 0.01889700 0.01890992 0.01892198 0.01893323 0.01894373 0.01895352
#> [115] 0.01896267 0.01897120 0.01897916 0.01898659
#>
#> Slot "UFR":
#> [1] 0.019
#>
#> Slot "T_UFR":
#> [1] 20
#>
#> Slot "extrapvalues":
#> [1] 0.01421997 0.01346633 0.01309000 0.01325966 0.01380001 0.01457817
#> [7] 0.01548999 0.01646887 0.01747000 0.01845969 0.01940000 0.02026282
#> [13] 0.02104000 0.02173254 0.02235999 0.02294028 0.02348000 0.02398368
#> [19] 0.02446000 0.02491572 0.02535001 0.02575976 0.02614000 0.02648531
#> [25] 0.02679000 0.02705033 0.02727000 0.02745312 0.02760000 0.02771092
#> [31] 0.02779000 0.02784175 0.02787000 0.02787694 0.02786000 0.02781813
#> [37] 0.02776000 0.02769399 0.02762000 0.02753726 0.02745001 0.02736182
#> [43] 0.02727000 0.02717184 0.02707000 0.02696698 0.02686000 0.02674661
#> [49] 0.02663000 0.02651396 0.02640000 0.02628881 0.02618000 0.02607335
#> [55] 0.02597000 0.02587150 0.02578000 0.02569811 0.02563000 0.02557910
#> [61] 0.02554482 0.02552573 0.02552053 0.02552807 0.02554730 0.02557726
#> [67] 0.02561711 0.02566608 0.02572346 0.02578861 0.02586097 0.02594000
#> [73] 0.02602524 0.02611625 0.02621263 0.02631402 0.02642010 0.02653057
#> [79] 0.02664515 0.02676359 0.02688567 0.02701119 0.02713993 0.02727175
#> [85] 0.02740647 0.02754395 0.02768405 0.02782666 0.02797167 0.02811896
#> [91] 0.02826846 0.02842007 0.02857372 0.02872933 0.02888685 0.02904621
#> [97] 0.02920736 0.02937025 0.02953483 0.02970108 0.02986894 0.03003839
#> [103] 0.03020940 0.03038194 0.03055600 0.03073153 0.03090854 0.03108700
#> [109] 0.03126690 0.03144822 0.03163096 0.03181510 0.03200065 0.03218758
#> [115] 0.03237589 0.03256559 0.03275667 0.03294913 0.03314297
#>
# Nelson-Siegel extrapolation
(yc <- ycextra(yM = txZC, matsin = u, matsout = t,
method="NS", typeres="prices", UFR = 0.029))
#>
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#> An object of class "ycInterExtra"
#> Slot "matsin":
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
#> [26] 26 27 28 29 30
#>
#> Slot "observedvalues":
#> [1] 0.01422 0.01309 0.01380 0.01549 0.01747 0.01940 0.02104 0.02236 0.02348
#> [10] 0.02446 0.02535 0.02614 0.02679 0.02727 0.02760 0.02779 0.02787 0.02786
#> [19] 0.02776 0.02762 0.02745 0.02727 0.02707 0.02686 0.02663 0.02640 0.02618
#> [28] 0.02597 0.02578 0.02563
#>
#> Slot "method":
#> [1] "NS"
#>
#> Slot "typeres":
#> [1] "prices"
#>
#> Slot "coefficients":
#> [1] 0.02900000 0.01005020 -0.07201655 0.81325186
#>
#> Slot "matsout":
#> [1] 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
#> [16] 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5
#> [31] 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5 22.0 22.5 23.0
#> [46] 23.5 24.0 24.5 25.0 25.5 26.0 26.5 27.0 27.5 28.0 28.5 29.0 29.5 30.0 30.5
#> [61] 31.0 31.5 32.0 32.5 33.0 33.5 34.0 34.5 35.0 35.5 36.0 36.5 37.0 37.5 38.0
#> [76] 38.5 39.0 39.5 40.0 40.5 41.0 41.5 42.0 42.5 43.0 43.5 44.0 44.5 45.0 45.5
#> [91] 46.0 46.5 47.0 47.5 48.0 48.5 49.0 49.5 50.0 50.5 51.0 51.5 52.0 52.5 53.0
#> [106] 53.5 54.0 54.5 55.0 55.5 56.0 56.5 57.0 57.5 58.0 58.5 59.0 59.5 60.0
#>
#> Slot "fittedvalues":
#> [1] 0.9858057 0.9821699 0.9763443 0.9682798 0.9585276 0.9476927 0.9362596
#> [8] 0.9245682 0.9128393 0.9012080 0.8897531 0.8785177 0.8675231 0.8567775
#> [15] 0.8462820 0.8360331 0.8260253 0.8162519 0.8067058 0.7973797 0.7882663
#> [22] 0.7793586 0.7706499 0.7621336 0.7538034 0.7456533 0.7376776 0.7298707
#> [29] 0.7222272 0.7147423 0.7074108 0.7002283 0.6931901 0.6862920 0.6795298
#> [36] 0.6728996 0.6663976 0.6600199 0.6537632 0.6476240 0.6415991 0.6356852
#> [43] 0.6298793 0.6241785 0.6185800 0.6130810 0.6076790 0.6023713 0.5971555
#> [50] 0.5920292 0.5869903 0.5820364 0.5771653 0.5723752 0.5676639 0.5630295
#> [57] 0.5584702 0.5539842 0.5495696 0.5452248 0.5409482 0.5367382 0.5325932
#> [64] 0.5285117 0.5244923 0.5205336 0.5166341 0.5127927 0.5090080 0.5052787
#> [71] 0.5016037 0.4979817 0.4944117 0.4908925 0.4874231 0.4840023 0.4806293
#> [78] 0.4773029 0.4740222 0.4707864 0.4675944 0.4644454 0.4613385 0.4582729
#> [85] 0.4552478 0.4522624 0.4493159 0.4464075 0.4435365 0.4407022 0.4379040
#> [92] 0.4351410 0.4324127 0.4297183 0.4270574 0.4244292 0.4218331 0.4192686
#> [99] 0.4167351 0.4142321 0.4117589 0.4093151 0.4069001 0.4045134 0.4021546
#> [106] 0.3998232 0.3975186 0.3952404 0.3929882 0.3907615 0.3885599 0.3863830
#> [113] 0.3842303 0.3821015 0.3799961 0.3779138 0.3758543 0.3738170 0.3718017
#>
#> Slot "residuals":
#> [1] -1.787091e-04 9.755542e-04 -6.222499e-04 -1.529966e-03 -1.626622e-03
#> [6] -1.251217e-03 -7.752977e-04 -3.449035e-04 7.814843e-05 4.990730e-04
#> [11] 9.311931e-04 1.339491e-03 1.666472e-03 1.869587e-03 1.959616e-03
#> [16] 1.939640e-03 1.834368e-03 1.659681e-03 1.412329e-03 1.139713e-03
#> [21] 8.497262e-04 5.606477e-04 2.610544e-04 -4.023958e-05 -3.542300e-04
#> [26] -6.617596e-04 -9.535463e-04 -1.230205e-03 -1.482267e-03 -1.690192e-03
#>
#> Slot "fwdrates":
#> [1] 0.006045518 0.009586839 0.014716932 0.019229546 0.022609813 0.024946018
#> [7] 0.026484188 0.027464582 0.028075099 0.028448694 0.028674214 0.028808871
#> [13] 0.028888557 0.028935363 0.028962682 0.028978541 0.028987705 0.028992977
#> [19] 0.028996000 0.028997728 0.028998712 0.028999272 0.028999589 0.028999768
#> [25] 0.028999870 0.028999927 0.028999959 0.028999977 0.028999987 0.028999993
#> [31] 0.028999996 0.028999998 0.028999999 0.028999999 0.029000000 0.029000000
#> [37] 0.029000000 0.029000000 0.029000000 0.029000000 0.029000000 0.029000000
#> [43] 0.029000000 0.029000000 0.029000000 0.029000000 0.029000000 0.029000000
#> [49] 0.029000000 0.029000000 0.029000000 0.029000000 0.029000000 0.029000000
#> [55] 0.029000000 0.029000000 0.029000000 0.029000000 0.029000000 0.029000000
#> [61] 0.029000000 0.029000000 0.029000000 0.029000000 0.029000000 0.029000000
#> [67] 0.029000000 0.029000000 0.029000000 0.029000000 0.029000000 0.029000000
#> [73] 0.029000000 0.029000000 0.029000000 0.029000000 0.029000000 0.029000000
#> [79] 0.029000000 0.029000000 0.029000000 0.029000000 0.029000000 0.029000000
#> [85] 0.029000000 0.029000000 0.029000000 0.029000000 0.029000000 0.029000000
#> [91] 0.029000000 0.029000000 0.029000000 0.029000000 0.029000000 0.029000000
#> [97] 0.029000000 0.029000000 0.029000000 0.029000000 0.029000000 0.029000000
#> [103] 0.029000000 0.029000000 0.029000000 0.029000000 0.029000000 0.029000000
#> [109] 0.029000000 0.029000000 0.029000000 0.029000000 0.029000000 0.029000000
#> [115] 0.029000000 0.029000000 0.029000000 0.029000000 0.029000000
#>
#> Slot "UFR":
#> [1] 0.029
#>
#> Slot "T_UFR":
#> numeric(0)
#>
#> Slot "extrapvalues":
#> [1] 0.9858057 0.9821699 0.9763443 0.9682798 0.9585276 0.9476927 0.9362596
#> [8] 0.9245682 0.9128393 0.9012080 0.8897531 0.8785177 0.8675231 0.8567775
#> [15] 0.8462820 0.8360331 0.8260253 0.8162519 0.8067058 0.7973797 0.7882663
#> [22] 0.7793586 0.7706499 0.7621336 0.7538034 0.7456533 0.7376776 0.7298707
#> [29] 0.7222272 0.7147423 0.7074108 0.7002283 0.6931901 0.6862920 0.6795298
#> [36] 0.6728996 0.6663976 0.6600199 0.6537632 0.6476240 0.6415991 0.6356852
#> [43] 0.6298793 0.6241785 0.6185800 0.6130810 0.6076790 0.6023713 0.5971555
#> [50] 0.5920292 0.5869903 0.5820364 0.5771653 0.5723752 0.5676639 0.5630295
#> [57] 0.5584702 0.5539842 0.5495696 0.5452248 0.5409482 0.5367382 0.5325932
#> [64] 0.5285117 0.5244923 0.5205336 0.5166341 0.5127927 0.5090080 0.5052787
#> [71] 0.5016037 0.4979817 0.4944117 0.4908925 0.4874231 0.4840023 0.4806293
#> [78] 0.4773029 0.4740222 0.4707864 0.4675944 0.4644454 0.4613385 0.4582729
#> [85] 0.4552478 0.4522624 0.4493159 0.4464075 0.4435365 0.4407022 0.4379040
#> [92] 0.4351410 0.4324127 0.4297183 0.4270574 0.4244292 0.4218331 0.4192686
#> [99] 0.4167351 0.4142321 0.4117589 0.4093151 0.4069001 0.4045134 0.4021546
#> [106] 0.3998232 0.3975186 0.3952404 0.3929882 0.3907615 0.3885599 0.3863830
#> [113] 0.3842303 0.3821015 0.3799961 0.3779138 0.3758543 0.3738170 0.3718017
#>