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Fourier Analysis of UVXY (ProShares Trust Ultra VIX Short)


UVXY (ProShares Trust Ultra VIX Short) appears to have interesting cyclic behaviour every 28 weeks (286026*sine), 25 weeks (256312.8*sine), and 7 weeks (82714.95*cosine).

UVXY (ProShares Trust Ultra VIX Short) has an average price of 409,628.7 (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 10/4/2011 to 1/17/2017 for UVXY (ProShares Trust Ultra VIX Short), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0409,628.7   0 
1741,536.9 220,700.6 (1*2π)/277277 weeks
2600,211.2 341,423.9 (2*2π)/277139 weeks
3464,089.6 384,931.2 (3*2π)/27792 weeks
4356,737.3 383,859.5 (4*2π)/27769 weeks
5281,509.7 364,499.8 (5*2π)/27755 weeks
6229,168.9 343,735.8 (6*2π)/27746 weeks
7188,639.7 328,019.6 (7*2π)/27740 weeks
8153,148.3 315,046.1 (8*2π)/27735 weeks
9116,559.6 304,255.9 (9*2π)/27731 weeks
1077,147.99 286,026 (10*2π)/27728 weeks
1144,027.66 256,312.8 (11*2π)/27725 weeks
1224,752.79 220,453.2 (12*2π)/27723 weeks
1319,913.29 189,351.8 (13*2π)/27721 weeks
1421,886.89 167,409 (14*2π)/27720 weeks
1525,063.83 154,745.7 (15*2π)/27718 weeks
1624,163.29 148,570.1 (16*2π)/27717 weeks
1716,789.61 143,230.7 (17*2π)/27716 weeks
185,759.751 134,482.7 (18*2π)/27715 weeks
19-6,439.605 120,120.1 (19*2π)/27715 weeks
20-15,357.71 98,104.27 (20*2π)/27714 weeks
21-13,550.43 72,768.1 (21*2π)/27713 weeks
22-2,518.925 52,466.51 (22*2π)/27713 weeks
2312,889.8 40,021.57 (23*2π)/27712 weeks
2428,969.92 35,583.36 (24*2π)/27712 weeks
2540,764.96 39,525.82 (25*2π)/27711 weeks
2644,288.81 45,388.77 (26*2π)/27711 weeks
2742,430.42 47,405.17 (27*2π)/27710 weeks
2840,327.64 44,666.59 (28*2π)/27710 weeks
2941,081.25 39,517.23 (29*2π)/27710 weeks
3045,346.23 35,899.04 (30*2π)/2779 weeks
3149,049.61 35,463.41 (31*2π)/2779 weeks
3250,609.6 35,334.97 (32*2π)/2779 weeks
3352,268.28 34,016.01 (33*2π)/2778 weeks
3454,359.48 34,151.16 (34*2π)/2778 weeks
3553,967.32 34,147.77 (35*2π)/2778 weeks
3653,064.31 30,941.85 (36*2π)/2778 weeks
3755,742.09 25,602.15 (37*2π)/2777 weeks
3862,750.96 21,617.35 (38*2π)/2777 weeks
3972,285.44 22,830.26 (39*2π)/2777 weeks
4079,563.37 29,276.4 (40*2π)/2777 weeks
4182,714.95 37,929.18 (41*2π)/2777 weeks
4281,917.99 46,914.93 (42*2π)/2777 weeks
4377,337.27 54,471.01 (43*2π)/2776 weeks
4469,834.24 58,973.18 (44*2π)/2776 weeks
4562,132.26 58,508.09 (45*2π)/2776 weeks
4657,640.9 55,015.14 (46*2π)/2776 weeks
4756,941.86 51,906.13 (47*2π)/2776 weeks
4857,577.7 51,666.29 (48*2π)/2776 weeks
4956,762.32 53,051.68 (49*2π)/2776 weeks
5054,749.52 54,243.36 (50*2π)/2776 weeks
5152,171.08 55,192.6 (51*2π)/2775 weeks
5249,110.03 55,771.08 (52*2π)/2775 weeks
5344,908.7 56,343.67 (53*2π)/2775 weeks
5439,185.25 54,384.09 (54*2π)/2775 weeks
5535,300.41 49,500.74 (55*2π)/2775 weeks
5634,581.66 44,056.16 (56*2π)/2775 weeks
5736,029.23 40,002.47 (57*2π)/2775 weeks
5838,727 37,960.55 (58*2π)/2775 weeks
5941,027.3 38,481.21 (59*2π)/2775 weeks
6041,757.19 40,480.75 (60*2π)/2775 weeks
6140,413.14 42,990.86 (61*2π)/2775 weeks
6236,561.95 44,695.64 (62*2π)/2774 weeks
6331,881.88 43,642.18 (63*2π)/2774 weeks
6428,256.84 41,272.18 (64*2π)/2774 weeks
6525,003.23 38,231.58 (65*2π)/2774 weeks
6621,972.29 34,049.01 (66*2π)/2774 weeks
6720,208.5 28,448.33 (67*2π)/2774 weeks
6820,718.35 22,129.86 (68*2π)/2774 weeks
6923,415.14 16,964.6 (69*2π)/2774 weeks
7027,236.16 13,264.8 (70*2π)/2774 weeks
7131,748.06 11,251.04 (71*2π)/2774 weeks
7235,899.75 11,397.59 (72*2π)/2774 weeks
7338,532.31 12,534.5 (73*2π)/2774 weeks
7440,063.66 13,732.76 (74*2π)/2774 weeks
7541,227 14,671.78 (75*2π)/2774 weeks
7641,996.14 15,669.9 (76*2π)/2774 weeks
7742,553.93 16,880.05 (77*2π)/2774 weeks
7842,213.31 18,374.2 (78*2π)/2774 weeks
7940,785.36 19,044.68 (79*2π)/2774 weeks
8039,561.09 18,314.83 (80*2π)/2773 weeks
8139,295.84 17,073.46 (81*2π)/2773 weeks
8240,072.99 16,165.45 (82*2π)/2773 weeks
8340,819.27 16,413.14 (83*2π)/2773 weeks
8440,794.98 16,466.72 (84*2π)/2773 weeks
8541,209.21 16,128.03 (85*2π)/2773 weeks
8642,428.49 16,284.85 (86*2π)/2773 weeks
8743,373.5 18,049.68 (87*2π)/2773 weeks
8842,649.57 20,105.21 (88*2π)/2773 weeks
8941,204.41 21,250.44 (89*2π)/2773 weeks
9039,959.61 22,101.04 (90*2π)/2773 weeks
9138,455.04 23,181.82 (91*2π)/2773 weeks
9236,026.55 24,224.57 (92*2π)/2773 weeks
9333,019.23 24,152.92 (93*2π)/2773 weeks
9430,469.31 23,365.89 (94*2π)/2773 weeks
9528,075.32 22,790.39 (95*2π)/2773 weeks
9624,812.52 22,017.76 (96*2π)/2773 weeks
9720,943.57 19,940.32 (97*2π)/2773 weeks
9817,599.57 16,254.62 (98*2π)/2773 weeks
9915,542.47 11,654.96 (99*2π)/2773 weeks
10014,649.47 7,063.615 (100*2π)/2773 weeks
10114,170.2 2,399.401 (101*2π)/2773 weeks
10214,829.64 -2,937.299 (102*2π)/2773 weeks
10317,300.45 -7,818.699 (103*2π)/2773 weeks
10420,628.53 -11,098.44 (104*2π)/2773 weeks
10523,900.1 -13,268.05 (105*2π)/2773 weeks
10626,637.09 -14,464.11 (106*2π)/2773 weeks
10728,503.7 -15,473.27 (107*2π)/2773 weeks
10829,875.57 -17,306.9 (108*2π)/2773 weeks
10932,006.58 -19,801.45 (109*2π)/2773 weeks
11035,324.32 -22,427.29 (110*2π)/2773 weeks
11140,046 -24,056.87 (111*2π)/2772 weeks
11245,288.34 -23,623.37 (112*2π)/2772 weeks
11349,405.86 -21,313.37 (113*2π)/2772 weeks
11451,534.94 -18,284.81 (114*2π)/2772 weeks
11551,973.66 -16,257.12 (115*2π)/2772 weeks
11652,319.93 -15,757.59 (116*2π)/2772 weeks
11753,447.54 -15,890.82 (117*2π)/2772 weeks
11855,561.13 -16,274.84 (118*2π)/2772 weeks
11959,022.92 -16,022.47 (119*2π)/2772 weeks
12063,547.23 -13,646.79 (120*2π)/2772 weeks
12166,756.16 -8,218.98 (121*2π)/2772 weeks
12266,531.47 -1,548.059 (122*2π)/2772 weeks
12363,051.48 3,767.11 (123*2π)/2772 weeks
12457,766.23 6,440.091 (124*2π)/2772 weeks
12552,375.04 6,182.584 (125*2π)/2772 weeks
12648,124.25 3,112.999 (126*2π)/2772 weeks
12746,732.58 -1,677.539 (127*2π)/2772 weeks
12849,019.48 -5,972.516 (128*2π)/2772 weeks
12953,251.75 -6,843.948 (129*2π)/2772 weeks
13056,151.61 -4,485.153 (130*2π)/2772 weeks
13155,905.95 -1,173.901 (131*2π)/2772 weeks
13253,111.62 110.6575 (132*2π)/2772 weeks
13350,615.8 -1,672.52 (133*2π)/2772 weeks
13450,428.84 -5,041.746 (134*2π)/2772 weeks
13552,910.86 -7,884.012 (135*2π)/2772 weeks
13657,011.66 -8,843.79 (136*2π)/2772 weeks
13761,572.58 -7,199.958 (137*2π)/2772 weeks
13864,666.21 -2,779.788 (138*2π)/2772 weeks
13964,666.21 2,779.788 (139*2π)/2772 weeks
14061,572.58 7,199.958 (140*2π)/2772 weeks
14157,011.66 8,843.79 (141*2π)/2772 weeks
14252,910.86 7,884.012 (142*2π)/2772 weeks
14350,428.84 5,041.746 (143*2π)/2772 weeks
14450,615.8 1,672.52 (144*2π)/2772 weeks
14553,111.62 -110.6575 (145*2π)/2772 weeks
14655,905.95 1,173.901 (146*2π)/2772 weeks
14756,151.61 4,485.153 (147*2π)/2772 weeks
14853,251.75 6,843.948 (148*2π)/2772 weeks
14949,019.48 5,972.516 (149*2π)/2772 weeks
15046,732.58 1,677.539 (150*2π)/2772 weeks
15148,124.25 -3,112.999 (151*2π)/2772 weeks
15252,375.04 -6,182.584 (152*2π)/2772 weeks
15357,766.23 -6,440.091 (153*2π)/2772 weeks
15463,051.48 -3,767.11 (154*2π)/2772 weeks
15566,531.47 1,548.059 (155*2π)/2772 weeks
15666,756.16 8,218.98 (156*2π)/2772 weeks
15763,547.23 13,646.79 (157*2π)/2772 weeks
15859,022.92 16,022.47 (158*2π)/2772 weeks
15955,561.13 16,274.84 (159*2π)/2772 weeks
16053,447.54 15,890.82 (160*2π)/2772 weeks
16152,319.93 15,757.59 (161*2π)/2772 weeks
16251,973.66 16,257.12 (162*2π)/2772 weeks
16351,534.94 18,284.81 (163*2π)/2772 weeks
16449,405.86 21,313.37 (164*2π)/2772 weeks
16545,288.34 23,623.37 (165*2π)/2772 weeks
16640,046 24,056.87 (166*2π)/2772 weeks
16735,324.32 22,427.29 (167*2π)/2772 weeks
16832,006.58 19,801.45 (168*2π)/2772 weeks
16929,875.57 17,306.9 (169*2π)/2772 weeks
17028,503.7 15,473.27 (170*2π)/2772 weeks
17126,637.09 14,464.11 (171*2π)/2772 weeks
17223,900.1 13,268.05 (172*2π)/2772 weeks
17320,628.53 11,098.44 (173*2π)/2772 weeks
17417,300.45 7,818.699 (174*2π)/2772 weeks
17514,829.64 2,937.299 (175*2π)/2772 weeks
17614,170.2 -2,399.401 (176*2π)/2772 weeks
17714,649.47 -7,063.615 (177*2π)/2772 weeks
17815,542.47 -11,654.96 (178*2π)/2772 weeks
17917,599.57 -16,254.62 (179*2π)/2772 weeks
18020,943.57 -19,940.32 (180*2π)/2772 weeks
18124,812.52 -22,017.76 (181*2π)/2772 weeks
18228,075.32 -22,790.39 (182*2π)/2772 weeks
18330,469.31 -23,365.89 (183*2π)/2772 weeks
18433,019.23 -24,152.92 (184*2π)/2772 weeks
18536,026.55 -24,224.57 (185*2π)/2771 weeks
18638,455.04 -23,181.82 (186*2π)/2771 weeks
18739,959.61 -22,101.04 (187*2π)/2771 weeks
18841,204.41 -21,250.44 (188*2π)/2771 weeks
18942,649.57 -20,105.21 (189*2π)/2771 weeks
19043,373.5 -18,049.68 (190*2π)/2771 weeks
19142,428.49 -16,284.85 (191*2π)/2771 weeks
19241,209.21 -16,128.03 (192*2π)/2771 weeks
19340,794.98 -16,466.72 (193*2π)/2771 weeks
19440,819.27 -16,413.14 (194*2π)/2771 weeks
19540,072.99 -16,165.45 (195*2π)/2771 weeks
19639,295.84 -17,073.46 (196*2π)/2771 weeks
19739,561.09 -18,314.83 (197*2π)/2771 weeks
19840,785.36 -19,044.68 (198*2π)/2771 weeks
19942,213.31 -18,374.2 (199*2π)/2771 weeks
20042,553.93 -16,880.05 (200*2π)/2771 weeks
20141,996.14 -15,669.9 (201*2π)/2771 weeks
20241,227 -14,671.78 (202*2π)/2771 weeks
20340,063.66 -13,732.76 (203*2π)/2771 weeks
20438,532.31 -12,534.5 (204*2π)/2771 weeks
20535,899.75 -11,397.59 (205*2π)/2771 weeks
20631,748.06 -11,251.04 (206*2π)/2771 weeks
20727,236.16 -13,264.8 (207*2π)/2771 weeks
20823,415.14 -16,964.6 (208*2π)/2771 weeks
20920,718.35 -22,129.86 (209*2π)/2771 weeks
21020,208.5 -28,448.33 (210*2π)/2771 weeks
21121,972.29 -34,049.01 (211*2π)/2771 weeks
21225,003.23 -38,231.58 (212*2π)/2771 weeks
21328,256.84 -41,272.18 (213*2π)/2771 weeks
21431,881.88 -43,642.18 (214*2π)/2771 weeks
21536,561.95 -44,695.64 (215*2π)/2771 weeks
21640,413.14 -42,990.86 (216*2π)/2771 weeks
21741,757.19 -40,480.75 (217*2π)/2771 weeks
21841,027.3 -38,481.21 (218*2π)/2771 weeks
21938,727 -37,960.55 (219*2π)/2771 weeks
22036,029.23 -40,002.47 (220*2π)/2771 weeks
22134,581.66 -44,056.16 (221*2π)/2771 weeks
22235,300.41 -49,500.74 (222*2π)/2771 weeks
22339,185.25 -54,384.09 (223*2π)/2771 weeks
22444,908.7 -56,343.67 (224*2π)/2771 weeks
22549,110.03 -55,771.08 (225*2π)/2771 weeks
22652,171.08 -55,192.6 (226*2π)/2771 weeks
22754,749.52 -54,243.36 (227*2π)/2771 weeks
22856,762.32 -53,051.68 (228*2π)/2771 weeks
22957,577.7 -51,666.29 (229*2π)/2771 weeks
23056,941.86 -51,906.13 (230*2π)/2771 weeks
23157,640.9 -55,015.14 (231*2π)/2771 weeks
23262,132.26 -58,508.09 (232*2π)/2771 weeks
23369,834.24 -58,973.18 (233*2π)/2771 weeks
23477,337.27 -54,471.01 (234*2π)/2771 weeks
23581,917.99 -46,914.93 (235*2π)/2771 weeks
23682,714.95 -37,929.18 (236*2π)/2771 weeks
23779,563.37 -29,276.4 (237*2π)/2771 weeks
23872,285.44 -22,830.26 (238*2π)/2771 weeks
23962,750.96 -21,617.35 (239*2π)/2771 weeks
24055,742.09 -25,602.15 (240*2π)/2771 weeks
24153,064.31 -30,941.85 (241*2π)/2771 weeks
24253,967.32 -34,147.77 (242*2π)/2771 weeks
24354,359.48 -34,151.16 (243*2π)/2771 weeks
24452,268.28 -34,016.01 (244*2π)/2771 weeks
24550,609.6 -35,334.97 (245*2π)/2771 weeks
24649,049.61 -35,463.41 (246*2π)/2771 weeks
24745,346.23 -35,899.04 (247*2π)/2771 weeks
24841,081.25 -39,517.23 (248*2π)/2771 weeks
24940,327.64 -44,666.59 (249*2π)/2771 weeks
25042,430.42 -47,405.17 (250*2π)/2771 weeks
25144,288.81 -45,388.77 (251*2π)/2771 weeks
25240,764.96 -39,525.82 (252*2π)/2771 weeks
25328,969.92 -35,583.36 (253*2π)/2771 weeks
25412,889.8 -40,021.57 (254*2π)/2771 weeks
255-2,518.925 -52,466.51 (255*2π)/2771 weeks
256-13,550.43 -72,768.1 (256*2π)/2771 weeks
257-15,357.71 -98,104.27 (257*2π)/2771 weeks
258-6,439.605 -120,120.1 (258*2π)/2771 weeks
2595,759.751 -134,482.7 (259*2π)/2771 weeks
26016,789.61 -143,230.7 (260*2π)/2771 weeks
26124,163.29 -148,570.1 (261*2π)/2771 weeks
26225,063.83 -154,745.7 (262*2π)/2771 weeks
26321,886.89 -167,409 (263*2π)/2771 weeks
26419,913.29 -189,351.8 (264*2π)/2771 weeks
26524,752.79 -220,453.2 (265*2π)/2771 weeks
26644,027.66 -256,312.8 (266*2π)/2771 weeks
26777,147.99 -286,026 (267*2π)/2771 weeks
268116,559.6 -304,255.9 (268*2π)/2771 weeks
269153,148.3 -315,046.1 (269*2π)/2771 weeks
270188,639.7 -328,019.6 (270*2π)/2771 weeks
271229,168.9 -343,735.8 (271*2π)/2771 weeks
272281,509.7 -364,499.8 (272*2π)/2771 weeks
273356,737.3 -383,859.5 (273*2π)/2771 weeks
274464,089.6 -384,931.2 (274*2π)/2771 weeks
275600,211.2 -341,423.9 (275*2π)/2771 weeks

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