Calculates the sigma scaling of the chain, and optionally plots the result.
calc_sigma_scaling(chain, plot = FALSE)Arguments
- chain
Vector of n length, where n is the number of trials or sampler iterations
- plot
Boolean. Whether to additionally plot the result.
Value
A list containing the vector of possible lags, the sd of the distances at each lag, their log10 counterparts, and the calculated intercept and slope.
Details
Sigma scaling is defined as the slope of the regression connecting log time lags and the standard deviation of value changes across time lags. Markets show values of 0.5.
Examples
set.seed(1)
chain1 <- sampler_mh(1, "norm", c(0,1), diag(1))
calc_sigma_scaling(chain1[[1]], plot = TRUE)
#> $lag
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
#> [19] 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
#> [37] 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
#> [55] 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72
#> [73] 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90
#> [91] 91 92 93 94 95 96 97 98 99 100 101 102
#>
#> $log_lag
#> [1] 0.0000000 0.3010300 0.4771213 0.6020600 0.6989700 0.7781513 0.8450980
#> [8] 0.9030900 0.9542425 1.0000000 1.0413927 1.0791812 1.1139434 1.1461280
#> [15] 1.1760913 1.2041200 1.2304489 1.2552725 1.2787536 1.3010300 1.3222193
#> [22] 1.3424227 1.3617278 1.3802112 1.3979400 1.4149733 1.4313638 1.4471580
#> [29] 1.4623980 1.4771213 1.4913617 1.5051500 1.5185139 1.5314789 1.5440680
#> [36] 1.5563025 1.5682017 1.5797836 1.5910646 1.6020600 1.6127839 1.6232493
#> [43] 1.6334685 1.6434527 1.6532125 1.6627578 1.6720979 1.6812412 1.6901961
#> [50] 1.6989700 1.7075702 1.7160033 1.7242759 1.7323938 1.7403627 1.7481880
#> [57] 1.7558749 1.7634280 1.7708520 1.7781513 1.7853298 1.7923917 1.7993405
#> [64] 1.8061800 1.8129134 1.8195439 1.8260748 1.8325089 1.8388491 1.8450980
#> [71] 1.8512583 1.8573325 1.8633229 1.8692317 1.8750613 1.8808136 1.8864907
#> [78] 1.8920946 1.8976271 1.9030900 1.9084850 1.9138139 1.9190781 1.9242793
#> [85] 1.9294189 1.9344985 1.9395193 1.9444827 1.9493900 1.9542425 1.9590414
#> [92] 1.9637878 1.9684829 1.9731279 1.9777236 1.9822712 1.9867717 1.9912261
#> [99] 1.9956352 2.0000000 2.0043214 2.0086002
#>
#> $sds
#> [1] 0.6554206 0.8710101 1.0034985 1.0960127 1.1611904 1.2049326 1.2345926
#> [8] 1.2595104 1.2708884 1.2669402 1.2742124 1.2834349 1.2885459 1.2800990
#> [15] 1.2812005 1.2898789 1.3049639 1.3189057 1.3222918 1.3357071 1.3343457
#> [22] 1.3233383 1.3081025 1.2886969 1.2883123 1.3034216 1.3252610 1.3175539
#> [29] 1.3092352 1.3001075 1.2856377 1.2780053 1.2676980 1.2528074 1.2547195
#> [36] 1.2857501 1.3102554 1.3237884 1.3461923 1.3697272 1.3894854 1.4087657
#> [43] 1.4140893 1.4080247 1.3902201 1.3822379 1.3871251 1.3843969 1.3807283
#> [50] 1.3975809 1.4106889 1.3969380 1.3793140 1.3618938 1.3494642 1.3317206
#> [57] 1.3257360 1.3304557 1.3284470 1.3248134 1.3465174 1.3648130 1.3731731
#> [64] 1.3813399 1.3887305 1.4074104 1.4092117 1.3949106 1.3785142 1.3713388
#> [71] 1.3842391 1.3986769 1.4043774 1.4047372 1.4261118 1.4445472 1.4442605
#> [78] 1.4562652 1.4732892 1.4809510 1.4795165 1.4825966 1.4697102 1.4489517
#> [85] 1.4395264 1.4443550 1.4339104 1.4222052 1.4209442 1.4279155 1.4270024
#> [92] 1.4427819 1.4421180 1.4364234 1.4426135 1.4429096 1.4425540 1.4512988
#> [99] 1.4525725 1.4543142 1.4518143 1.4363062
#>
#> $log_sds
#> [1] -0.183479915 -0.059976800 0.001516722 0.039815604 0.064903449
#> [6] 0.080962772 0.091523673 0.100201744 0.104107408 0.102756105
#> [11] 0.105241825 0.108373848 0.110099903 0.107243551 0.107617116
#> [16] 0.110548934 0.115598486 0.120213759 0.121327292 0.125711251
#> [21] 0.125268354 0.121670869 0.116641790 0.110150777 0.110021141
#> [26] 0.115084914 0.122301425 0.119768403 0.117017660 0.113979270
#> [31] 0.109118588 0.106532666 0.103015822 0.097884298 0.098546660
#> [36] 0.109156550 0.117355944 0.121818577 0.129107101 0.136634076
#> [41] 0.142853998 0.148838764 0.150476821 0.148610278 0.143083577
#> [46] 0.140582807 0.142115624 0.141260627 0.140108241 0.145376960
#> [51] 0.149431258 0.145177118 0.139663136 0.134143255 0.130161381
#> [56] 0.124413122 0.122457048 0.124000404 0.123344225 0.122154721
#> [61] 0.129211956 0.135073166 0.137725298 0.140300559 0.142617967
#> [66] 0.148420743 0.148976255 0.144546379 0.139411251 0.137144778
#> [71] 0.141211097 0.145717414 0.147483839 0.147595079 0.154153559
#> [76] 0.159731729 0.159645522 0.163240470 0.168288006 0.170540681
#> [81] 0.170119812 0.171023010 0.167231709 0.161053908 0.158219620
#> [86] 0.159673945 0.156522009 0.152962251 0.152577019 0.154702519
#> [91] 0.154424711 0.159200679 0.159000786 0.157282484 0.159149989
#> [96] 0.159239109 0.159132082 0.161756847 0.162137824 0.162658242
#> [101] 0.161911084 0.157247040
#>
#> $intercept
#> [1] -0.02822949
#>
#> $slope
#> [1] 0.09810482
#>