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Fourier Analysis of TVIX (VelocityShares Daily 2x VIX ST ETN)


TVIX (VelocityShares Daily 2x VIX ST ETN) appears to have interesting cyclic behaviour every 35 weeks (42948.12*sine), 25 weeks (31584.4*sine), and 32 weeks (26953.28*sine).

TVIX (VelocityShares Daily 2x VIX ST ETN) has an average price of 287,259.4 (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 7/17/2017 for TVIX (VelocityShares Daily 2x VIX ST ETN), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0287,259.4   0 
1297,011.3 377,530.4 (1*2π)/347347 weeks
2-40,861.29 287,062.2 (2*2π)/347174 weeks
3-70,602.97 73,806.52 (3*2π)/347116 weeks
427,068.7 31,596.03 (4*2π)/34787 weeks
536,860.04 82,166.83 (5*2π)/34769 weeks
6-11,422.72 77,601.29 (6*2π)/34758 weeks
7-16,226.5 34,818.7 (7*2π)/34750 weeks
811,023.67 24,979.34 (8*2π)/34743 weeks
914,695.88 40,187.24 (9*2π)/34739 weeks
10381.1651 42,948.12 (10*2π)/34735 weeks
11-8,117.069 26,953.28 (11*2π)/34732 weeks
124,640.588 15,976.36 (12*2π)/34729 weeks
1312,452.46 26,268.59 (13*2π)/34727 weeks
141,216.612 31,584.4 (14*2π)/34725 weeks
15-5,544.104 18,745.77 (15*2π)/34723 weeks
165,465.801 12,716.11 (16*2π)/34722 weeks
178,823.9 20,933.35 (17*2π)/34720 weeks
18933.7529 22,837.85 (18*2π)/34719 weeks
19-1,874.059 14,633.13 (19*2π)/34718 weeks
204,687.768 11,364.91 (20*2π)/34717 weeks
216,708.979 17,269.28 (21*2π)/34717 weeks
22548.4415 17,039.09 (22*2π)/34716 weeks
231,071.613 11,479.36 (23*2π)/34715 weeks
244,371.035 12,292.53 (24*2π)/34714 weeks
253,419.387 12,862.34 (25*2π)/34714 weeks
263,044.977 13,029.52 (26*2π)/34713 weeks
271,490.199 11,586.45 (27*2π)/34713 weeks
283,238.555 9,680.072 (28*2π)/34712 weeks
294,163.026 11,688.46 (29*2π)/34712 weeks
301,298.908 10,658.34 (30*2π)/34712 weeks
313,643.208 8,797.015 (31*2π)/34711 weeks
323,628.77 10,970.51 (32*2π)/34711 weeks
331,141.909 9,514.552 (33*2π)/34711 weeks
343,174.643 7,159.72 (34*2π)/34710 weeks
354,923.863 9,510.251 (35*2π)/34710 weeks
361,914.544 10,802.24 (36*2π)/34710 weeks
37208.6325 6,613.384 (37*2π)/3479 weeks
385,468.487 5,499.554 (38*2π)/3479 weeks
394,980.622 11,154.52 (39*2π)/3479 weeks
40-1,114.901 8,964.601 (40*2π)/3479 weeks
412,641.849 3,126.144 (41*2π)/3478 weeks
426,734.575 8,146.129 (42*2π)/3478 weeks
431,405.425 10,009.2 (43*2π)/3478 weeks
44590.3382 5,144.918 (44*2π)/3478 weeks
454,518.22 5,146.299 (45*2π)/3478 weeks
464,081.585 7,877.77 (46*2π)/3478 weeks
471,467.423 7,222.523 (47*2π)/3477 weeks
482,619.904 5,001.198 (48*2π)/3477 weeks
493,576.226 6,176.419 (49*2π)/3477 weeks
502,681.814 6,043.43 (50*2π)/3477 weeks
513,234.674 5,770.126 (51*2π)/3477 weeks
522,603.063 6,279.117 (52*2π)/3477 weeks
532,118.341 5,018.53 (53*2π)/3477 weeks
543,766.197 4,467.253 (54*2π)/3476 weeks
553,699.362 6,744.953 (55*2π)/3476 weeks
561,179.067 5,586.807 (56*2π)/3476 weeks
572,793.317 3,221.164 (57*2π)/3476 weeks
584,859.133 5,306.209 (58*2π)/3476 weeks
592,020.661 6,878.046 (59*2π)/3476 weeks
601,160.481 3,343.507 (60*2π)/3476 weeks
614,665.045 3,396.252 (61*2π)/3476 weeks
623,684.558 6,528.341 (62*2π)/3476 weeks
63932.5698 4,912.82 (63*2π)/3476 weeks
642,680.559 2,394.709 (64*2π)/3475 weeks
655,103.354 4,545.735 (65*2π)/3475 weeks
661,996.955 6,360.391 (66*2π)/3475 weeks
671,281.372 2,794.895 (67*2π)/3475 weeks
684,211.46 2,979.587 (68*2π)/3475 weeks
693,697.188 5,252.748 (69*2π)/3475 weeks
701,867.355 4,508.06 (70*2π)/3475 weeks
712,210.398 3,050.732 (71*2π)/3475 weeks
723,662.809 2,963.152 (72*2π)/3475 weeks
733,709.039 4,618.221 (73*2π)/3475 weeks
742,047.862 4,385.368 (74*2π)/3475 weeks
752,047.289 2,747.517 (75*2π)/3475 weeks
763,595.607 2,615.519 (76*2π)/3475 weeks
774,097.828 4,199.268 (77*2π)/3475 weeks
781,797.537 4,822.261 (78*2π)/3474 weeks
791,545.246 1,760.14 (79*2π)/3474 weeks
804,574.87 2,234.395 (80*2π)/3474 weeks
813,726.728 4,965.383 (81*2π)/3474 weeks
821,109.056 3,751.354 (82*2π)/3474 weeks
832,413.957 1,395.267 (83*2π)/3474 weeks
844,571.04 2,685.864 (84*2π)/3474 weeks
852,975.052 4,484.343 (85*2π)/3474 weeks
861,668.874 3,085.912 (86*2π)/3474 weeks
872,589.949 1,737.406 (87*2π)/3474 weeks
883,978.572 2,349.931 (88*2π)/3474 weeks
893,436.5 4,017.634 (89*2π)/3474 weeks
901,488.053 3,220.168 (90*2π)/3474 weeks
912,551.653 1,275.892 (91*2π)/3474 weeks
924,239.915 2,268.888 (92*2π)/3474 weeks
933,097.343 3,965.912 (93*2π)/3474 weeks
941,623.7 2,734.262 (94*2π)/3474 weeks
952,609.994 1,156.031 (95*2π)/3474 weeks
964,319.336 2,247.571 (96*2π)/3474 weeks
972,881.933 3,890.415 (97*2π)/3474 weeks
981,426.497 2,122.327 (98*2π)/3474 weeks
993,324.676 1,000.572 (99*2π)/3474 weeks
1003,961.019 2,793.022 (100*2π)/3473 weeks
1012,324.585 3,180.198 (101*2π)/3473 weeks
1022,009.581 1,488.881 (102*2π)/3473 weeks
1033,788.346 1,509.359 (103*2π)/3473 weeks
1043,069.904 3,039.672 (104*2π)/3473 weeks
1052,143.296 1,911.077 (105*2π)/3473 weeks
1063,210.511 1,467.885 (106*2π)/3473 weeks
1073,241.817 2,543.306 (107*2π)/3473 weeks
1082,148.615 1,933.97 (108*2π)/3473 weeks
1093,296.82 1,259.389 (109*2π)/3473 weeks
1103,306.719 2,514.513 (110*2π)/3473 weeks
1112,095.189 1,985.251 (111*2π)/3473 weeks
1123,001.871 1,055.695 (112*2π)/3473 weeks
1133,524.135 2,040.335 (113*2π)/3473 weeks
1142,415.036 2,251.392 (114*2π)/3473 weeks
1152,619.511 1,055.674 (115*2π)/3473 weeks
1163,477.188 1,731.779 (116*2π)/3473 weeks
1172,544.182 2,061.08 (117*2π)/3473 weeks
1182,675.539 1,029.943 (118*2π)/3473 weeks
1193,527.579 1,653.986 (119*2π)/3473 weeks
1202,503.445 2,135.866 (120*2π)/3473 weeks
1212,316.429 858.3865 (121*2π)/3473 weeks
1223,731.313 1,030.578 (122*2π)/3473 weeks
1233,149.3 2,433.169 (123*2π)/3473 weeks
1241,711.189 1,427.513 (124*2π)/3473 weeks
1253,121.67 101.839 (125*2π)/3473 weeks
1264,045.076 1,924.566 (126*2π)/3473 weeks
1272,086.936 2,169.355 (127*2π)/3473 weeks
1282,266.999 440.1382 (128*2π)/3473 weeks
1293,608.66 866.5911 (129*2π)/3473 weeks
1303,159.065 1,655.747 (130*2π)/3473 weeks
1312,523.465 1,580.027 (131*2π)/3473 weeks
1322,442.775 767.6144 (132*2π)/3473 weeks
1333,225.518 628.9453 (133*2π)/3473 weeks
1343,386.4 1,492.198 (134*2π)/3473 weeks
1352,457.301 1,430.798 (135*2π)/3473 weeks
1362,496.901 744.6179 (136*2π)/3473 weeks
1373,152.291 479.8512 (137*2π)/3473 weeks
1383,419.886 1,273.055 (138*2π)/3473 weeks
1392,516.689 1,528.228 (139*2π)/3472 weeks
1402,309.575 419.0152 (140*2π)/3472 weeks
1413,391.324 359.4597 (141*2π)/3472 weeks
1423,398.034 1,414.938 (142*2π)/3472 weeks
1432,185.981 1,261.555 (143*2π)/3472 weeks
1442,584.446 8.68402 (144*2π)/3472 weeks
1453,711.3 688.8285 (145*2π)/3472 weeks
1462,695.11 1,425.828 (146*2π)/3472 weeks
1472,395.851 415.8856 (147*2π)/3472 weeks
1483,243.497 374.7863 (148*2π)/3472 weeks
1492,903.961 1,003.995 (149*2π)/3472 weeks
1502,734.964 424.334 (150*2π)/3472 weeks
1513,116.735 714.5692 (151*2π)/3472 weeks
1522,549.243 730.4503 (152*2π)/3472 weeks
1532,906.796 18.84573 (153*2π)/3472 weeks
1543,417.112 793.1923 (154*2π)/3472 weeks
1552,426.797 1,013.4 (155*2π)/3472 weeks
1562,442.96 -298.2215 (156*2π)/3472 weeks
1573,808.166 276.5138 (157*2π)/3472 weeks
1582,817.2 1,407.599 (158*2π)/3472 weeks
1591,782.594 22.8252 (159*2π)/3472 weeks
1603,654.17 -643.2928 (160*2π)/3472 weeks
1613,598.448 1,292.567 (161*2π)/3472 weeks
1621,816.061 845.6664 (162*2π)/3472 weeks
1632,499.163 -887.2245 (163*2π)/3472 weeks
1644,172.857 55.81394 (164*2π)/3472 weeks
1652,811.55 1,560.51 (165*2π)/3472 weeks
1661,593.614 -142.0362 (166*2π)/3472 weeks
1673,375.609 -983.9517 (167*2π)/3472 weeks
1683,957.745 789.5851 (168*2π)/3472 weeks
1692,103.49 1,004.5 (169*2π)/3472 weeks
1702,185.127 -709.1776 (170*2π)/3472 weeks
1713,606.666 -460.5212 (171*2π)/3472 weeks
1723,373.992 644.2357 (172*2π)/3472 weeks
1732,336.45 514.2403 (173*2π)/3472 weeks
1742,336.45 -514.2403 (174*2π)/3472 weeks
1753,373.992 -644.2357 (175*2π)/3472 weeks
1763,606.666 460.5212 (176*2π)/3472 weeks
1772,185.127 709.1776 (177*2π)/3472 weeks
1782,103.49 -1,004.5 (178*2π)/3472 weeks
1793,957.745 -789.5851 (179*2π)/3472 weeks
1803,375.609 983.9517 (180*2π)/3472 weeks
1811,593.614 142.0362 (181*2π)/3472 weeks
1822,811.55 -1,560.51 (182*2π)/3472 weeks
1834,172.857 -55.81394 (183*2π)/3472 weeks
1842,499.163 887.2245 (184*2π)/3472 weeks
1851,816.061 -845.6664 (185*2π)/3472 weeks
1863,598.448 -1,292.567 (186*2π)/3472 weeks
1873,654.17 643.2928 (187*2π)/3472 weeks
1881,782.594 -22.8252 (188*2π)/3472 weeks
1892,817.2 -1,407.599 (189*2π)/3472 weeks
1903,808.166 -276.5138 (190*2π)/3472 weeks
1912,442.96 298.2215 (191*2π)/3472 weeks
1922,426.797 -1,013.4 (192*2π)/3472 weeks
1933,417.112 -793.1923 (193*2π)/3472 weeks
1942,906.796 -18.84573 (194*2π)/3472 weeks
1952,549.243 -730.4503 (195*2π)/3472 weeks
1963,116.735 -714.5692 (196*2π)/3472 weeks
1972,734.964 -424.334 (197*2π)/3472 weeks
1982,903.961 -1,003.995 (198*2π)/3472 weeks
1993,243.497 -374.7863 (199*2π)/3472 weeks
2002,395.851 -415.8856 (200*2π)/3472 weeks
2012,695.11 -1,425.828 (201*2π)/3472 weeks
2023,711.3 -688.8285 (202*2π)/3472 weeks
2032,584.446 -8.68402 (203*2π)/3472 weeks
2042,185.981 -1,261.555 (204*2π)/3472 weeks
2053,398.034 -1,414.938 (205*2π)/3472 weeks
2063,391.324 -359.4597 (206*2π)/3472 weeks
2072,309.575 -419.0152 (207*2π)/3472 weeks
2082,516.689 -1,528.228 (208*2π)/3472 weeks
2093,419.886 -1,273.055 (209*2π)/3472 weeks
2103,152.291 -479.8512 (210*2π)/3472 weeks
2112,496.901 -744.6179 (211*2π)/3472 weeks
2122,457.301 -1,430.798 (212*2π)/3472 weeks
2133,386.4 -1,492.198 (213*2π)/3472 weeks
2143,225.518 -628.9453 (214*2π)/3472 weeks
2152,442.775 -767.6144 (215*2π)/3472 weeks
2162,523.465 -1,580.027 (216*2π)/3472 weeks
2173,159.065 -1,655.747 (217*2π)/3472 weeks
2183,608.66 -866.5911 (218*2π)/3472 weeks
2192,266.999 -440.1382 (219*2π)/3472 weeks
2202,086.936 -2,169.355 (220*2π)/3472 weeks
2214,045.076 -1,924.566 (221*2π)/3472 weeks
2223,121.67 -101.839 (222*2π)/3472 weeks
2231,711.189 -1,427.513 (223*2π)/3472 weeks
2243,149.3 -2,433.169 (224*2π)/3472 weeks
2253,731.313 -1,030.578 (225*2π)/3472 weeks
2262,316.429 -858.3865 (226*2π)/3472 weeks
2272,503.445 -2,135.866 (227*2π)/3472 weeks
2283,527.579 -1,653.986 (228*2π)/3472 weeks
2292,675.539 -1,029.943 (229*2π)/3472 weeks
2302,544.182 -2,061.08 (230*2π)/3472 weeks
2313,477.188 -1,731.779 (231*2π)/3472 weeks
2322,619.511 -1,055.674 (232*2π)/3471 weeks
2332,415.036 -2,251.392 (233*2π)/3471 weeks
2343,524.135 -2,040.335 (234*2π)/3471 weeks
2353,001.871 -1,055.695 (235*2π)/3471 weeks
2362,095.189 -1,985.251 (236*2π)/3471 weeks
2373,306.719 -2,514.513 (237*2π)/3471 weeks
2383,296.82 -1,259.389 (238*2π)/3471 weeks
2392,148.615 -1,933.97 (239*2π)/3471 weeks
2403,241.817 -2,543.306 (240*2π)/3471 weeks
2413,210.511 -1,467.885 (241*2π)/3471 weeks
2422,143.296 -1,911.077 (242*2π)/3471 weeks
2433,069.904 -3,039.672 (243*2π)/3471 weeks
2443,788.346 -1,509.359 (244*2π)/3471 weeks
2452,009.581 -1,488.881 (245*2π)/3471 weeks
2462,324.585 -3,180.198 (246*2π)/3471 weeks
2473,961.019 -2,793.022 (247*2π)/3471 weeks
2483,324.676 -1,000.572 (248*2π)/3471 weeks
2491,426.497 -2,122.327 (249*2π)/3471 weeks
2502,881.933 -3,890.415 (250*2π)/3471 weeks
2514,319.336 -2,247.571 (251*2π)/3471 weeks
2522,609.994 -1,156.031 (252*2π)/3471 weeks
2531,623.7 -2,734.262 (253*2π)/3471 weeks
2543,097.343 -3,965.912 (254*2π)/3471 weeks
2554,239.915 -2,268.888 (255*2π)/3471 weeks
2562,551.653 -1,275.892 (256*2π)/3471 weeks
2571,488.053 -3,220.168 (257*2π)/3471 weeks
2583,436.5 -4,017.634 (258*2π)/3471 weeks
2593,978.572 -2,349.931 (259*2π)/3471 weeks
2602,589.949 -1,737.406 (260*2π)/3471 weeks
2611,668.874 -3,085.912 (261*2π)/3471 weeks
2622,975.052 -4,484.343 (262*2π)/3471 weeks
2634,571.04 -2,685.864 (263*2π)/3471 weeks
2642,413.957 -1,395.267 (264*2π)/3471 weeks
2651,109.056 -3,751.354 (265*2π)/3471 weeks
2663,726.728 -4,965.383 (266*2π)/3471 weeks
2674,574.87 -2,234.395 (267*2π)/3471 weeks
2681,545.246 -1,760.14 (268*2π)/3471 weeks
2691,797.537 -4,822.261 (269*2π)/3471 weeks
2704,097.828 -4,199.268 (270*2π)/3471 weeks
2713,595.607 -2,615.519 (271*2π)/3471 weeks
2722,047.289 -2,747.517 (272*2π)/3471 weeks
2732,047.862 -4,385.368 (273*2π)/3471 weeks
2743,709.039 -4,618.221 (274*2π)/3471 weeks
2753,662.809 -2,963.152 (275*2π)/3471 weeks
2762,210.398 -3,050.732 (276*2π)/3471 weeks
2771,867.355 -4,508.06 (277*2π)/3471 weeks
2783,697.188 -5,252.748 (278*2π)/3471 weeks
2794,211.46 -2,979.587 (279*2π)/3471 weeks
2801,281.372 -2,794.895 (280*2π)/3471 weeks
2811,996.955 -6,360.391 (281*2π)/3471 weeks
2825,103.354 -4,545.735 (282*2π)/3471 weeks
2832,680.559 -2,394.709 (283*2π)/3471 weeks
284932.5698 -4,912.82 (284*2π)/3471 weeks
2853,684.558 -6,528.341 (285*2π)/3471 weeks
2864,665.045 -3,396.252 (286*2π)/3471 weeks
2871,160.481 -3,343.507 (287*2π)/3471 weeks
2882,020.661 -6,878.046 (288*2π)/3471 weeks
2894,859.133 -5,306.209 (289*2π)/3471 weeks
2902,793.317 -3,221.164 (290*2π)/3471 weeks
2911,179.067 -5,586.807 (291*2π)/3471 weeks
2923,699.362 -6,744.953 (292*2π)/3471 weeks
2933,766.197 -4,467.253 (293*2π)/3471 weeks
2942,118.341 -5,018.53 (294*2π)/3471 weeks
2952,603.063 -6,279.117 (295*2π)/3471 weeks
2963,234.674 -5,770.126 (296*2π)/3471 weeks
2972,681.814 -6,043.43 (297*2π)/3471 weeks
2983,576.226 -6,176.419 (298*2π)/3471 weeks
2992,619.904 -5,001.198 (299*2π)/3471 weeks
3001,467.423 -7,222.523 (300*2π)/3471 weeks
3014,081.585 -7,877.77 (301*2π)/3471 weeks
3024,518.22 -5,146.299 (302*2π)/3471 weeks
303590.3382 -5,144.918 (303*2π)/3471 weeks
3041,405.425 -10,009.2 (304*2π)/3471 weeks
3056,734.575 -8,146.129 (305*2π)/3471 weeks
3062,641.849 -3,126.144 (306*2π)/3471 weeks
307-1,114.901 -8,964.601 (307*2π)/3471 weeks
3084,980.622 -11,154.52 (308*2π)/3471 weeks
3095,468.487 -5,499.554 (309*2π)/3471 weeks
310208.6325 -6,613.384 (310*2π)/3471 weeks
3111,914.544 -10,802.24 (311*2π)/3471 weeks
3124,923.863 -9,510.251 (312*2π)/3471 weeks
3133,174.643 -7,159.72 (313*2π)/3471 weeks
3141,141.909 -9,514.552 (314*2π)/3471 weeks
3153,628.77 -10,970.51 (315*2π)/3471 weeks
3163,643.208 -8,797.015 (316*2π)/3471 weeks
3171,298.908 -10,658.34 (317*2π)/3471 weeks
3184,163.026 -11,688.46 (318*2π)/3471 weeks
3193,238.555 -9,680.072 (319*2π)/3471 weeks
3201,490.199 -11,586.45 (320*2π)/3471 weeks
3213,044.977 -13,029.52 (321*2π)/3471 weeks
3223,419.387 -12,862.34 (322*2π)/3471 weeks
3234,371.035 -12,292.53 (323*2π)/3471 weeks
3241,071.613 -11,479.36 (324*2π)/3471 weeks
325548.4415 -17,039.09 (325*2π)/3471 weeks
3266,708.979 -17,269.28 (326*2π)/3471 weeks
3274,687.768 -11,364.91 (327*2π)/3471 weeks
328-1,874.059 -14,633.13 (328*2π)/3471 weeks
329933.7529 -22,837.85 (329*2π)/3471 weeks
3308,823.9 -20,933.35 (330*2π)/3471 weeks
3315,465.801 -12,716.11 (331*2π)/3471 weeks
332-5,544.104 -18,745.77 (332*2π)/3471 weeks
3331,216.612 -31,584.4 (333*2π)/3471 weeks
33412,452.46 -26,268.59 (334*2π)/3471 weeks
3354,640.588 -15,976.36 (335*2π)/3471 weeks
336-8,117.069 -26,953.28 (336*2π)/3471 weeks
337381.1651 -42,948.12 (337*2π)/3471 weeks
33814,695.88 -40,187.24 (338*2π)/3471 weeks
33911,023.67 -24,979.34 (339*2π)/3471 weeks
340-16,226.5 -34,818.7 (340*2π)/3471 weeks
341-11,422.72 -77,601.29 (341*2π)/3471 weeks
34236,860.04 -82,166.83 (342*2π)/3471 weeks
34327,068.7 -31,596.03 (343*2π)/3471 weeks
344-70,602.97 -73,806.52 (344*2π)/3471 weeks
345-40,861.29 -287,062.2 (345*2π)/3471 weeks



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