#obtenemos los datos desde el sitio de yahoo de disney
NVCRdata <- pdfetch_YAHOO("DIS",from = c("2019-01-01"),to = c("2020-01-01"), interval = '1d')
NVCRdata
## DIS.open DIS.high DIS.low DIS.close DIS.adjclose DIS.volume
## 2019-01-02 108.10 109.14 107.73 108.97 107.6543 9723500
## 2019-01-03 108.48 108.65 105.94 106.33 105.0462 10594700
## 2019-01-04 107.94 110.75 107.25 109.61 108.2866 10122800
## 2019-01-07 109.91 111.40 109.30 110.56 109.2251 6714700
## 2019-01-08 111.80 112.56 111.17 111.42 110.0748 8730700
## 2019-01-09 111.80 112.80 111.56 112.67 111.3097 5931900
## 2019-01-10 111.99 112.91 111.50 112.80 111.4381 6160100
## 2019-01-11 112.18 112.92 111.73 112.65 111.2899 4819100
## 2019-01-14 111.65 112.70 111.43 112.42 111.0627 6980600
## 2019-01-15 112.30 113.18 110.61 111.76 110.4107 9800900
## 2019-01-16 111.45 112.01 110.81 110.91 109.5709 5899900
## 2019-01-17 110.72 111.26 110.16 111.01 109.6697 6392000
## 2019-01-18 111.86 111.93 110.83 111.04 109.6993 8554700
## 2019-01-22 110.62 111.33 109.75 110.60 109.2647 6986700
## 2019-01-23 111.19 111.84 110.00 111.12 109.7784 6845600
## 2019-01-24 111.00 111.11 109.93 110.55 109.2153 6716800
## 2019-01-25 111.47 111.50 110.66 111.09 109.7487 5706900
## 2019-01-28 110.76 110.99 109.95 110.81 109.4721 6178800
## 2019-01-29 110.65 110.93 110.00 110.90 109.5610 5253700
## 2019-01-30 110.30 110.58 108.96 110.13 108.8003 7853800
## 2019-01-31 110.10 111.54 110.01 111.52 110.1735 8351600
## 2019-02-01 111.97 112.05 110.93 111.30 109.9562 6557700
## 2019-02-04 111.41 111.98 110.68 111.80 110.4502 7037000
## 2019-02-05 112.02 112.74 111.45 112.66 111.2998 13619800
## 2019-02-06 113.85 113.92 111.07 111.41 110.0649 14229000
## 2019-02-07 111.05 111.11 109.81 110.95 109.6104 8658100
## 2019-02-08 110.46 111.54 110.06 111.51 110.1637 6395500
## 2019-02-11 111.77 111.81 109.25 109.44 108.1187 11086400
## 2019-02-12 110.21 110.83 109.15 109.20 107.8816 7610200
## 2019-02-13 109.24 110.48 109.23 110.20 108.8695 6919700
## 2019-02-14 109.85 111.50 109.54 110.66 109.3239 6324300
## 2019-02-15 111.40 112.63 111.03 112.59 111.2306 8197300
## 2019-02-19 112.91 113.77 112.83 113.51 112.1395 8169600
## 2019-02-20 113.60 114.09 113.29 113.68 112.3075 7081500
## 2019-02-21 113.40 114.54 112.87 114.29 112.9101 9480100
## 2019-02-22 114.63 115.77 113.95 115.25 113.8585 8734700
## 2019-02-25 115.62 115.80 113.46 113.59 112.2186 9327700
## 2019-02-26 113.65 114.01 112.85 113.50 112.1296 8956000
## 2019-02-27 113.10 113.51 112.46 112.78 111.4183 7249500
## 2019-02-28 112.90 113.43 112.75 112.84 111.4776 6716700
## 2019-03-01 113.45 114.44 113.45 114.01 112.6335 6996900
## 2019-03-04 114.42 114.42 113.09 114.33 112.9496 6015000
## 2019-03-05 114.23 114.54 113.76 114.00 112.6236 5225100
## 2019-03-06 114.00 115.05 114.00 114.85 113.4633 7352800
## 2019-03-07 114.85 114.90 113.47 114.01 112.6335 6324000
## 2019-03-08 113.46 113.84 112.90 113.81 112.4359 6549100
## 2019-03-11 114.04 115.00 114.03 114.75 113.3645 6952700
## 2019-03-12 114.72 115.30 114.04 114.73 113.3448 9920300
## 2019-03-13 114.84 114.85 113.72 114.09 112.7125 17994500
## 2019-03-14 114.12 114.77 113.93 114.48 113.0978 17409600
## 2019-03-15 114.50 115.48 113.68 114.96 113.5720 14932700
## 2019-03-18 113.03 114.00 112.46 113.12 111.7542 21769800
## 2019-03-19 112.95 113.71 109.80 110.00 108.6719 45384400
## 2019-03-20 110.31 110.88 108.05 109.99 108.6620 35588700
## 2019-03-21 110.10 110.15 108.37 108.66 107.3481 27438900
## 2019-03-22 108.33 109.00 107.51 108.23 106.9233 24133800
## 2019-03-25 108.49 109.07 107.32 107.79 106.4886 18187500
## 2019-03-26 108.40 110.34 108.27 110.14 108.8102 16693100
## 2019-03-27 110.45 111.09 109.73 110.28 108.9485 10794800
## 2019-03-28 110.60 111.27 110.24 110.71 109.3733 11748900
## 2019-03-29 111.56 111.60 110.39 111.03 109.6895 16358800
## 2019-04-01 111.59 112.87 111.38 112.51 111.1516 10785100
## 2019-04-02 113.15 113.31 111.92 111.96 110.6082 9231800
## 2019-04-03 112.70 113.11 112.21 112.52 111.1615 10534900
## 2019-04-04 113.24 114.86 113.03 114.75 113.3645 14378400
## 2019-04-05 114.97 115.13 114.31 115.00 113.6115 10907900
## 2019-04-08 115.00 115.83 114.64 114.96 113.5720 11054200
## 2019-04-09 115.61 117.16 115.28 116.86 115.4491 17340300
## 2019-04-10 117.58 118.03 116.28 117.16 115.7455 14091100
## 2019-04-11 117.73 117.86 116.32 116.60 115.1922 12784500
## 2019-04-12 127.91 130.90 126.36 130.06 128.4897 65253500
## 2019-04-15 131.05 132.70 129.79 132.04 130.4458 32773700
## 2019-04-16 131.75 132.13 129.56 129.90 128.3316 14564300
## 2019-04-17 129.81 132.36 129.28 131.75 130.1593 14253700
## 2019-04-18 131.77 132.87 131.11 132.45 130.8508 11890600
## 2019-04-22 131.90 132.20 131.03 131.68 130.0901 10197500
## 2019-04-23 133.39 134.24 132.65 133.36 131.7499 12159300
## 2019-04-24 133.11 135.75 132.72 135.10 133.4689 11449500
## 2019-04-25 135.36 138.88 134.84 137.24 135.5830 16382500
## 2019-04-26 138.70 140.04 137.51 139.92 138.2307 14167600
## 2019-04-29 142.19 142.37 137.61 139.30 137.6181 25746100
## 2019-04-30 139.12 139.39 136.03 136.97 135.3163 15253100
## 2019-05-01 137.49 138.17 136.24 136.38 134.7334 8906700
## 2019-05-02 135.38 135.69 132.38 134.14 132.5204 16580400
## 2019-05-03 135.22 135.31 133.78 134.33 132.7081 8874400
## 2019-05-06 132.54 135.33 132.30 135.00 133.3701 9955600
## 2019-05-07 135.35 135.97 132.76 133.44 131.8289 10972700
## 2019-05-08 133.50 135.70 133.31 134.99 133.3602 15423500
## 2019-05-09 135.03 136.48 132.84 133.59 131.9771 15297100
## 2019-05-10 133.01 134.32 131.23 134.04 132.4216 9858500
## 2019-05-13 131.50 132.66 130.55 131.34 129.7542 11389900
## 2019-05-14 133.52 134.66 132.05 133.20 131.5918 12001700
## 2019-05-15 132.55 135.21 132.04 134.68 133.0539 9734100
## 2019-05-16 135.29 136.40 134.81 135.50 133.8640 9689400
## 2019-05-17 134.26 135.98 134.03 135.04 133.4096 8964200
## 2019-05-20 134.25 134.40 133.25 133.91 132.2932 8009000
## 2019-05-21 134.57 134.57 133.11 134.09 132.4710 7050300
## 2019-05-22 133.82 134.17 133.39 133.85 132.2339 5093700
## 2019-05-23 132.71 133.55 131.95 132.73 131.1275 6743300
## 2019-05-24 133.10 133.29 132.22 132.79 131.1867 4570100
## 2019-05-28 133.21 134.04 132.59 132.62 131.0188 8938400
## 2019-05-29 131.96 132.15 130.78 131.57 129.9815 7749600
## 2019-05-30 131.88 132.68 131.34 132.20 130.6039 5274000
## 2019-05-31 130.96 132.93 130.78 132.04 130.4458 7420700
## 2019-06-03 132.02 132.95 131.49 132.47 130.8706 7901400
## 2019-06-04 133.45 134.88 132.92 134.82 133.1922 8247500
## 2019-06-05 135.41 136.00 134.94 135.94 134.2987 6842800
## 2019-06-06 136.51 137.44 135.73 137.21 135.5534 6027300
## 2019-06-07 137.60 138.76 137.33 138.04 136.3733 7026300
## 2019-06-10 138.88 138.88 136.07 137.07 135.4151 8479500
## 2019-06-11 137.59 137.75 134.94 135.08 133.4491 6352200
## 2019-06-12 135.09 136.28 134.82 135.72 134.0814 5537000
## 2019-06-13 137.95 141.85 137.61 141.74 140.0287 17939500
## 2019-06-14 142.05 142.95 140.53 141.65 139.9398 11125200
## 2019-06-17 140.81 141.48 139.11 140.97 139.2680 8542700
## 2019-06-18 141.99 143.51 138.97 139.24 137.5589 11231400
## 2019-06-19 139.51 141.07 138.58 140.92 139.2186 6877100
## 2019-06-20 141.98 142.23 139.91 142.02 140.3053 8485800
## 2019-06-21 141.95 142.00 140.00 140.23 138.5369 14150000
## 2019-06-24 140.12 140.47 137.80 139.22 137.5391 10497400
## 2019-06-25 139.02 140.41 138.67 139.94 138.2504 14675400
## 2019-06-26 140.36 140.74 139.51 140.40 138.7048 8842100
## 2019-06-27 141.00 141.74 138.92 139.30 137.6181 6466300
## 2019-06-28 139.41 140.21 138.61 139.64 137.9540 20078800
## 2019-07-01 140.45 141.95 139.22 141.65 139.9398 8972400
## 2019-07-02 141.40 142.86 141.27 142.53 140.8091 7554100
## 2019-07-03 142.70 143.00 142.00 142.98 141.2537 4150900
## 2019-07-05 141.42 142.89 140.70 142.45 141.6016 5596000
## 2019-07-08 142.18 142.23 140.97 141.02 140.1801 4993900
## 2019-07-09 140.06 141.72 139.75 141.61 140.7666 7396300
## 2019-07-10 142.40 144.25 142.01 143.54 142.6851 9533700
## 2019-07-11 144.01 145.34 143.54 143.56 142.7050 10471100
## 2019-07-12 144.15 145.43 144.00 144.88 144.0172 8510000
## 2019-07-15 145.13 145.36 143.97 145.06 144.1961 5289200
## 2019-07-16 144.75 144.99 143.81 144.30 143.4406 5854700
## 2019-07-17 144.60 144.68 142.37 142.57 141.7209 5296400
## 2019-07-18 142.46 142.46 140.17 141.63 140.7865 8031700
## 2019-07-19 142.24 142.24 139.74 139.85 139.0171 6109900
## 2019-07-22 141.25 141.44 140.01 140.84 140.0012 7706400
## 2019-07-23 141.65 142.54 140.27 141.26 140.4187 7514500
## 2019-07-24 141.40 141.59 140.40 141.29 140.4485 5896600
## 2019-07-25 141.40 143.23 141.04 143.21 142.3571 7294400
## 2019-07-26 143.74 145.19 143.05 144.65 143.7885 8139400
## 2019-07-29 145.59 147.15 145.17 146.39 145.5182 11674100
## 2019-07-30 145.76 146.80 144.61 144.93 144.0668 6563100
## 2019-07-31 144.99 145.00 142.34 143.01 142.1583 9710700
## 2019-08-01 143.34 144.53 141.26 141.85 141.0052 8911700
## 2019-08-02 140.99 142.22 139.94 141.71 140.8660 6539100
## 2019-08-05 139.14 140.23 137.03 138.30 137.4763 10669700
## 2019-08-06 140.41 141.95 138.37 141.87 141.0251 18818900
## 2019-08-07 134.93 135.87 132.26 134.86 134.0568 29084500
## 2019-08-08 137.90 138.00 136.01 137.89 137.0688 14054800
## 2019-08-09 137.10 139.24 136.76 138.52 137.6950 8811900
## 2019-08-12 137.31 137.57 135.23 135.75 134.9415 7918900
## 2019-08-13 135.00 137.92 135.00 137.01 136.1940 8145400
## 2019-08-14 135.06 135.15 132.68 132.85 132.0588 11797700
## 2019-08-15 133.50 134.28 132.47 133.41 132.6155 7590100
## 2019-08-16 134.02 135.50 133.83 135.20 134.3948 6353800
## 2019-08-19 136.79 137.62 134.28 135.29 134.4843 11741800
## 2019-08-20 133.33 136.04 133.26 135.13 134.3252 8628000
## 2019-08-21 134.61 136.06 134.05 135.76 134.9515 6325000
## 2019-08-22 136.20 136.67 134.69 136.08 135.2696 6967100
## 2019-08-23 135.51 136.44 131.02 131.67 130.8858 10190900
## 2019-08-26 134.19 134.64 132.55 134.61 133.8083 8093800
## 2019-08-27 135.77 135.99 134.19 134.49 133.6890 6013600
## 2019-08-28 134.06 136.73 133.52 136.55 135.7368 5950500
## 2019-08-29 138.12 138.68 137.42 137.84 137.0191 6532700
## 2019-08-30 138.29 138.50 136.76 137.26 136.4425 5622200
## 2019-09-03 136.37 136.42 135.06 136.31 135.4982 5997400
## 2019-09-04 136.74 138.20 136.39 137.89 137.0688 4285400
## 2019-09-05 138.92 139.27 138.32 138.84 138.0131 5143500
## 2019-09-06 139.13 139.81 138.25 139.55 138.7189 4090000
## 2019-09-09 139.58 140.08 138.48 138.83 138.0032 5458700
## 2019-09-10 138.12 138.44 134.58 135.79 134.9813 10974600
## 2019-09-11 135.56 136.24 134.93 136.19 135.3789 7896400
## 2019-09-12 136.84 138.67 136.54 137.50 136.6811 7333900
## 2019-09-13 137.85 138.22 137.11 138.02 137.1980 5209100
## 2019-09-16 136.29 137.24 135.30 135.80 134.9912 6329300
## 2019-09-17 135.80 136.73 135.67 136.31 135.4982 4726500
## 2019-09-18 136.41 137.07 135.72 136.80 135.9853 6857900
## 2019-09-19 137.00 137.36 133.00 133.30 132.5061 12216100
## 2019-09-20 133.03 133.23 131.61 132.27 131.4823 25231600
## 2019-09-23 131.99 132.89 131.89 132.46 131.6711 6096100
## 2019-09-24 134.01 134.15 131.50 131.97 131.1840 11904000
## 2019-09-25 131.79 133.42 131.22 133.09 132.2974 6523000
## 2019-09-26 133.14 133.30 129.06 131.27 130.4882 11615100
## 2019-09-27 130.10 131.00 128.92 129.96 129.1860 8401300
## 2019-09-30 130.35 130.86 129.82 130.32 129.5439 5532500
## 2019-10-01 130.80 131.78 129.51 129.55 128.7785 5978500
## 2019-10-02 128.51 129.22 127.57 129.14 128.3709 8296100
## 2019-10-03 128.60 129.43 127.54 128.15 127.3868 8498700
## 2019-10-04 128.69 130.44 128.61 130.27 129.4942 6732900
## 2019-10-07 130.27 131.57 129.04 130.90 130.1204 5784100
## 2019-10-08 129.90 130.04 128.37 128.47 127.7049 6526000
## 2019-10-09 129.10 129.85 128.06 129.33 128.5598 5004600
## 2019-10-10 129.22 130.14 128.88 129.34 128.5697 4512000
## 2019-10-11 130.30 130.99 129.84 130.02 129.2457 6559000
## 2019-10-14 130.13 130.30 129.48 129.70 128.9276 3710300
## 2019-10-15 130.01 130.89 129.40 129.76 128.9872 5914700
## 2019-10-16 129.76 131.83 129.70 130.86 130.0807 7610800
## 2019-10-17 132.53 133.44 130.51 132.37 131.5816 8005100
## 2019-10-18 132.37 133.16 130.89 130.89 130.1105 8694000
## 2019-10-21 131.44 131.73 130.02 130.26 129.4842 6257100
## 2019-10-22 133.15 133.68 132.10 132.40 131.6115 9291600
## 2019-10-23 132.45 132.68 130.76 131.13 130.3490 5970800
## 2019-10-24 131.52 131.70 129.63 130.26 129.4842 5746300
## 2019-10-25 130.50 131.76 130.03 130.90 130.1204 6696000
## 2019-10-28 131.45 132.08 130.14 130.53 129.7526 8940300
## 2019-10-29 130.50 130.77 129.44 129.48 128.7089 9305100
## 2019-10-30 129.69 130.31 129.15 129.60 128.8282 10880000
## 2019-10-31 129.53 130.15 128.75 129.92 129.1463 9628300
## 2019-11-01 130.99 132.80 130.51 132.75 131.9594 8507600
## 2019-11-04 134.12 134.14 132.47 132.92 132.1284 7631800
## 2019-11-05 132.77 132.77 130.89 131.45 130.6671 7404500
## 2019-11-06 131.60 131.66 130.66 131.27 130.4882 9132500
## 2019-11-07 132.35 133.70 131.75 132.96 132.1682 18047600
## 2019-11-08 140.22 140.25 136.74 137.96 137.1384 24175900
## 2019-11-11 137.50 138.56 136.21 136.74 135.9256 10138400
## 2019-11-12 138.03 139.34 136.74 138.58 137.7547 17284000
## 2019-11-13 138.58 149.92 136.84 148.72 147.8343 45725400
## 2019-11-14 148.00 150.63 146.28 147.15 146.2736 28393600
## 2019-11-15 147.14 147.20 144.21 144.67 143.8084 13733400
## 2019-11-18 144.75 149.04 143.69 147.65 146.7707 15353100
## 2019-11-19 148.18 149.48 146.80 148.38 147.4963 11504300
## 2019-11-20 148.09 148.99 146.03 146.93 146.0549 9448400
## 2019-11-21 147.16 147.47 146.26 146.90 146.0251 6241400
## 2019-11-22 147.21 149.44 146.68 148.29 147.4068 9639400
## 2019-11-25 148.80 150.21 147.70 149.69 148.7985 11316800
## 2019-11-26 151.75 153.41 150.61 151.64 150.7369 24949900
## 2019-11-27 152.30 152.57 151.15 151.48 150.5779 6155400
## 2019-11-29 151.48 152.47 151.01 151.58 150.6773 6284900
## 2019-12-02 152.94 152.97 149.10 150.62 149.7230 10351000
## 2019-12-03 147.74 149.11 146.87 148.58 147.6951 9273800
## 2019-12-04 149.30 149.33 148.18 148.28 147.3969 7684800
## 2019-12-05 148.69 148.83 147.10 147.44 146.5619 7363300
## 2019-12-06 148.40 148.61 147.18 147.66 146.7806 7084900
## 2019-12-09 147.96 148.51 145.40 146.21 145.3392 11515000
## 2019-12-10 145.26 146.85 145.05 146.10 145.2299 7084100
## 2019-12-11 147.39 147.89 146.76 147.59 146.7110 8253700
## 2019-12-12 147.92 148.93 147.25 147.76 146.8800 7748300
## 2019-12-13 147.43 147.80 146.31 146.38 146.3800 9350100
## 2019-12-16 147.59 148.65 146.55 148.46 148.4600 9134400
## 2019-12-17 148.10 148.46 147.62 147.73 147.7300 8776100
## 2019-12-18 147.77 147.95 146.19 146.26 146.2600 9467800
## 2019-12-19 146.18 146.80 145.32 146.15 146.1500 10243900
## 2019-12-20 147.15 147.88 145.77 146.88 146.8800 12629900
## 2019-12-23 145.91 146.33 144.33 144.68 144.6800 9314000
## 2019-12-24 144.58 145.43 144.45 145.29 145.2900 3508500
## 2019-12-26 145.40 145.86 145.17 145.70 145.7000 4422000
## 2019-12-27 146.05 146.51 145.45 145.75 145.7500 5495300
## 2019-12-30 145.75 145.87 143.40 143.77 143.7700 6602800
## 2019-12-31 143.67 144.77 143.26 144.63 144.6300 5662900
#Obtenemos la columna que es de nuestro interés, la cual será de DIS.close
Novocure <- NVCRdata[,4]
length(Novocure)
## [1] 252
#Convertimos en una serie temporal
tsNovoCure <- ts(Novocure, start = c(2019,1),frequency=365)
#Graficamos
plot(tsNovoCure)
#Se calculan las diferencias de la serie de datos con logaritmo
l_NovoCure<-diff(log(tsNovoCure))
plot(l_NovoCure)
#Calculo parámetros iniciales manera 1
Delta <- 1/365
alpha <- mean(l_NovoCure)/Delta
sigma <- sqrt(var(l_NovoCure)/Delta)
mu <- alpha +0.5*sigma^2
x0<-tsNovoCure[1]
#Calculo parámetros iniciales manera 2
x <- tsNovoCure
gBm <- setModel(drift="mu*x", diffusion="sigma*x", xinit=x0)
## Warning in yuima.warn("Solution variable (lhs) not specified. Trying to use state variables."):
## YUIMA: Solution variable (lhs) not specified. Trying to use state variables.
mod <- setYuima(model=gBm, data=setData(tsNovoCure, delta=Delta))
set.seed(123)
fit <- qmle(mod, start=list(mu=0, sigma=1),
lower=list(mu=0.1, sigma=0.1),
upper=list(mu=100, sigma=10))
summary(fit)
## Quasi-Maximum likelihood estimation
##
## Call:
## qmle(yuima = mod, start = list(mu = 0, sigma = 1), lower = list(mu = 0.1,
## sigma = 0.1), upper = list(mu = 100, sigma = 10))
##
## Coefficients:
## Estimate Std. Error
## sigma 0.2727174 0.01223059
## mu 0.4480226 0.32886867
##
## -2 log L: 1021.129
#comparación
coef(fit)
## sigma mu
## 0.2727174 0.4480226
sigma
## DIS.close
## DIS.close 0.2677428
mu
## DIS.close
## DIS.close 0.4475313
#Sigma 0.2727174 0.4480226
#Sigma 0.2677428
#mu 0.4475313
gbm_vec <- function(nsim = 10000, t = 25, mu = 0, sigma = 0.1, S0 = 100, dt = 1./365) {
# matrix of random draws - one for each day for each simulation
epsilon <- matrix(rnorm(t*nsim), ncol = nsim, nrow = t)
# get GBM and convert to price paths
gbm <- exp((mu - sigma * sigma / 2) * dt + sigma * epsilon * sqrt(dt))
gbm <- apply(rbind(rep(S0, nsim), gbm), 2, cumprod)
return(gbm)
}
gBm
##
## Diffusion process
## Number of equations: 1
## Number of Wiener noises: 1
## Parametric model with 2 parameters
valores_simulados <- simulate(gBm, true.parameter = list(mu=mu, sigma=sigma))
## Warning in yuima.warn("'delta' (re)defined."):
## YUIMA: 'delta' (re)defined.
plot(valores_simulados)
#PROBAR CON FORMA 1 Y FORMA 2
nsim <- 1000
t <- 365
mu <- 0.4475313
sigma <- 0.2677428
S0 <- 108.97
dt = 1/365
gbm <- gbm_vec(nsim, t, mu, sigma, S0, dt)
gbm_df <- as.data.frame(gbm) %>%
mutate(ix = 1:nrow(gbm)) %>%
pivot_longer(-ix, names_to = 'sim', values_to = 'price')
gbm_df %>%
ggplot(aes(x=ix, y=price, color=sim)) +
geom_line() +
theme(legend.position = 'none')
data.frame(price = gbm[259, ]) %>%
ggplot(aes(x = price)) +
geom_histogram(aes(y = ..density..), binwidth = 0.1) +
geom_density() +
ggtitle('terminal price distribution')
D <- gbm[259, ] %>%
density()
D$x[which.max(D$y)]
## [1] 147.6409