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Fourier Analysis of TVIX (VelocityShares Daily 2X VIX Short-Term ETN)


TVIX (VelocityShares Daily 2X VIX Short-Term ETN) appears to have interesting cyclic behaviour every 36 weeks (42518.8*sine), 33 weeks (33565.15*sine), and 28 weeks (11160.89*cosine).

TVIX (VelocityShares Daily 2X VIX Short-Term ETN) has an average price of 276,886.7 (topmost row, frequency = 0).



Click on the checkboxes shown on the right to see how the various frequencies contribute to the graph. Look for large magnitude coefficients (sine or cosine), as these are associated with frequencies which contribute most to the associated stock plot. If you find a large magnitude coefficient which dramatically changes the graph, look at the associated "Period" in weeks, as you may have found a significant recurring cycle for the stock of interest.

Right click on the graph above to see the menu of operations (download, full screen, etc.)

Fourier Analysis

Using data from 11/30/2010 to 10/16/2017 for TVIX (VelocityShares Daily 2X VIX Short-Term ETN), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0276,886.7   0 
1301,056.2 359,181.6 (1*2π)/360360 weeks
2-25,382.04 292,497 (2*2π)/360180 weeks
3-76,215.94 87,050.46 (3*2π)/360120 weeks
415,464.31 26,440.24 (4*2π)/36090 weeks
541,337.13 71,817.8 (5*2π)/36072 weeks
6-2,628.855 81,828.48 (6*2π)/36060 weeks
7-19,436.18 42,899.36 (7*2π)/36051 weeks
83,753.807 22,118.87 (8*2π)/36045 weeks
916,084.74 34,439.59 (9*2π)/36040 weeks
106,046.518 42,518.8 (10*2π)/36036 weeks
11-7,082.025 33,565.15 (11*2π)/36033 weeks
12-2,373.581 17,354.63 (12*2π)/36030 weeks
1311,160.89 19,195.04 (13*2π)/36028 weeks
147,876.314 30,003.91 (14*2π)/36026 weeks
15-4,220.37 26,333.07 (15*2π)/36024 weeks
16-1,647.002 13,159.02 (16*2π)/36023 weeks
178,395.971 14,746.51 (17*2π)/36021 weeks
186,300.931 22,179.87 (18*2π)/36020 weeks
19-1,235.21 20,122.52 (19*2π)/36019 weeks
20-449.4344 12,233.15 (20*2π)/36018 weeks
216,011.557 11,783.39 (21*2π)/36017 weeks
225,349.806 17,550.44 (22*2π)/36016 weeks
23-27.06223 15,493.5 (23*2π)/36016 weeks
241,632.816 10,739.05 (24*2π)/36015 weeks
254,194.303 12,076.51 (25*2π)/36014 weeks
263,285.526 12,364.13 (26*2π)/36014 weeks
272,898.972 12,565.16 (27*2π)/36013 weeks
281,439.506 11,199.91 (28*2π)/36013 weeks
292,998.11 9,327.477 (29*2π)/36012 weeks
304,147.743 11,060.27 (30*2π)/36012 weeks
311,385.954 10,740.58 (31*2π)/36012 weeks
323,083.812 8,326.809 (32*2π)/36011 weeks
333,879.994 10,241.73 (33*2π)/36011 weeks
341,361.141 9,926.212 (34*2π)/36011 weeks
352,227.339 7,103.328 (35*2π)/36010 weeks
364,781.902 8,183.094 (36*2π)/36010 weeks
373,088.462 10,509.89 (37*2π)/36010 weeks
38.2415 8,360.83 (38*2π)/3609 weeks
392,966.513 4,507.636 (39*2π)/3609 weeks
406,358.402 8,422.617 (40*2π)/3609 weeks
411,348.328 11,115.24 (41*2π)/3609 weeks
42-723.784 5,044.931 (42*2π)/3609 weeks
435,622.947 4,166.274 (43*2π)/3608 weeks
444,737.738 9,860.407 (44*2π)/3608 weeks
4567.64156 8,050.167 (45*2π)/3608 weeks
461,947.453 4,107.162 (46*2π)/3608 weeks
474,697.915 5,885.397 (47*2π)/3608 weeks
483,256.336 7,884.368 (48*2π)/3608 weeks
491,258.337 6,270.518 (49*2π)/3607 weeks
502,950.617 4,880.213 (50*2π)/3607 weeks
513,308.063 6,103.452 (51*2π)/3607 weeks
522,588.697 5,708.949 (52*2π)/3607 weeks
533,144.775 5,623.386 (53*2π)/3607 weeks
542,448.904 6,029.647 (54*2π)/3607 weeks
552,050.476 4,816.55 (55*2π)/3607 weeks
563,586.781 4,282.058 (56*2π)/3606 weeks
573,707.825 6,400.662 (57*2π)/3606 weeks
581,226.326 5,664.01 (58*2π)/3606 weeks
592,290.634 3,205.844 (59*2π)/3606 weeks
604,671.802 4,562.733 (60*2π)/3606 weeks
612,712.562 6,785.358 (61*2π)/3606 weeks
62685.8981 4,085.756 (62*2π)/3606 weeks
633,700.136 2,613.052 (63*2π)/3606 weeks
644,451.114 5,648.077 (64*2π)/3606 weeks
651,431.101 5,780.306 (65*2π)/3606 weeks
661,488.465 2,876.716 (66*2π)/3605 weeks
674,413.457 2,929.446 (67*2π)/3605 weeks
683,760.112 6,102.237 (68*2π)/3605 weeks
69667.1749 4,505.461 (69*2π)/3605 weeks
702,746.916 2,125.6 (70*2π)/3605 weeks
714,336.531 3,953.639 (71*2π)/3605 weeks
722,643.783 5,144.36 (72*2π)/3605 weeks
731,733.681 3,760.766 (73*2π)/3605 weeks
742,543.3 2,695.057 (74*2π)/3605 weeks
753,839.976 3,234.6 (75*2π)/3605 weeks
763,131.239 4,669.483 (76*2π)/3605 weeks
771,790.883 3,926.913 (77*2π)/3605 weeks
782,234.946 2,442.352 (78*2π)/3605 weeks
793,635.32 2,651.332 (79*2π)/3605 weeks
803,831.614 4,263.461 (80*2π)/3605 weeks
811,542.365 4,515.802 (81*2π)/3604 weeks
821,597.086 1,606.512 (82*2π)/3604 weeks
834,414.001 2,161.232 (83*2π)/3604 weeks
843,687.014 4,739.967 (84*2π)/3604 weeks
851,140.627 3,816.804 (85*2π)/3604 weeks
862,054.512 1,442.091 (86*2π)/3604 weeks
874,284.854 2,217.24 (87*2π)/3604 weeks
883,309.361 4,297.259 (88*2π)/3604 weeks
891,677.713 3,340.081 (89*2π)/3604 weeks
902,114.82 1,851.688 (90*2π)/3604 weeks
913,548.331 1,922.559 (91*2π)/3604 weeks
923,802.871 3,436.427 (92*2π)/3604 weeks
931,961.056 3,763.305 (93*2π)/3604 weeks
941,671.577 1,686.083 (94*2π)/3604 weeks
953,581.844 1,488.184 (95*2π)/3604 weeks
963,901.538 3,317.025 (96*2π)/3604 weeks
972,003.871 3,476.777 (97*2π)/3604 weeks
981,700.462 1,790.738 (98*2π)/3604 weeks
993,409.959 1,181.931 (99*2π)/3604 weeks
1004,010.312 3,045.017 (100*2π)/3604 weeks
1011,954.731 3,474.174 (101*2π)/3604 weeks
1021,709.847 1,342.904 (102*2π)/3604 weeks
1033,710.105 1,329.041 (103*2π)/3603 weeks
1043,513.009 3,022.62 (104*2π)/3603 weeks
1051,960.916 2,816.297 (105*2π)/3603 weeks
1062,177.711 1,201.498 (106*2π)/3603 weeks
1073,770.6 1,703.757 (107*2π)/3603 weeks
1082,776.271 2,924.167 (108*2π)/3603 weeks
1092,099.343 1,756.818 (109*2π)/3603 weeks
1103,122.42 1,432.214 (110*2π)/3603 weeks
1113,134.043 2,445.149 (111*2π)/3603 weeks
1122,076.251 1,933.396 (112*2π)/3603 weeks
1133,068.561 1,159.171 (113*2π)/3603 weeks
1143,314.679 2,317.813 (114*2π)/3603 weeks
1152,098.079 2,137.129 (115*2π)/3603 weeks
1162,636.961 1,014.687 (116*2π)/3603 weeks
1173,458.315 1,705.84 (117*2π)/3603 weeks
1182,630.461 2,330.797 (118*2π)/3603 weeks
1192,208.482 1,278.144 (119*2π)/3603 weeks
1203,290.908 1,277.946 (120*2π)/3603 weeks
1212,844.778 2,109.273 (121*2π)/3603 weeks
1222,259.306 1,352.658 (122*2π)/3603 weeks
1233,218.134 1,098.396 (123*2π)/3603 weeks
1243,017.24 2,097.452 (124*2π)/3603 weeks
1252,035.251 1,533.542 (125*2π)/3603 weeks
1262,866.195 554.4042 (126*2π)/3603 weeks
1273,687.561 1,646.286 (127*2π)/3603 weeks
1282,348.724 2,325.482 (128*2π)/3603 weeks
1291,803.993 693.1364 (129*2π)/3603 weeks
1303,635.016 377.4566 (130*2π)/3603 weeks
1313,469.912 2,295.741 (131*2π)/3603 weeks
1321,767.753 1,688.865 (132*2π)/3603 weeks
1332,497.795 295.3226 (133*2π)/3603 weeks
1343,502.22 1,041.104 (134*2π)/3603 weeks
1352,971.813 1,611.168 (135*2π)/3603 weeks
1362,377.457 1,475.398 (136*2π)/3603 weeks
1372,385.256 705.8994 (137*2π)/3603 weeks
1383,121.255 613.4621 (138*2π)/3603 weeks
1393,277.123 1,421.979 (139*2π)/3603 weeks
1402,397.481 1,422.069 (140*2π)/3603 weeks
1412,381.326 764.2089 (141*2π)/3603 weeks
1422,929.599 435.09 (142*2π)/3603 weeks
1433,351.342 1,088.208 (143*2π)/3603 weeks
1442,635.695 1,542.519 (144*2π)/3603 weeks
1452,086.337 667.9642 (145*2π)/3602 weeks
1463,014.127 189.8714 (146*2π)/3602 weeks
1473,461.184 1,051.867 (147*2π)/3602 weeks
1482,477.694 1,520.16 (148*2π)/3602 weeks
1492,085.743 364.7179 (149*2π)/3602 weeks
1503,298.337 123.0365 (150*2π)/3602 weeks
1513,206.663 1,341.673 (151*2π)/3602 weeks
1522,204.962 905.1903 (152*2π)/3602 weeks
1532,700.636 175.0047 (153*2π)/3602 weeks
1543,178.427 735.5187 (154*2π)/3602 weeks
1552,546.106 791.4038 (155*2π)/3602 weeks
1562,862.292 377.604 (156*2π)/3602 weeks
1572,866.398 831.0509 (157*2π)/3602 weeks
1582,382.853 478.1842 (158*2π)/3602 weeks
1593,070.805 68.73344 (159*2π)/3602 weeks
1603,148.393 951.1384 (160*2π)/3602 weeks
1612,167.333 813.2726 (161*2π)/3602 weeks
1622,582.182 -399.9692 (162*2π)/3602 weeks
1633,685.781 453.196 (163*2π)/3602 weeks
1642,580.713 1,345.365 (164*2π)/3602 weeks
1651,742.079 -63.41388 (165*2π)/3602 weeks
1663,532.476 -612.2375 (166*2π)/3602 weeks
1673,518.715 1,209.559 (167*2π)/3602 weeks
1681,819.355 931.412 (168*2π)/3602 weeks
1692,221.256 -766.407 (169*2π)/3602 weeks
1703,930.214 -236.43 (170*2π)/3602 weeks
1713,104.373 1,464.744 (171*2π)/3602 weeks
1721,493.204 347.1012 (172*2π)/3602 weeks
1732,764.489 -1,053.13 (173*2π)/3602 weeks
1743,985.613 202.8156 (174*2π)/3602 weeks
1752,584.45 1,276.444 (175*2π)/3602 weeks
1761,746.089 -166.6323 (176*2π)/3602 weeks
1773,060.713 -814.9243 (177*2π)/3602 weeks
1783,536.615 241.5099 (178*2π)/3602 weeks
1792,685.213 748.5283 (179*2π)/3602 weeks
1802,072.277   (180*2π)/3602 weeks
1812,685.213 -748.5283 (181*2π)/3602 weeks
1823,536.615 -241.5099 (182*2π)/3602 weeks
1833,060.713 814.9243 (183*2π)/3602 weeks
1841,746.089 166.6323 (184*2π)/3602 weeks
1852,584.45 -1,276.444 (185*2π)/3602 weeks
1863,985.613 -202.8156 (186*2π)/3602 weeks
1872,764.489 1,053.13 (187*2π)/3602 weeks
1881,493.204 -347.1012 (188*2π)/3602 weeks
1893,104.373 -1,464.744 (189*2π)/3602 weeks
1903,930.214 236.43 (190*2π)/3602 weeks
1912,221.256 766.407 (191*2π)/3602 weeks
1921,819.355 -931.412 (192*2π)/3602 weeks
1933,518.715 -1,209.559 (193*2π)/3602 weeks
1943,532.476 612.2375 (194*2π)/3602 weeks
1951,742.079 63.41388 (195*2π)/3602 weeks
1962,580.713 -1,345.365 (196*2π)/3602 weeks
1973,685.781 -453.196 (197*2π)/3602 weeks
1982,582.182 399.9692 (198*2π)/3602 weeks
1992,167.333 -813.2726 (199*2π)/3602 weeks
2003,148.393 -951.1384 (200*2π)/3602 weeks
2013,070.805 -68.73344 (201*2π)/3602 weeks
2022,382.853 -478.1842 (202*2π)/3602 weeks
2032,866.398 -831.0509 (203*2π)/3602 weeks
2042,862.292 -377.604 (204*2π)/3602 weeks
2052,546.106 -791.4038 (205*2π)/3602 weeks
2063,178.427 -735.5187 (206*2π)/3602 weeks
2072,700.636 -175.0047 (207*2π)/3602 weeks
2082,204.962 -905.1903 (208*2π)/3602 weeks
2093,206.663 -1,341.673 (209*2π)/3602 weeks
2103,298.337 -123.0365 (210*2π)/3602 weeks
2112,085.743 -364.7179 (211*2π)/3602 weeks
2122,477.694 -1,520.16 (212*2π)/3602 weeks
2133,461.184 -1,051.867 (213*2π)/3602 weeks
2143,014.127 -189.8714 (214*2π)/3602 weeks
2152,086.337 -667.9642 (215*2π)/3602 weeks
2162,635.695 -1,542.519 (216*2π)/3602 weeks
2173,351.342 -1,088.208 (217*2π)/3602 weeks
2182,929.599 -435.09 (218*2π)/3602 weeks
2192,381.326 -764.2089 (219*2π)/3602 weeks
2202,397.481 -1,422.069 (220*2π)/3602 weeks
2213,277.123 -1,421.979 (221*2π)/3602 weeks
2223,121.255 -613.4621 (222*2π)/3602 weeks
2232,385.256 -705.8994 (223*2π)/3602 weeks
2242,377.457 -1,475.398 (224*2π)/3602 weeks
2252,971.813 -1,611.168 (225*2π)/3602 weeks
2263,502.22 -1,041.104 (226*2π)/3602 weeks
2272,497.795 -295.3226 (227*2π)/3602 weeks
2281,767.753 -1,688.865 (228*2π)/3602 weeks
2293,469.912 -2,295.741 (229*2π)/3602 weeks
2303,635.016 -377.4566 (230*2π)/3602 weeks
2311,803.993 -693.1364 (231*2π)/3602 weeks
2322,348.724 -2,325.482 (232*2π)/3602 weeks
2333,687.561 -1,646.286 (233*2π)/3602 weeks
2342,866.195 -554.4042 (234*2π)/3602 weeks
2352,035.251 -1,533.542 (235*2π)/3602 weeks
2363,017.24 -2,097.452 (236*2π)/3602 weeks
2373,218.134 -1,098.396 (237*2π)/3602 weeks
2382,259.306 -1,352.658 (238*2π)/3602 weeks
2392,844.778 -2,109.273 (239*2π)/3602 weeks
2403,290.908 -1,277.946 (240*2π)/3602 weeks
2412,208.482 -1,278.144 (241*2π)/3601 weeks
2422,630.461 -2,330.797 (242*2π)/3601 weeks
2433,458.315 -1,705.84 (243*2π)/3601 weeks
2442,636.961 -1,014.687 (244*2π)/3601 weeks
2452,098.079 -2,137.129 (245*2π)/3601 weeks
2463,314.679 -2,317.813 (246*2π)/3601 weeks
2473,068.561 -1,159.171 (247*2π)/3601 weeks
2482,076.251 -1,933.396 (248*2π)/3601 weeks
2493,134.043 -2,445.149 (249*2π)/3601 weeks
2503,122.42 -1,432.214 (250*2π)/3601 weeks
2512,099.343 -1,756.818 (251*2π)/3601 weeks
2522,776.271 -2,924.167 (252*2π)/3601 weeks
2533,770.6 -1,703.757 (253*2π)/3601 weeks
2542,177.711 -1,201.498 (254*2π)/3601 weeks
2551,960.916 -2,816.297 (255*2π)/3601 weeks
2563,513.009 -3,022.62 (256*2π)/3601 weeks
2573,710.105 -1,329.041 (257*2π)/3601 weeks
2581,709.847 -1,342.904 (258*2π)/3601 weeks
2591,954.731 -3,474.174 (259*2π)/3601 weeks
2604,010.312 -3,045.017 (260*2π)/3601 weeks
2613,409.959 -1,181.931 (261*2π)/3601 weeks
2621,700.462 -1,790.738 (262*2π)/3601 weeks
2632,003.871 -3,476.777 (263*2π)/3601 weeks
2643,901.538 -3,317.025 (264*2π)/3601 weeks
2653,581.844 -1,488.184 (265*2π)/3601 weeks
2661,671.577 -1,686.083 (266*2π)/3601 weeks
2671,961.056 -3,763.305 (267*2π)/3601 weeks
2683,802.871 -3,436.427 (268*2π)/3601 weeks
2693,548.331 -1,922.559 (269*2π)/3601 weeks
2702,114.82 -1,851.688 (270*2π)/3601 weeks
2711,677.713 -3,340.081 (271*2π)/3601 weeks
2723,309.361 -4,297.259 (272*2π)/3601 weeks
2734,284.854 -2,217.24 (273*2π)/3601 weeks
2742,054.512 -1,442.091 (274*2π)/3601 weeks
2751,140.627 -3,816.804 (275*2π)/3601 weeks
2763,687.014 -4,739.967 (276*2π)/3601 weeks
2774,414.001 -2,161.232 (277*2π)/3601 weeks
2781,597.086 -1,606.512 (278*2π)/3601 weeks
2791,542.365 -4,515.802 (279*2π)/3601 weeks
2803,831.614 -4,263.461 (280*2π)/3601 weeks
2813,635.32 -2,651.332 (281*2π)/3601 weeks
2822,234.946 -2,442.352 (282*2π)/3601 weeks
2831,790.883 -3,926.913 (283*2π)/3601 weeks
2843,131.239 -4,669.483 (284*2π)/3601 weeks
2853,839.976 -3,234.6 (285*2π)/3601 weeks
2862,543.3 -2,695.057 (286*2π)/3601 weeks
2871,733.681 -3,760.766 (287*2π)/3601 weeks
2882,643.783 -5,144.36 (288*2π)/3601 weeks
2894,336.531 -3,953.639 (289*2π)/3601 weeks
2902,746.916 -2,125.6 (290*2π)/3601 weeks
291667.1749 -4,505.461 (291*2π)/3601 weeks
2923,760.112 -6,102.237 (292*2π)/3601 weeks
2934,413.457 -2,929.446 (293*2π)/3601 weeks
2941,488.465 -2,876.716 (294*2π)/3601 weeks
2951,431.101 -5,780.306 (295*2π)/3601 weeks
2964,451.114 -5,648.077 (296*2π)/3601 weeks
2973,700.136 -2,613.052 (297*2π)/3601 weeks
298685.8981 -4,085.756 (298*2π)/3601 weeks
2992,712.562 -6,785.358 (299*2π)/3601 weeks
3004,671.802 -4,562.733 (300*2π)/3601 weeks
3012,290.634 -3,205.844 (301*2π)/3601 weeks
3021,226.326 -5,664.01 (302*2π)/3601 weeks
3033,707.825 -6,400.662 (303*2π)/3601 weeks
3043,586.781 -4,282.058 (304*2π)/3601 weeks
3052,050.476 -4,816.55 (305*2π)/3601 weeks
3062,448.904 -6,029.647 (306*2π)/3601 weeks
3073,144.775 -5,623.386 (307*2π)/3601 weeks
3082,588.697 -5,708.949 (308*2π)/3601 weeks
3093,308.063 -6,103.452 (309*2π)/3601 weeks
3102,950.617 -4,880.213 (310*2π)/3601 weeks
3111,258.337 -6,270.518 (311*2π)/3601 weeks
3123,256.336 -7,884.368 (312*2π)/3601 weeks
3134,697.915 -5,885.397 (313*2π)/3601 weeks
3141,947.453 -4,107.162 (314*2π)/3601 weeks
31567.64156 -8,050.167 (315*2π)/3601 weeks
3164,737.738 -9,860.407 (316*2π)/3601 weeks
3175,622.947 -4,166.274 (317*2π)/3601 weeks
318-723.784 -5,044.931 (318*2π)/3601 weeks
3191,348.328 -11,115.24 (319*2π)/3601 weeks
3206,358.402 -8,422.617 (320*2π)/3601 weeks
3212,966.513 -4,507.636 (321*2π)/3601 weeks
322.2415 -8,360.83 (322*2π)/3601 weeks
3233,088.462 -10,509.89 (323*2π)/3601 weeks
3244,781.902 -8,183.094 (324*2π)/3601 weeks
3252,227.339 -7,103.328 (325*2π)/3601 weeks
3261,361.141 -9,926.212 (326*2π)/3601 weeks
3273,879.994 -10,241.73 (327*2π)/3601 weeks
3283,083.812 -8,326.809 (328*2π)/3601 weeks
3291,385.954 -10,740.58 (329*2π)/3601 weeks
3304,147.743 -11,060.27 (330*2π)/3601 weeks
3312,998.11 -9,327.477 (331*2π)/3601 weeks
3321,439.506 -11,199.91 (332*2π)/3601 weeks
3332,898.972 -12,565.16 (333*2π)/3601 weeks
3343,285.526 -12,364.13 (334*2π)/3601 weeks
3354,194.303 -12,076.51 (335*2π)/3601 weeks
3361,632.816 -10,739.05 (336*2π)/3601 weeks
337-27.06223 -15,493.5 (337*2π)/3601 weeks
3385,349.806 -17,550.44 (338*2π)/3601 weeks
3396,011.557 -11,783.39 (339*2π)/3601 weeks
340-449.4344 -12,233.15 (340*2π)/3601 weeks
341-1,235.21 -20,122.52 (341*2π)/3601 weeks
3426,300.931 -22,179.87 (342*2π)/3601 weeks
3438,395.971 -14,746.51 (343*2π)/3601 weeks
344-1,647.002 -13,159.02 (344*2π)/3601 weeks
345-4,220.37 -26,333.07 (345*2π)/3601 weeks
3467,876.314 -30,003.91 (346*2π)/3601 weeks
34711,160.89 -19,195.04 (347*2π)/3601 weeks
348-2,373.581 -17,354.63 (348*2π)/3601 weeks
349-7,082.025 -33,565.15 (349*2π)/3601 weeks
3506,046.518 -42,518.8 (350*2π)/3601 weeks
35116,084.74 -34,439.59 (351*2π)/3601 weeks
3523,753.807 -22,118.87 (352*2π)/3601 weeks
353-19,436.18 -42,899.36 (353*2π)/3601 weeks
354-2,628.855 -81,828.48 (354*2π)/3601 weeks
35541,337.13 -71,817.8 (355*2π)/3601 weeks
35615,464.31 -26,440.24 (356*2π)/3601 weeks
357-76,215.94 -87,050.46 (357*2π)/3601 weeks
358-25,382.04 -292,497 (358*2π)/3601 weeks



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