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Fourier Analysis of UVXY (ProShares Ultra VIX Short-Term Futures ETF)


UVXY (ProShares Ultra VIX Short-Term Futures ETF) appears to have interesting cyclic behaviour every 32 weeks (36774.89*sine), 29 weeks (33452.96*sine), and 21 weeks (11330.43*cosine).

UVXY (ProShares Ultra VIX Short-Term Futures ETF) has an average price of 203,163.4 (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 10/4/2011 to 11/6/2017 for UVXY (ProShares Ultra VIX Short-Term Futures ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0203,163.4   0 
1276,701.8 218,840.7 (1*2π)/319319 weeks
293,463.86 246,825.3 (2*2π)/319160 weeks
3-14,893.6 175,597.7 (3*2π)/319106 weeks
4-41,105.86 93,369.72 (4*2π)/31980 weeks
5-22,012.8 42,396.78 (5*2π)/31964 weeks
66,100.145 30,375.14 (6*2π)/31953 weeks
718,433.36 37,555.7 (7*2π)/31946 weeks
812,582.24 46,084.31 (8*2π)/31940 weeks
94,465.594 40,868.91 (9*2π)/31935 weeks
102,947.555 36,774.89 (10*2π)/31932 weeks
11-740.3222 33,452.96 (11*2π)/31929 weeks
12-3,719.318 26,136.97 (12*2π)/31927 weeks
13-1,590.776 18,883.84 (13*2π)/31925 weeks
145,844.075 14,359.66 (14*2π)/31923 weeks
1511,330.43 19,667.47 (15*2π)/31921 weeks
168,015.788 25,328.22 (16*2π)/31920 weeks
171,958.278 25,239.11 (17*2π)/31919 weeks
18-2,462.331 20,275.49 (18*2π)/31918 weeks
19-3,060.719 14,297.28 (19*2π)/31917 weeks
201,888.63 8,622.352 (20*2π)/31916 weeks
218,651.085 10,274.06 (21*2π)/31915 weeks
229,499.874 17,269.01 (22*2π)/31915 weeks
232,857.16 19,028.76 (23*2π)/31914 weeks
24336.3022 14,917.83 (24*2π)/31913 weeks
25729.3853 12,749.63 (25*2π)/31913 weeks
26529.0033 11,036.9 (26*2π)/31912 weeks
271,052.187 7,716.763 (27*2π)/31912 weeks
286,754.249 6,494.577 (28*2π)/31911 weeks
298,872.94 11,868.16 (29*2π)/31911 weeks
305,038.336 16,018.13 (30*2π)/31911 weeks
31-542.8584 14,399.97 (31*2π)/31910 weeks
32-2,587.56 9,068.591 (32*2π)/31910 weeks
33-52.5127 4,219.761 (33*2π)/31910 weeks
346,380.702 2,881.283 (34*2π)/3199 weeks
3510,387 9,033.002 (35*2π)/3199 weeks
366,100.861 15,217.59 (36*2π)/3199 weeks
37-1,927.933 13,605.73 (37*2π)/3199 weeks
38-3,186.603 5,247.77 (38*2π)/3198 weeks
393,477.93 2,185.648 (39*2π)/3198 weeks
407,175.239 5,833.334 (40*2π)/3198 weeks
415,550.085 9,692.524 (41*2π)/3198 weeks
422,654.44 9,367.864 (42*2π)/3198 weeks
431,156.949 7,595.452 (43*2π)/3197 weeks
442,425 5,193.094 (44*2π)/3197 weeks
454,417.953 6,180.912 (45*2π)/3197 weeks
463,318.2 7,864.042 (46*2π)/3197 weeks
471,359.529 6,563.314 (47*2π)/3197 weeks
482,252.453 4,191.989 (48*2π)/3197 weeks
494,750.264 3,973.649 (49*2π)/3197 weeks
506,321.353 6,733.351 (50*2π)/3196 weeks
513,377.267 9,320.8 (51*2π)/3196 weeks
5234.94114 7,486.938 (52*2π)/3196 weeks
53-220.9614 3,505.238 (53*2π)/3196 weeks
543,302.409 1,195.351 (54*2π)/3196 weeks
557,035.825 3,638.875 (55*2π)/3196 weeks
566,115.755 7,756.597 (56*2π)/3196 weeks
572,284.125 8,560.547 (57*2π)/3196 weeks
58-49.21698 5,955.921 (58*2π)/3196 weeks
59380.0729 2,702.909 (59*2π)/3195 weeks
603,964.452 1,097.577 (60*2π)/3195 weeks
616,500.43 4,283.396 (61*2π)/3195 weeks
624,144.942 6,755.831 (62*2π)/3195 weeks
632,107.418 5,807.683 (63*2π)/3195 weeks
642,060.862 4,067.577 (64*2π)/3195 weeks
652,825.592 3,916.281 (65*2π)/3195 weeks
662,795.28 3,774.628 (66*2π)/3195 weeks
673,261.292 3,459.63 (67*2π)/3195 weeks
683,287.744 3,622.468 (68*2π)/3195 weeks
693,727.943 3,526.208 (69*2π)/3195 weeks
704,339.236 4,000.172 (70*2π)/3195 weeks
713,485.427 5,638.265 (71*2π)/3194 weeks
72991.8472 4,734.398 (72*2π)/3194 weeks
731,589.163 1,899.906 (73*2π)/3194 weeks
743,783.699 1,567.436 (74*2π)/3194 weeks
755,049.728 3,179.47 (75*2π)/3194 weeks
764,108.268 4,682.986 (76*2π)/3194 weeks
772,639.394 4,719.683 (77*2π)/3194 weeks
781,855.455 3,233.439 (78*2π)/3194 weeks
792,828.55 2,663.057 (79*2π)/3194 weeks
803,015.38 2,793.636 (80*2π)/3194 weeks
812,913.017 2,471.837 (81*2π)/3194 weeks
823,850.164 2,192.401 (82*2π)/3194 weeks
834,407.292 3,359.998 (83*2π)/3194 weeks
843,391.533 4,065.135 (84*2π)/3194 weeks
852,211.082 3,904.091 (85*2π)/3194 weeks
861,892.816 2,495.546 (86*2π)/3194 weeks
872,370.553 1,701.43 (87*2π)/3194 weeks
883,549.678 1,128.953 (88*2π)/3194 weeks
894,950.747 2,091.384 (89*2π)/3194 weeks
904,599.134 4,053.218 (90*2π)/3194 weeks
912,427.476 4,586.948 (91*2π)/3194 weeks
921,082.767 2,858.614 (92*2π)/3193 weeks
931,577.903 951.9962 (93*2π)/3193 weeks
943,596.594 -22.24559 (94*2π)/3193 weeks
955,799.567 1,709.261 (95*2π)/3193 weeks
964,594.057 4,497.394 (96*2π)/3193 weeks
971,875.304 4,273.118 (97*2π)/3193 weeks
98769.6119 1,991.177 (98*2π)/3193 weeks
992,513.474 -146.0646 (99*2π)/3193 weeks
1004,944.224 1,036.709 (100*2π)/3193 weeks
1014,363.141 3,210.317 (101*2π)/3193 weeks
1022,406.478 3,212.073 (102*2π)/3193 weeks
1032,085.918 1,557.149 (103*2π)/3193 weeks
1043,253.84 888.1297 (104*2π)/3193 weeks
1054,306.234 1,788.437 (105*2π)/3193 weeks
1063,399.464 3,179.3 (106*2π)/3193 weeks
1071,767.036 2,399.529 (107*2π)/3193 weeks
1081,989.959 529.7573 (108*2π)/3193 weeks
1093,953.121 110.4988 (109*2π)/3193 weeks
1104,923.129 1,801.965 (110*2π)/3193 weeks
1113,835.195 3,305.642 (111*2π)/3193 weeks
1121,926.629 2,957.436 (112*2π)/3193 weeks
1131,322.447 1,171.851 (113*2π)/3193 weeks
1142,654.031 -350.2753 (114*2π)/3193 weeks
1154,655.18 243.9183 (115*2π)/3193 weeks
1164,645.521 2,385.782 (116*2π)/3193 weeks
1172,914.092 2,782.405 (117*2π)/3193 weeks
1182,127.456 1,659.26 (118*2π)/3193 weeks
1192,755.664 932.6672 (119*2π)/3193 weeks
1202,811.447 1,029.99 (120*2π)/3193 weeks
1213,151.006 637.7245 (121*2π)/3193 weeks
1223,635.347 803.4985 (122*2π)/3193 weeks
1233,875.423 1,423.607 (123*2π)/3193 weeks
1243,178.046 1,782.103 (124*2π)/3193 weeks
1252,972.281 1,525.519 (125*2π)/3193 weeks
1262,513.026 1,375.306 (126*2π)/3193 weeks
1272,439.927 666.7312 (127*2π)/3193 weeks
1283,033.285 23.08307 (128*2π)/3192 weeks
1293,998.16 417.3675 (129*2π)/3192 weeks
1304,117.485 1,286.925 (130*2π)/3192 weeks
1313,418.606 2,115.09 (131*2π)/3192 weeks
1322,056.105 1,719.981 (132*2π)/3192 weeks
1331,845.695 146.5885 (133*2π)/3192 weeks
1343,424.676 -564.9811 (134*2π)/3192 weeks
1354,247.997 618.8166 (135*2π)/3192 weeks
1363,603.471 1,587.032 (136*2π)/3192 weeks
1372,438.904 1,154.327 (137*2π)/3192 weeks
1382,900.864 47.4477 (138*2π)/3192 weeks
1393,828.708 552.0043 (139*2π)/3192 weeks
1403,340.075 1,526.151 (140*2π)/3192 weeks
1411,996.549 1,072.136 (141*2π)/3192 weeks
1422,148.646 -431.8898 (142*2π)/3192 weeks
1433,663.717 -1,173.859 (143*2π)/3192 weeks
1445,165.274 394.13 (144*2π)/3192 weeks
1454,189.73 2,291.437 (145*2π)/3192 weeks
1461,860.843 2,452.786 (146*2π)/3192 weeks
147583.9572 -64.71363 (147*2π)/3192 weeks
1482,489.116 -1,942.216 (148*2π)/3192 weeks
1494,693.546 -1,393.712 (149*2π)/3192 weeks
1505,438.921 687.8311 (150*2π)/3192 weeks
1513,955.684 2,566.008 (151*2π)/3192 weeks
1521,496.343 2,023.799 (152*2π)/3192 weeks
153949.044 -382.6862 (153*2π)/3192 weeks
1542,499.664 -1,858.139 (154*2π)/3192 weeks
1554,555.076 -1,278.156 (155*2π)/3192 weeks
1564,781.624 573.6594 (156*2π)/3192 weeks
1573,496.829 1,369.101 (157*2π)/3192 weeks
1582,644.109 923.0274 (158*2π)/3192 weeks
1592,276.579 324.739 (159*2π)/3192 weeks
1602,276.579 -324.739 (160*2π)/3192 weeks
1612,644.109 -923.0274 (161*2π)/3192 weeks
1623,496.829 -1,369.101 (162*2π)/3192 weeks
1634,781.624 -573.6594 (163*2π)/3192 weeks
1644,555.076 1,278.156 (164*2π)/3192 weeks
1652,499.664 1,858.139 (165*2π)/3192 weeks
166949.044 382.6862 (166*2π)/3192 weeks
1671,496.343 -2,023.799 (167*2π)/3192 weeks
1683,955.684 -2,566.008 (168*2π)/3192 weeks
1695,438.921 -687.8311 (169*2π)/3192 weeks
1704,693.546 1,393.712 (170*2π)/3192 weeks
1712,489.116 1,942.216 (171*2π)/3192 weeks
172583.9572 64.71363 (172*2π)/3192 weeks
1731,860.843 -2,452.786 (173*2π)/3192 weeks
1744,189.73 -2,291.437 (174*2π)/3192 weeks
1755,165.274 -394.13 (175*2π)/3192 weeks
1763,663.717 1,173.859 (176*2π)/3192 weeks
1772,148.646 431.8898 (177*2π)/3192 weeks
1781,996.549 -1,072.136 (178*2π)/3192 weeks
1793,340.075 -1,526.151 (179*2π)/3192 weeks
1803,828.708 -552.0043 (180*2π)/3192 weeks
1812,900.864 -47.4477 (181*2π)/3192 weeks
1822,438.904 -1,154.327 (182*2π)/3192 weeks
1833,603.471 -1,587.032 (183*2π)/3192 weeks
1844,247.997 -618.8166 (184*2π)/3192 weeks
1853,424.676 564.9811 (185*2π)/3192 weeks
1861,845.695 -146.5885 (186*2π)/3192 weeks
1872,056.105 -1,719.981 (187*2π)/3192 weeks
1883,418.606 -2,115.09 (188*2π)/3192 weeks
1894,117.485 -1,286.925 (189*2π)/3192 weeks
1903,998.16 -417.3675 (190*2π)/3192 weeks
1913,033.285 -23.08307 (191*2π)/3192 weeks
1922,439.927 -666.7312 (192*2π)/3192 weeks
1932,513.026 -1,375.306 (193*2π)/3192 weeks
1942,972.281 -1,525.519 (194*2π)/3192 weeks
1953,178.046 -1,782.103 (195*2π)/3192 weeks
1963,875.423 -1,423.607 (196*2π)/3192 weeks
1973,635.347 -803.4985 (197*2π)/3192 weeks
1983,151.006 -637.7245 (198*2π)/3192 weeks
1992,811.447 -1,029.99 (199*2π)/3192 weeks
2002,755.664 -932.6672 (200*2π)/3192 weeks
2012,127.456 -1,659.26 (201*2π)/3192 weeks
2022,914.092 -2,782.405 (202*2π)/3192 weeks
2034,645.521 -2,385.782 (203*2π)/3192 weeks
2044,655.18 -243.9183 (204*2π)/3192 weeks
2052,654.031 350.2753 (205*2π)/3192 weeks
2061,322.447 -1,171.851 (206*2π)/3192 weeks
2071,926.629 -2,957.436 (207*2π)/3192 weeks
2083,835.195 -3,305.642 (208*2π)/3192 weeks
2094,923.129 -1,801.965 (209*2π)/3192 weeks
2103,953.121 -110.4988 (210*2π)/3192 weeks
2111,989.959 -529.7573 (211*2π)/3192 weeks
2121,767.036 -2,399.529 (212*2π)/3192 weeks
2133,399.464 -3,179.3 (213*2π)/3191 weeks
2144,306.234 -1,788.437 (214*2π)/3191 weeks
2153,253.84 -888.1297 (215*2π)/3191 weeks
2162,085.918 -1,557.149 (216*2π)/3191 weeks
2172,406.478 -3,212.073 (217*2π)/3191 weeks
2184,363.141 -3,210.317 (218*2π)/3191 weeks
2194,944.224 -1,036.709 (219*2π)/3191 weeks
2202,513.474 146.0646 (220*2π)/3191 weeks
221769.6119 -1,991.177 (221*2π)/3191 weeks
2221,875.304 -4,273.118 (222*2π)/3191 weeks
2234,594.057 -4,497.394 (223*2π)/3191 weeks
2245,799.567 -1,709.261 (224*2π)/3191 weeks
2253,596.594 22.24559 (225*2π)/3191 weeks
2261,577.903 -951.9962 (226*2π)/3191 weeks
2271,082.767 -2,858.614 (227*2π)/3191 weeks
2282,427.476 -4,586.948 (228*2π)/3191 weeks
2294,599.134 -4,053.218 (229*2π)/3191 weeks
2304,950.747 -2,091.384 (230*2π)/3191 weeks
2313,549.678 -1,128.953 (231*2π)/3191 weeks
2322,370.553 -1,701.43 (232*2π)/3191 weeks
2331,892.816 -2,495.546 (233*2π)/3191 weeks
2342,211.082 -3,904.091 (234*2π)/3191 weeks
2353,391.533 -4,065.135 (235*2π)/3191 weeks
2364,407.292 -3,359.998 (236*2π)/3191 weeks
2373,850.164 -2,192.401 (237*2π)/3191 weeks
2382,913.017 -2,471.837 (238*2π)/3191 weeks
2393,015.38 -2,793.636 (239*2π)/3191 weeks
2402,828.55 -2,663.057 (240*2π)/3191 weeks
2411,855.455 -3,233.439 (241*2π)/3191 weeks
2422,639.394 -4,719.683 (242*2π)/3191 weeks
2434,108.268 -4,682.986 (243*2π)/3191 weeks
2445,049.728 -3,179.47 (244*2π)/3191 weeks
2453,783.699 -1,567.436 (245*2π)/3191 weeks
2461,589.163 -1,899.906 (246*2π)/3191 weeks
247991.8472 -4,734.398 (247*2π)/3191 weeks
2483,485.427 -5,638.265 (248*2π)/3191 weeks
2494,339.236 -4,000.172 (249*2π)/3191 weeks
2503,727.943 -3,526.208 (250*2π)/3191 weeks
2513,287.744 -3,622.468 (251*2π)/3191 weeks
2523,261.292 -3,459.63 (252*2π)/3191 weeks
2532,795.28 -3,774.628 (253*2π)/3191 weeks
2542,825.592 -3,916.281 (254*2π)/3191 weeks
2552,060.862 -4,067.577 (255*2π)/3191 weeks
2562,107.418 -5,807.683 (256*2π)/3191 weeks
2574,144.942 -6,755.831 (257*2π)/3191 weeks
2586,500.43 -4,283.396 (258*2π)/3191 weeks
2593,964.452 -1,097.577 (259*2π)/3191 weeks
260380.0729 -2,702.909 (260*2π)/3191 weeks
261-49.21698 -5,955.921 (261*2π)/3191 weeks
2622,284.125 -8,560.547 (262*2π)/3191 weeks
2636,115.755 -7,756.597 (263*2π)/3191 weeks
2647,035.825 -3,638.875 (264*2π)/3191 weeks
2653,302.409 -1,195.351 (265*2π)/3191 weeks
266-220.9614 -3,505.238 (266*2π)/3191 weeks
26734.94114 -7,486.938 (267*2π)/3191 weeks
2683,377.267 -9,320.8 (268*2π)/3191 weeks
2696,321.353 -6,733.351 (269*2π)/3191 weeks
2704,750.264 -3,973.649 (270*2π)/3191 weeks
2712,252.453 -4,191.989 (271*2π)/3191 weeks
2721,359.529 -6,563.314 (272*2π)/3191 weeks
2733,318.2 -7,864.042 (273*2π)/3191 weeks
2744,417.953 -6,180.912 (274*2π)/3191 weeks
2752,425 -5,193.094 (275*2π)/3191 weeks
2761,156.949 -7,595.452 (276*2π)/3191 weeks
2772,654.44 -9,367.864 (277*2π)/3191 weeks
2785,550.085 -9,692.524 (278*2π)/3191 weeks
2797,175.239 -5,833.334 (279*2π)/3191 weeks
2803,477.93 -2,185.648 (280*2π)/3191 weeks
281-3,186.603 -5,247.77 (281*2π)/3191 weeks
282-1,927.933 -13,605.73 (282*2π)/3191 weeks
2836,100.861 -15,217.59 (283*2π)/3191 weeks
28410,387 -9,033.002 (284*2π)/3191 weeks
2856,380.702 -2,881.283 (285*2π)/3191 weeks
286-52.5127 -4,219.761 (286*2π)/3191 weeks
287-2,587.56 -9,068.591 (287*2π)/3191 weeks
288-542.8584 -14,399.97 (288*2π)/3191 weeks
2895,038.336 -16,018.13 (289*2π)/3191 weeks
2908,872.94 -11,868.16 (290*2π)/3191 weeks
2916,754.249 -6,494.577 (291*2π)/3191 weeks
2921,052.187 -7,716.763 (292*2π)/3191 weeks
293529.0033 -11,036.9 (293*2π)/3191 weeks
294729.3853 -12,749.63 (294*2π)/3191 weeks
295336.3022 -14,917.83 (295*2π)/3191 weeks
2962,857.16 -19,028.76 (296*2π)/3191 weeks
2979,499.874 -17,269.01 (297*2π)/3191 weeks
2988,651.085 -10,274.06 (298*2π)/3191 weeks
2991,888.63 -8,622.352 (299*2π)/3191 weeks
300-3,060.719 -14,297.28 (300*2π)/3191 weeks
301-2,462.331 -20,275.49 (301*2π)/3191 weeks
3021,958.278 -25,239.11 (302*2π)/3191 weeks
3038,015.788 -25,328.22 (303*2π)/3191 weeks
30411,330.43 -19,667.47 (304*2π)/3191 weeks
3055,844.075 -14,359.66 (305*2π)/3191 weeks
306-1,590.776 -18,883.84 (306*2π)/3191 weeks
307-3,719.318 -26,136.97 (307*2π)/3191 weeks
308-740.3222 -33,452.96 (308*2π)/3191 weeks
3092,947.555 -36,774.89 (309*2π)/3191 weeks
3104,465.594 -40,868.91 (310*2π)/3191 weeks
31112,582.24 -46,084.31 (311*2π)/3191 weeks
31218,433.36 -37,555.7 (312*2π)/3191 weeks
3136,100.145 -30,375.14 (313*2π)/3191 weeks
314-22,012.8 -42,396.78 (314*2π)/3191 weeks
315-41,105.86 -93,369.72 (315*2π)/3191 weeks
316-14,893.6 -175,597.7 (316*2π)/3191 weeks
31793,463.86 -246,825.3 (317*2π)/3191 weeks



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