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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 27 weeks (38692.08*sine), 30 weeks (35660.48*sine), and 18 weeks (12830.34*cosine).

UVXY (ProShares Ultra VIX Short-Term Futures ETF) has an average price of 141,444.2 (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 7/10/2017 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
0141,444.2   0 
1229,327.7 121,413.6 (1*2π)/302302 weeks
2136,194.5 169,886.5 (2*2π)/302151 weeks
354,810.32 163,752.1 (3*2π)/302101 weeks
42,434.72 129,361.7 (4*2π)/30276 weeks
5-19,979.59 87,750.11 (5*2π)/30260 weeks
6-20,266.03 54,179.57 (6*2π)/30250 weeks
7-9,103.605 34,094.3 (7*2π)/30243 weeks
83,045.051 26,648.35 (8*2π)/30238 weeks
912,414.88 28,560.71 (9*2π)/30234 weeks
1012,809.42 35,660.48 (10*2π)/30230 weeks
115,063.88 38,692.08 (11*2π)/30227 weeks
12-3,502.311 34,012.59 (12*2π)/30225 weeks
13-7,120.066 24,015.85 (13*2π)/30223 weeks
14-3,779.991 15,401.33 (14*2π)/30222 weeks
152,352.601 11,116.3 (15*2π)/30220 weeks
168,794.268 11,218.94 (16*2π)/30219 weeks
1712,830.34 15,063.87 (17*2π)/30218 weeks
1812,774.54 20,475.07 (18*2π)/30217 weeks
199,406.351 24,194.32 (19*2π)/30216 weeks
204,011.226 25,706.08 (20*2π)/30215 weeks
21-2,447.997 23,892.73 (21*2π)/30214 weeks
22-7,069.949 17,236.65 (22*2π)/30214 weeks
23-5,948.079 9,502.442 (23*2π)/30213 weeks
24-1,248.769 4,831.845 (24*2π)/30213 weeks
254,290.035 3,710.796 (25*2π)/30212 weeks
269,243.446 5,404.069 (26*2π)/30212 weeks
2712,042.08 10,586.5 (27*2π)/30211 weeks
289,907.649 15,972.42 (28*2π)/30211 weeks
294,558.707 17,966.88 (29*2π)/30210 weeks
30-352.7202 15,741.01 (30*2π)/30210 weeks
31-2,356.543 11,138.29 (31*2π)/30210 weeks
32-763.2092 6,649.245 (32*2π)/3029 weeks
332,870.763 5,364.202 (33*2π)/3029 weeks
345,071.982 6,638.677 (34*2π)/3029 weeks
355,308.53 7,947.704 (35*2π)/3029 weeks
365,522.5 8,395.425 (36*2π)/3028 weeks
375,791.01 10,034.33 (37*2π)/3028 weeks
383,739.641 11,733.51 (38*2π)/3028 weeks
39360.0771 11,057.88 (39*2π)/3028 weeks
40-1,450.501 7,729.994 (40*2π)/3028 weeks
41-623.8646 3,931.552 (41*2π)/3027 weeks
422,838.612 1,782.771 (42*2π)/3027 weeks
436,358.611 2,759.704 (43*2π)/3027 weeks
447,944.756 5,324.395 (44*2π)/3027 weeks
457,848.836 7,858.718 (45*2π)/3027 weeks
466,500.086 10,015.47 (46*2π)/3027 weeks
474,100.204 11,248.04 (47*2π)/3026 weeks
48805.3554 11,057.57 (48*2π)/3026 weeks
49-1,925.11 8,333.458 (49*2π)/3026 weeks
50-2,262.197 4,418.162 (50*2π)/3026 weeks
51-16.8167 1,330.438 (51*2π)/3026 weeks
523,303.01 707.6062 (52*2π)/3026 weeks
535,440.706 1,972.016 (53*2π)/3026 weeks
546,236.708 3,386.576 (54*2π)/3026 weeks
556,605.161 4,563.702 (55*2π)/3025 weeks
566,650.323 5,824.267 (56*2π)/3025 weeks
576,415.848 7,409.244 (57*2π)/3025 weeks
584,615.877 9,298.505 (58*2π)/3025 weeks
591,460.323 9,167.048 (59*2π)/3025 weeks
60-730.7 7,034.79 (60*2π)/3025 weeks
61-1,094.674 4,241.054 (61*2π)/3025 weeks
62-153.1959 1,949.206 (62*2π)/3025 weeks
631,799.143 452.8129 (63*2π)/3025 weeks
644,115.998 432.9511 (64*2π)/3025 weeks
655,873.521 1,455.281 (65*2π)/3025 weeks
666,745.538 3,191.924 (66*2π)/3025 weeks
676,427.03 5,225.874 (67*2π)/3025 weeks
684,772.673 6,264.421 (68*2π)/3024 weeks
693,532.665 5,885.136 (69*2π)/3024 weeks
702,943.973 5,567.919 (70*2π)/3024 weeks
712,331.944 5,374.419 (71*2π)/3024 weeks
721,430.632 4,812.214 (72*2π)/3024 weeks
73858.8242 3,620.19 (73*2π)/3024 weeks
741,134.312 2,031.612 (74*2π)/3024 weeks
752,310.371 1,152.108 (75*2π)/3024 weeks
763,538.308 968.4601 (76*2π)/3024 weeks
774,659.349 1,287.385 (77*2π)/3024 weeks
785,555.56 2,310.578 (78*2π)/3024 weeks
795,444.323 3,725.522 (79*2π)/3024 weeks
804,570.54 4,547.611 (80*2π)/3024 weeks
813,460.001 4,568.664 (81*2π)/3024 weeks
822,824.184 4,140.602 (82*2π)/3024 weeks
832,526.984 3,528.153 (83*2π)/3024 weeks
842,645.765 3,158.48 (84*2π)/3024 weeks
852,554.61 3,168.733 (85*2π)/3024 weeks
862,015.848 2,873.883 (86*2π)/3024 weeks
871,797.411 1,862.829 (87*2π)/3023 weeks
882,412.461 840.9164 (88*2π)/3023 weeks
893,715.145 377.3051 (89*2π)/3023 weeks
905,085.528 1,151.592 (90*2π)/3023 weeks
915,186.048 2,564.741 (91*2π)/3023 weeks
924,492.943 3,288.215 (92*2π)/3023 weeks
933,798.698 3,368.468 (93*2π)/3023 weeks
943,549.065 3,299.129 (94*2π)/3023 weeks
953,040.964 3,602.429 (95*2π)/3023 weeks
961,999.845 3,275.553 (96*2π)/3023 weeks
971,461.707 2,015.995 (97*2π)/3023 weeks
982,079.053 807.0995 (98*2π)/3023 weeks
993,239 447.5821 (99*2π)/3023 weeks
1004,065.132 1,010.817 (100*2π)/3023 weeks
1014,091.911 1,591.482 (101*2π)/3023 weeks
1024,009.361 1,802.114 (102*2π)/3023 weeks
1034,077.304 2,055.925 (103*2π)/3023 weeks
1043,825.662 2,562.49 (104*2π)/3023 weeks
1053,082.616 2,697.025 (105*2π)/3023 weeks
1062,405.637 2,112.252 (106*2π)/3023 weeks
1072,461.44 1,185.862 (107*2π)/3023 weeks
1083,255.455 664.2329 (108*2π)/3023 weeks
1094,085.167 1,093.122 (109*2π)/3023 weeks
1103,967.577 1,974.754 (110*2π)/3023 weeks
1113,257.303 2,142.171 (111*2π)/3023 weeks
1122,846.455 1,719.448 (112*2π)/3023 weeks
1132,875.348 1,359.348 (113*2π)/3023 weeks
1142,951.906 998.8893 (114*2π)/3023 weeks
1153,351.657 838.7711 (115*2π)/3023 weeks
1163,674.002 1,035.369 (116*2π)/3023 weeks
1173,597.263 1,425.472 (117*2π)/3023 weeks
1183,277.556 1,442.522 (118*2π)/3023 weeks
1192,993.534 1,294.655 (119*2π)/3023 weeks
1202,903.406 811.3906 (120*2π)/3023 weeks
1213,277.639 359.7615 (121*2π)/3022 weeks
1223,987.312 422.9821 (122*2π)/3022 weeks
1234,381.813 1,029.073 (123*2π)/3022 weeks
1244,191.214 1,851.554 (124*2π)/3022 weeks
1253,343.915 2,250.625 (125*2π)/3022 weeks
1262,511.429 1,918.725 (126*2π)/3022 weeks
1272,158.882 1,329.136 (127*2π)/3022 weeks
1281,889.774 708.2023 (128*2π)/3022 weeks
1291,916.904 -215.0911 (129*2π)/3022 weeks
1302,651.262 -1,271.558 (130*2π)/3022 weeks
1314,267.381 -1,509.888 (131*2π)/3022 weeks
1325,569.356 -417.9164 (132*2π)/3022 weeks
1335,708.335 1,204.382 (133*2π)/3022 weeks
1344,898.599 2,363.253 (134*2π)/3022 weeks
1353,666.266 2,905.863 (135*2π)/3022 weeks
1362,391.63 2,817.449 (136*2π)/3022 weeks
1371,007.075 2,035.923 (137*2π)/3022 weeks
138234.3737 291.2804 (138*2π)/3022 weeks
139807.8099 -1,942.026 (139*2π)/3022 weeks
1403,120.739 -3,185.01 (140*2π)/3022 weeks
1415,570.189 -2,386.697 (141*2π)/3022 weeks
1426,728.465 -143.1727 (142*2π)/3022 weeks
1435,938.317 2,207.008 (143*2π)/3022 weeks
1443,827.543 3,135.455 (144*2π)/3022 weeks
1451,977.475 2,393.062 (145*2π)/3022 weeks
1461,175.866 875.798 (146*2π)/3022 weeks
1471,459.796 -513.774 (147*2π)/3022 weeks
1482,273.33 -1,419.606 (148*2π)/3022 weeks
1493,454.156 -1,789.333 (149*2π)/3022 weeks
1504,684.634 -1,244.474 (150*2π)/3022 weeks
1515,187.972   (151*2π)/3022 weeks
1524,684.634 1,244.474 (152*2π)/3022 weeks
1533,454.156 1,789.333 (153*2π)/3022 weeks
1542,273.33 1,419.606 (154*2π)/3022 weeks
1551,459.796 513.774 (155*2π)/3022 weeks
1561,175.866 -875.798 (156*2π)/3022 weeks
1571,977.475 -2,393.062 (157*2π)/3022 weeks
1583,827.543 -3,135.455 (158*2π)/3022 weeks
1595,938.317 -2,207.008 (159*2π)/3022 weeks
1606,728.465 143.1727 (160*2π)/3022 weeks
1615,570.189 2,386.697 (161*2π)/3022 weeks
1623,120.739 3,185.01 (162*2π)/3022 weeks
163807.8099 1,942.026 (163*2π)/3022 weeks
164234.3737 -291.2804 (164*2π)/3022 weeks
1651,007.075 -2,035.923 (165*2π)/3022 weeks
1662,391.63 -2,817.449 (166*2π)/3022 weeks
1673,666.266 -2,905.863 (167*2π)/3022 weeks
1684,898.599 -2,363.253 (168*2π)/3022 weeks
1695,708.335 -1,204.382 (169*2π)/3022 weeks
1705,569.356 417.9164 (170*2π)/3022 weeks
1714,267.381 1,509.888 (171*2π)/3022 weeks
1722,651.262 1,271.558 (172*2π)/3022 weeks
1731,916.904 215.0911 (173*2π)/3022 weeks
1741,889.774 -708.2023 (174*2π)/3022 weeks
1752,158.882 -1,329.136 (175*2π)/3022 weeks
1762,511.429 -1,918.725 (176*2π)/3022 weeks
1773,343.915 -2,250.625 (177*2π)/3022 weeks
1784,191.214 -1,851.554 (178*2π)/3022 weeks
1794,381.813 -1,029.073 (179*2π)/3022 weeks
1803,987.312 -422.9821 (180*2π)/3022 weeks
1813,277.639 -359.7615 (181*2π)/3022 weeks
1822,903.406 -811.3906 (182*2π)/3022 weeks
1832,993.534 -1,294.655 (183*2π)/3022 weeks
1843,277.556 -1,442.522 (184*2π)/3022 weeks
1853,597.263 -1,425.472 (185*2π)/3022 weeks
1863,674.002 -1,035.369 (186*2π)/3022 weeks
1873,351.657 -838.7711 (187*2π)/3022 weeks
1882,951.906 -998.8893 (188*2π)/3022 weeks
1892,875.348 -1,359.348 (189*2π)/3022 weeks
1902,846.455 -1,719.448 (190*2π)/3022 weeks
1913,257.303 -2,142.171 (191*2π)/3022 weeks
1923,967.577 -1,974.754 (192*2π)/3022 weeks
1934,085.167 -1,093.122 (193*2π)/3022 weeks
1943,255.455 -664.2329 (194*2π)/3022 weeks
1952,461.44 -1,185.862 (195*2π)/3022 weeks
1962,405.637 -2,112.252 (196*2π)/3022 weeks
1973,082.616 -2,697.025 (197*2π)/3022 weeks
1983,825.662 -2,562.49 (198*2π)/3022 weeks
1994,077.304 -2,055.925 (199*2π)/3022 weeks
2004,009.361 -1,802.114 (200*2π)/3022 weeks
2014,091.911 -1,591.482 (201*2π)/3022 weeks
2024,065.132 -1,010.817 (202*2π)/3021 weeks
2033,239 -447.5821 (203*2π)/3021 weeks
2042,079.053 -807.0995 (204*2π)/3021 weeks
2051,461.707 -2,015.995 (205*2π)/3021 weeks
2061,999.845 -3,275.553 (206*2π)/3021 weeks
2073,040.964 -3,602.429 (207*2π)/3021 weeks
2083,549.065 -3,299.129 (208*2π)/3021 weeks
2093,798.698 -3,368.468 (209*2π)/3021 weeks
2104,492.943 -3,288.215 (210*2π)/3021 weeks
2115,186.048 -2,564.741 (211*2π)/3021 weeks
2125,085.528 -1,151.592 (212*2π)/3021 weeks
2133,715.145 -377.3051 (213*2π)/3021 weeks
2142,412.461 -840.9164 (214*2π)/3021 weeks
2151,797.411 -1,862.829 (215*2π)/3021 weeks
2162,015.848 -2,873.883 (216*2π)/3021 weeks
2172,554.61 -3,168.733 (217*2π)/3021 weeks
2182,645.765 -3,158.48 (218*2π)/3021 weeks
2192,526.984 -3,528.153 (219*2π)/3021 weeks
2202,824.184 -4,140.602 (220*2π)/3021 weeks
2213,460.001 -4,568.664 (221*2π)/3021 weeks
2224,570.54 -4,547.611 (222*2π)/3021 weeks
2235,444.323 -3,725.522 (223*2π)/3021 weeks
2245,555.56 -2,310.578 (224*2π)/3021 weeks
2254,659.349 -1,287.385 (225*2π)/3021 weeks
2263,538.308 -968.4601 (226*2π)/3021 weeks
2272,310.371 -1,152.108 (227*2π)/3021 weeks
2281,134.312 -2,031.612 (228*2π)/3021 weeks
229858.8242 -3,620.19 (229*2π)/3021 weeks
2301,430.632 -4,812.214 (230*2π)/3021 weeks
2312,331.944 -5,374.419 (231*2π)/3021 weeks
2322,943.973 -5,567.919 (232*2π)/3021 weeks
2333,532.665 -5,885.136 (233*2π)/3021 weeks
2344,772.673 -6,264.421 (234*2π)/3021 weeks
2356,427.03 -5,225.874 (235*2π)/3021 weeks
2366,745.538 -3,191.924 (236*2π)/3021 weeks
2375,873.521 -1,455.281 (237*2π)/3021 weeks
2384,115.998 -432.9511 (238*2π)/3021 weeks
2391,799.143 -452.8129 (239*2π)/3021 weeks
240-153.1959 -1,949.206 (240*2π)/3021 weeks
241-1,094.674 -4,241.054 (241*2π)/3021 weeks
242-730.7 -7,034.79 (242*2π)/3021 weeks
2431,460.323 -9,167.048 (243*2π)/3021 weeks
2444,615.877 -9,298.505 (244*2π)/3021 weeks
2456,415.848 -7,409.244 (245*2π)/3021 weeks
2466,650.323 -5,824.267 (246*2π)/3021 weeks
2476,605.161 -4,563.702 (247*2π)/3021 weeks
2486,236.708 -3,386.576 (248*2π)/3021 weeks
2495,440.706 -1,972.016 (249*2π)/3021 weeks
2503,303.01 -707.6062 (250*2π)/3021 weeks
251-16.8167 -1,330.438 (251*2π)/3021 weeks
252-2,262.197 -4,418.162 (252*2π)/3021 weeks
253-1,925.11 -8,333.458 (253*2π)/3021 weeks
254805.3554 -11,057.57 (254*2π)/3021 weeks
2554,100.204 -11,248.04 (255*2π)/3021 weeks
2566,500.086 -10,015.47 (256*2π)/3021 weeks
2577,848.836 -7,858.718 (257*2π)/3021 weeks
2587,944.756 -5,324.395 (258*2π)/3021 weeks
2596,358.611 -2,759.704 (259*2π)/3021 weeks
2602,838.612 -1,782.771 (260*2π)/3021 weeks
261-623.8646 -3,931.552 (261*2π)/3021 weeks
262-1,450.501 -7,729.994 (262*2π)/3021 weeks
263360.0771 -11,057.88 (263*2π)/3021 weeks
2643,739.641 -11,733.51 (264*2π)/3021 weeks
2655,791.01 -10,034.33 (265*2π)/3021 weeks
2665,522.5 -8,395.425 (266*2π)/3021 weeks
2675,308.53 -7,947.704 (267*2π)/3021 weeks
2685,071.982 -6,638.677 (268*2π)/3021 weeks
2692,870.763 -5,364.202 (269*2π)/3021 weeks
270-763.2092 -6,649.245 (270*2π)/3021 weeks
271-2,356.543 -11,138.29 (271*2π)/3021 weeks
272-352.7202 -15,741.01 (272*2π)/3021 weeks
2734,558.707 -17,966.88 (273*2π)/3021 weeks
2749,907.649 -15,972.42 (274*2π)/3021 weeks
27512,042.08 -10,586.5 (275*2π)/3021 weeks
2769,243.446 -5,404.069 (276*2π)/3021 weeks
2774,290.035 -3,710.796 (277*2π)/3021 weeks
278-1,248.769 -4,831.845 (278*2π)/3021 weeks
279-5,948.079 -9,502.442 (279*2π)/3021 weeks
280-7,069.949 -17,236.65 (280*2π)/3021 weeks
281-2,447.997 -23,892.73 (281*2π)/3021 weeks
2824,011.226 -25,706.08 (282*2π)/3021 weeks
2839,406.351 -24,194.32 (283*2π)/3021 weeks
28412,774.54 -20,475.07 (284*2π)/3021 weeks
28512,830.34 -15,063.87 (285*2π)/3021 weeks
2868,794.268 -11,218.94 (286*2π)/3021 weeks
2872,352.601 -11,116.3 (287*2π)/3021 weeks
288-3,779.991 -15,401.33 (288*2π)/3021 weeks
289-7,120.066 -24,015.85 (289*2π)/3021 weeks
290-3,502.311 -34,012.59 (290*2π)/3021 weeks
2915,063.88 -38,692.08 (291*2π)/3021 weeks
29212,809.42 -35,660.48 (292*2π)/3021 weeks
29312,414.88 -28,560.71 (293*2π)/3021 weeks
2943,045.051 -26,648.35 (294*2π)/3021 weeks
295-9,103.605 -34,094.3 (295*2π)/3021 weeks
296-20,266.03 -54,179.57 (296*2π)/3021 weeks
297-19,979.59 -87,750.11 (297*2π)/3021 weeks
2982,434.72 -129,361.7 (298*2π)/3021 weeks
29954,810.32 -163,752.1 (299*2π)/3021 weeks
300136,194.5 -169,886.5 (300*2π)/3021 weeks



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