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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 29 weeks (283837.6*sine), 26 weeks (259172.5*sine), and 29 weeks (86615.67*cosine).

UVXY (ProShares Trust Ultra VIX Short) has an average price of 396,739 (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 3/20/2017 for UVXY (ProShares Trust Ultra VIX Short), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0396,739   0 
1722,048.1 208,552.4 (1*2π)/286286 weeks
2590,201.6 325,882.1 (2*2π)/286143 weeks
3460,903.6 371,157.2 (3*2π)/28695 weeks
4356,869.5 373,379.8 (4*2π)/28672 weeks
5282,380.9 356,243.3 (5*2π)/28657 weeks
6230,210 336,412.8 (6*2π)/28648 weeks
7190,916.8 320,801.7 (7*2π)/28641 weeks
8156,685.2 307,919 (8*2π)/28636 weeks
9123,428 297,968.1 (9*2π)/28632 weeks
1086,615.67 283,837.6 (10*2π)/28629 weeks
1152,513.58 259,172.5 (11*2π)/28626 weeks
1229,031.96 226,745.2 (12*2π)/28624 weeks
1320,054.94 194,710.5 (13*2π)/28622 weeks
1419,930.9 170,401.6 (14*2π)/28620 weeks
1523,095.39 154,580.2 (15*2π)/28619 weeks
1624,521.51 146,333.6 (16*2π)/28618 weeks
1720,706.15 141,843.7 (17*2π)/28617 weeks
1811,983.48 135,570.9 (18*2π)/28616 weeks
19793.0577 125,393.2 (19*2π)/28615 weeks
20-10,241.79 109,368.3 (20*2π)/28614 weeks
21-15,571.7 86,538.46 (21*2π)/28614 weeks
22-10,549.44 63,705.46 (22*2π)/28613 weeks
231,448.067 46,674.95 (23*2π)/28612 weeks
2416,298.39 36,983.78 (24*2π)/28612 weeks
2531,138.16 34,715.74 (25*2π)/28611 weeks
2640,670.12 39,363.67 (26*2π)/28611 weeks
2742,816.05 44,577.25 (27*2π)/28611 weeks
2840,780.65 45,819.59 (28*2π)/28610 weeks
2938,991.48 42,882.86 (29*2π)/28610 weeks
3039,949.73 37,988.5 (30*2π)/28610 weeks
3144,029.07 34,731.44 (31*2π)/2869 weeks
3247,488.71 34,345.89 (32*2π)/2869 weeks
3348,978.34 34,255.5 (33*2π)/2869 weeks
3450,460.2 33,022.32 (34*2π)/2868 weeks
3552,549.48 32,991.1 (35*2π)/2868 weeks
3652,416.39 33,207.21 (36*2π)/2868 weeks
3751,380.19 30,735.75 (37*2π)/2868 weeks
3853,160.76 25,786.66 (38*2π)/2868 weeks
3958,859.09 21,501.91 (39*2π)/2867 weeks
4067,673 21,229.81 (40*2π)/2867 weeks
4175,418.16 26,192.66 (41*2π)/2867 weeks
4279,550.18 33,948.96 (42*2π)/2867 weeks
4380,067.14 42,414.98 (43*2π)/2867 weeks
4476,973.86 50,206.88 (44*2π)/2867 weeks
4570,947.1 55,819.38 (45*2π)/2866 weeks
4663,240.87 57,405.4 (46*2π)/2866 weeks
4757,416.01 55,084.02 (47*2π)/2866 weeks
4855,119.13 51,565.24 (48*2π)/2866 weeks
4955,510.57 49,809.68 (49*2π)/2866 weeks
5055,637.78 50,559.44 (50*2π)/2866 weeks
5154,282.15 51,889.71 (51*2π)/2866 weeks
5252,197.33 52,887.2 (52*2π)/2866 weeks
5349,558.82 53,663.41 (53*2π)/2865 weeks
5446,555.93 54,229.61 (54*2π)/2865 weeks
5542,027.18 54,434.97 (55*2π)/2865 weeks
5636,821.67 51,717.73 (56*2π)/2865 weeks
5733,785.67 46,802.59 (57*2π)/2865 weeks
5833,623.35 41,877.45 (58*2π)/2865 weeks
5935,215.77 38,320.66 (59*2π)/2865 weeks
6037,823.59 36,710.38 (60*2π)/2865 weeks
6139,853.67 37,377.61 (61*2π)/2865 weeks
6240,424.13 39,322.95 (62*2π)/2865 weeks
6339,098.23 41,681.26 (63*2π)/2865 weeks
6435,476.42 43,283.02 (64*2π)/2864 weeks
6531,058.06 42,361.67 (65*2π)/2864 weeks
6627,624.33 40,171.73 (66*2π)/2864 weeks
6724,552.44 37,381.79 (67*2π)/2864 weeks
6821,644.42 33,641.13 (68*2π)/2864 weeks
6919,746.34 28,554.37 (69*2π)/2864 weeks
7019,733.22 22,636.26 (70*2π)/2864 weeks
7121,959.29 17,485.27 (71*2π)/2864 weeks
7225,327.29 13,648.68 (72*2π)/2864 weeks
7329,405.82 11,255.53 (73*2π)/2864 weeks
7433,588.39 10,791.24 (74*2π)/2864 weeks
7536,528.48 11,732.36 (75*2π)/2864 weeks
7638,342.89 12,901.07 (76*2π)/2864 weeks
7739,477.66 13,786.45 (77*2π)/2864 weeks
7840,358.63 14,754.64 (78*2π)/2864 weeks
7941,005.67 15,720.73 (79*2π)/2864 weeks
8041,212 17,064.56 (80*2π)/2864 weeks
8140,345.6 18,261.55 (81*2π)/2864 weeks
8238,896.75 18,268.32 (82*2π)/2863 weeks
8338,101.68 17,295.81 (83*2π)/2863 weeks
8438,222.96 16,123.74 (84*2π)/2863 weeks
8539,148.55 15,633.5 (85*2π)/2863 weeks
8639,547.34 15,994.53 (86*2π)/2863 weeks
8739,554.88 15,864.82 (87*2π)/2863 weeks
8840,110.7 15,565.42 (88*2π)/2863 weeks
8941,372.88 15,987.1 (89*2π)/2863 weeks
9041,993.66 17,851.14 (90*2π)/2863 weeks
9141,125.74 19,682.72 (91*2π)/2863 weeks
9239,775.65 20,661.58 (92*2π)/2863 weeks
9338,609.47 21,473.96 (93*2π)/2863 weeks
9437,169.39 22,501.58 (94*2π)/2863 weeks
9534,862.64 23,468.16 (95*2π)/2863 weeks
9632,038.08 23,404.74 (96*2π)/2863 weeks
9729,626.92 22,671.27 (97*2π)/2863 weeks
9827,411.35 22,109.61 (98*2π)/2863 weeks
9924,439.88 21,460.62 (99*2π)/2863 weeks
10020,833.81 19,716.35 (100*2π)/2863 weeks
10117,547.37 16,466.62 (101*2π)/2863 weeks
10215,354.79 12,243.66 (102*2π)/2863 weeks
10314,333.3 7,889.223 (103*2π)/2863 weeks
10413,806.76 3,632.959 (104*2π)/2863 weeks
10513,983.11 -1,255.692 (105*2π)/2863 weeks
10615,773.72 -6,123.825 (106*2π)/2863 weeks
10718,812.54 -9,743.28 (107*2π)/2863 weeks
10821,890.38 -12,149.11 (108*2π)/2863 weeks
10924,763.36 -13,572.71 (109*2π)/2863 weeks
11026,885.26 -14,511.58 (110*2π)/2863 weeks
11128,240.32 -15,738.29 (111*2π)/2863 weeks
11229,817.38 -17,880.54 (112*2π)/2863 weeks
11332,233.74 -20,342.27 (113*2π)/2863 weeks
11435,964.43 -22,548.11 (114*2π)/2863 weeks
11540,756.64 -23,416.88 (115*2π)/2862 weeks
11645,430.21 -22,251.79 (116*2π)/2862 weeks
11748,745.44 -19,709.58 (117*2π)/2862 weeks
11850,137.78 -16,992.18 (118*2π)/2862 weeks
11950,367.41 -15,497.59 (119*2π)/2862 weeks
12050,862.05 -15,264.03 (120*2π)/2862 weeks
12152,061.22 -15,460.58 (121*2π)/2862 weeks
12254,263.35 -15,788.49 (122*2π)/2862 weeks
12357,700.21 -15,380.04 (123*2π)/2862 weeks
12461,956.33 -12,821.19 (124*2π)/2862 weeks
12564,755.64 -7,540.852 (125*2π)/2862 weeks
12664,364.18 -1,285.386 (126*2π)/2862 weeks
12761,051.77 3,662.662 (127*2π)/2862 weeks
12856,099.3 6,207.021 (128*2π)/2862 weeks
12951,025.03 6,077.443 (129*2π)/2862 weeks
13046,886 3,380.864 (130*2π)/2862 weeks
13145,246.9 -1,026.386 (131*2π)/2862 weeks
13246,919.53 -5,315.334 (132*2π)/2862 weeks
13350,835.69 -6,745.807 (133*2π)/2862 weeks
13454,005.63 -5,012.319 (134*2π)/2862 weeks
13554,513.85 -1,857.411 (135*2π)/2862 weeks
13652,299.46 71.49069 (136*2π)/2862 weeks
13749,582.32 -835.2704 (137*2π)/2862 weeks
13848,588.4 -3,704.439 (138*2π)/2862 weeks
13950,110.31 -6,777.367 (139*2π)/2862 weeks
14053,485.93 -8,459.316 (140*2π)/2862 weeks
14157,737.88 -8,026.805 (141*2π)/2862 weeks
14261,540.26 -4,958.548 (142*2π)/2862 weeks
14363,048.05   (143*2π)/2862 weeks
14461,540.26 4,958.548 (144*2π)/2862 weeks
14557,737.88 8,026.805 (145*2π)/2862 weeks
14653,485.93 8,459.316 (146*2π)/2862 weeks
14750,110.31 6,777.367 (147*2π)/2862 weeks
14848,588.4 3,704.439 (148*2π)/2862 weeks
14949,582.32 835.2704 (149*2π)/2862 weeks
15052,299.46 -71.49069 (150*2π)/2862 weeks
15154,513.85 1,857.411 (151*2π)/2862 weeks
15254,005.63 5,012.319 (152*2π)/2862 weeks
15350,835.69 6,745.807 (153*2π)/2862 weeks
15446,919.53 5,315.334 (154*2π)/2862 weeks
15545,246.9 1,026.386 (155*2π)/2862 weeks
15646,886 -3,380.864 (156*2π)/2862 weeks
15751,025.03 -6,077.443 (157*2π)/2862 weeks
15856,099.3 -6,207.021 (158*2π)/2862 weeks
15961,051.77 -3,662.662 (159*2π)/2862 weeks
16064,364.18 1,285.386 (160*2π)/2862 weeks
16164,755.64 7,540.852 (161*2π)/2862 weeks
16261,956.33 12,821.19 (162*2π)/2862 weeks
16357,700.21 15,380.04 (163*2π)/2862 weeks
16454,263.35 15,788.49 (164*2π)/2862 weeks
16552,061.22 15,460.58 (165*2π)/2862 weeks
16650,862.05 15,264.03 (166*2π)/2862 weeks
16750,367.41 15,497.59 (167*2π)/2862 weeks
16850,137.78 16,992.18 (168*2π)/2862 weeks
16948,745.44 19,709.58 (169*2π)/2862 weeks
17045,430.21 22,251.79 (170*2π)/2862 weeks
17140,756.64 23,416.88 (171*2π)/2862 weeks
17235,964.43 22,548.11 (172*2π)/2862 weeks
17332,233.74 20,342.27 (173*2π)/2862 weeks
17429,817.38 17,880.54 (174*2π)/2862 weeks
17528,240.32 15,738.29 (175*2π)/2862 weeks
17626,885.26 14,511.58 (176*2π)/2862 weeks
17724,763.36 13,572.71 (177*2π)/2862 weeks
17821,890.38 12,149.11 (178*2π)/2862 weeks
17918,812.54 9,743.28 (179*2π)/2862 weeks
18015,773.72 6,123.825 (180*2π)/2862 weeks
18113,983.11 1,255.692 (181*2π)/2862 weeks
18213,806.76 -3,632.959 (182*2π)/2862 weeks
18314,333.3 -7,889.223 (183*2π)/2862 weeks
18415,354.79 -12,243.66 (184*2π)/2862 weeks
18517,547.37 -16,466.62 (185*2π)/2862 weeks
18620,833.81 -19,716.35 (186*2π)/2862 weeks
18724,439.88 -21,460.62 (187*2π)/2862 weeks
18827,411.35 -22,109.61 (188*2π)/2862 weeks
18929,626.92 -22,671.27 (189*2π)/2862 weeks
19032,038.08 -23,404.74 (190*2π)/2862 weeks
19134,862.64 -23,468.16 (191*2π)/2861 weeks
19237,169.39 -22,501.58 (192*2π)/2861 weeks
19338,609.47 -21,473.96 (193*2π)/2861 weeks
19439,775.65 -20,661.58 (194*2π)/2861 weeks
19541,125.74 -19,682.72 (195*2π)/2861 weeks
19641,993.66 -17,851.14 (196*2π)/2861 weeks
19741,372.88 -15,987.1 (197*2π)/2861 weeks
19840,110.7 -15,565.42 (198*2π)/2861 weeks
19939,554.88 -15,864.82 (199*2π)/2861 weeks
20039,547.34 -15,994.53 (200*2π)/2861 weeks
20139,148.55 -15,633.5 (201*2π)/2861 weeks
20238,222.96 -16,123.74 (202*2π)/2861 weeks
20338,101.68 -17,295.81 (203*2π)/2861 weeks
20438,896.75 -18,268.32 (204*2π)/2861 weeks
20540,345.6 -18,261.55 (205*2π)/2861 weeks
20641,212 -17,064.56 (206*2π)/2861 weeks
20741,005.67 -15,720.73 (207*2π)/2861 weeks
20840,358.63 -14,754.64 (208*2π)/2861 weeks
20939,477.66 -13,786.45 (209*2π)/2861 weeks
21038,342.89 -12,901.07 (210*2π)/2861 weeks
21136,528.48 -11,732.36 (211*2π)/2861 weeks
21233,588.39 -10,791.24 (212*2π)/2861 weeks
21329,405.82 -11,255.53 (213*2π)/2861 weeks
21425,327.29 -13,648.68 (214*2π)/2861 weeks
21521,959.29 -17,485.27 (215*2π)/2861 weeks
21619,733.22 -22,636.26 (216*2π)/2861 weeks
21719,746.34 -28,554.37 (217*2π)/2861 weeks
21821,644.42 -33,641.13 (218*2π)/2861 weeks
21924,552.44 -37,381.79 (219*2π)/2861 weeks
22027,624.33 -40,171.73 (220*2π)/2861 weeks
22131,058.06 -42,361.67 (221*2π)/2861 weeks
22235,476.42 -43,283.02 (222*2π)/2861 weeks
22339,098.23 -41,681.26 (223*2π)/2861 weeks
22440,424.13 -39,322.95 (224*2π)/2861 weeks
22539,853.67 -37,377.61 (225*2π)/2861 weeks
22637,823.59 -36,710.38 (226*2π)/2861 weeks
22735,215.77 -38,320.66 (227*2π)/2861 weeks
22833,623.35 -41,877.45 (228*2π)/2861 weeks
22933,785.67 -46,802.59 (229*2π)/2861 weeks
23036,821.67 -51,717.73 (230*2π)/2861 weeks
23142,027.18 -54,434.97 (231*2π)/2861 weeks
23246,555.93 -54,229.61 (232*2π)/2861 weeks
23349,558.82 -53,663.41 (233*2π)/2861 weeks
23452,197.33 -52,887.2 (234*2π)/2861 weeks
23554,282.15 -51,889.71 (235*2π)/2861 weeks
23655,637.78 -50,559.44 (236*2π)/2861 weeks
23755,510.57 -49,809.68 (237*2π)/2861 weeks
23855,119.13 -51,565.24 (238*2π)/2861 weeks
23957,416.01 -55,084.02 (239*2π)/2861 weeks
24063,240.87 -57,405.4 (240*2π)/2861 weeks
24170,947.1 -55,819.38 (241*2π)/2861 weeks
24276,973.86 -50,206.88 (242*2π)/2861 weeks
24380,067.14 -42,414.98 (243*2π)/2861 weeks
24479,550.18 -33,948.96 (244*2π)/2861 weeks
24575,418.16 -26,192.66 (245*2π)/2861 weeks
24667,673 -21,229.81 (246*2π)/2861 weeks
24758,859.09 -21,501.91 (247*2π)/2861 weeks
24853,160.76 -25,786.66 (248*2π)/2861 weeks
24951,380.19 -30,735.75 (249*2π)/2861 weeks
25052,416.39 -33,207.21 (250*2π)/2861 weeks
25152,549.48 -32,991.1 (251*2π)/2861 weeks
25250,460.2 -33,022.32 (252*2π)/2861 weeks
25348,978.34 -34,255.5 (253*2π)/2861 weeks
25447,488.71 -34,345.89 (254*2π)/2861 weeks
25544,029.07 -34,731.44 (255*2π)/2861 weeks
25639,949.73 -37,988.5 (256*2π)/2861 weeks
25738,991.48 -42,882.86 (257*2π)/2861 weeks
25840,780.65 -45,819.59 (258*2π)/2861 weeks
25942,816.05 -44,577.25 (259*2π)/2861 weeks
26040,670.12 -39,363.67 (260*2π)/2861 weeks
26131,138.16 -34,715.74 (261*2π)/2861 weeks
26216,298.39 -36,983.78 (262*2π)/2861 weeks
2631,448.067 -46,674.95 (263*2π)/2861 weeks
264-10,549.44 -63,705.46 (264*2π)/2861 weeks
265-15,571.7 -86,538.46 (265*2π)/2861 weeks
266-10,241.79 -109,368.3 (266*2π)/2861 weeks
267793.0577 -125,393.2 (267*2π)/2861 weeks
26811,983.48 -135,570.9 (268*2π)/2861 weeks
26920,706.15 -141,843.7 (269*2π)/2861 weeks
27024,521.51 -146,333.6 (270*2π)/2861 weeks
27123,095.39 -154,580.2 (271*2π)/2861 weeks
27219,930.9 -170,401.6 (272*2π)/2861 weeks
27320,054.94 -194,710.5 (273*2π)/2861 weeks
27429,031.96 -226,745.2 (274*2π)/2861 weeks
27552,513.58 -259,172.5 (275*2π)/2861 weeks
27686,615.67 -283,837.6 (276*2π)/2861 weeks
277123,428 -297,968.1 (277*2π)/2861 weeks
278156,685.2 -307,919 (278*2π)/2861 weeks
279190,916.8 -320,801.7 (279*2π)/2861 weeks
280230,210 -336,412.8 (280*2π)/2861 weeks
281282,380.9 -356,243.3 (281*2π)/2861 weeks
282356,869.5 -373,379.8 (282*2π)/2861 weeks
283460,903.6 -371,157.2 (283*2π)/2861 weeks
284590,201.6 -325,882.1 (284*2π)/2861 weeks

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