Back to list of Stocks    See Also: Seasonal Analysis of UVXYGenetic Algorithms Stock Portfolio Generator, and Fourier Calculator

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 31 weeks (37059.73*sine), 28 weeks (32591.71*sine), and 21 weeks (11161.93*cosine).

UVXY (ProShares Ultra VIX Short-Term Futures ETF) has an average price of 209,061.1 (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 9/5/2017 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
0209,061.1   0 
1278,863.2 228,433.1 (1*2π)/310310 weeks
287,078.02 251,490 (2*2π)/310155 weeks
3-20,660.99 172,833.3 (3*2π)/310103 weeks
4-41,586.64 88,087.23 (4*2π)/31078 weeks
5-18,000.45 39,371.3 (5*2π)/31062 weeks
69,601.364 31,782.63 (6*2π)/31052 weeks
719,324.06 41,156.42 (7*2π)/31044 weeks
810,175.12 47,153.55 (8*2π)/31039 weeks
94,129.768 40,364.32 (9*2π)/31034 weeks
102,112.202 37,059.73 (10*2π)/31031 weeks
11-2,237.225 32,591.71 (11*2π)/31028 weeks
12-3,362.997 24,031.93 (12*2π)/31026 weeks
13328.0695 16,746.45 (13*2π)/31024 weeks
149,442.657 16,220.38 (14*2π)/31022 weeks
1511,161.93 23,365.77 (15*2π)/31021 weeks
165,320.422 26,551.01 (16*2π)/31019 weeks
17-914.7322 23,998.14 (17*2π)/31018 weeks
18-3,081.331 17,843.33 (18*2π)/31017 weeks
19-1,223.052 10,749.77 (19*2π)/31016 weeks
206,298.135 8,984.034 (20*2π)/31016 weeks
2110,683.4 14,780.18 (21*2π)/31015 weeks
225,463.697 20,169.36 (22*2π)/31014 weeks
23539.1749 16,706.65 (23*2π)/31013 weeks
24679.8571 13,579.57 (24*2π)/31013 weeks
25608.3635 11,917.98 (25*2π)/31012 weeks
26601.9272 9,032.897 (26*2π)/31012 weeks
275,520.53 6,123.336 (27*2π)/31011 weeks
289,259.244 11,142.68 (28*2π)/31011 weeks
296,150.969 16,128.39 (29*2π)/31011 weeks
3028.16508 15,311.67 (30*2π)/31010 weeks
31-2,702.86 9,936.271 (31*2π)/31010 weeks
32-357.7524 4,641.708 (32*2π)/31010 weeks
336,253.585 2,854.179 (33*2π)/3109 weeks
3410,690.79 9,191.21 (34*2π)/3109 weeks
356,151.537 15,712.07 (35*2π)/3109 weeks
36-2,269.266 13,691.88 (36*2π)/3109 weeks
37-2,929.219 4,825.99 (37*2π)/3108 weeks
384,227.359 2,465.133 (38*2π)/3108 weeks
397,485.549 6,641.664 (39*2π)/3108 weeks
405,098.762 10,182.04 (40*2π)/3108 weeks
412,389.914 9,401.166 (41*2π)/3108 weeks
421,125.834 7,156.813 (42*2π)/3107 weeks
433,188.571 5,269.789 (43*2π)/3107 weeks
444,570.555 6,984.927 (44*2π)/3107 weeks
452,648.981 8,044.213 (45*2π)/3107 weeks
461,338.148 5,816.409 (46*2π)/3107 weeks
473,195.49 3,937.995 (47*2π)/3107 weeks
485,874.637 4,813.283 (48*2π)/3106 weeks
495,760.671 8,555.295 (49*2π)/3106 weeks
501,645.333 9,154.69 (50*2π)/3106 weeks
51-648.8273 5,828.589 (51*2π)/3106 weeks
521,265.991 1,939.278 (52*2π)/3106 weeks
535,891.462 1,968.756 (53*2π)/3106 weeks
547,307.864 6,346.448 (54*2π)/3106 weeks
553,980.361 9,027.266 (55*2π)/3106 weeks
56485.4204 7,343.502 (56*2π)/3106 weeks
57-66.08746 3,941.658 (57*2π)/3105 weeks
582,649.161 1,130.103 (58*2π)/3105 weeks
596,482.676 3,148.413 (59*2π)/3105 weeks
605,093.961 6,766.391 (60*2π)/3105 weeks
612,498.662 6,322.097 (61*2π)/3105 weeks
621,928.168 4,464.46 (62*2π)/3105 weeks
632,867.084 3,995.876 (63*2π)/3105 weeks
642,878.308 3,943.003 (64*2π)/3105 weeks
653,278.042 3,539.118 (65*2π)/3105 weeks
663,387.99 3,759.266 (66*2π)/3105 weeks
673,813.668 3,614.969 (67*2π)/3105 weeks
684,447.73 4,081.368 (68*2π)/3105 weeks
693,578.923 5,804.936 (69*2π)/3104 weeks
70967.0965 4,776.74 (70*2π)/3104 weeks
711,777.87 1,860.743 (71*2π)/3104 weeks
724,080.834 1,683.656 (72*2π)/3104 weeks
735,183.652 3,528.403 (73*2π)/3104 weeks
744,002.259 4,901.672 (74*2π)/3104 weeks
752,442.154 4,714.518 (75*2π)/3104 weeks
762,083.688 3,002.319 (76*2π)/3104 weeks
773,004.324 2,799.586 (77*2π)/3104 weeks
783,082.068 2,884.592 (78*2π)/3104 weeks
793,169.744 2,314.543 (79*2π)/3104 weeks
804,300.684 2,497.539 (80*2π)/3104 weeks
814,233.396 3,922.626 (81*2π)/3104 weeks
823,118.946 4,225.363 (82*2π)/3104 weeks
831,864.097 3,436.267 (83*2π)/3104 weeks
842,177.037 2,198.45 (84*2π)/3104 weeks
852,871.48 1,351.074 (85*2π)/3104 weeks
864,466.578 1,416.75 (86*2π)/3104 weeks
875,205.8 3,239.625 (87*2π)/3104 weeks
883,598.971 4,811.002 (88*2π)/3104 weeks
891,419.996 3,818.035 (89*2π)/3103 weeks
901,244.904 1,689.884 (90*2π)/3103 weeks
912,790.728 118.194 (91*2π)/3103 weeks
925,455.92 808.1376 (92*2π)/3103 weeks
935,488.36 4,002.765 (93*2π)/3103 weeks
942,583.405 4,755.873 (94*2π)/3103 weeks
95843.9555 2,727.531 (95*2π)/3103 weeks
961,972.397 98.92381 (96*2π)/3103 weeks
974,826.491 608.9919 (97*2π)/3103 weeks
984,746.268 3,067.212 (98*2π)/3103 weeks
992,694.773 3,458.813 (99*2π)/3103 weeks
1002,078.972 1,745.139 (100*2π)/3103 weeks
1013,252.499 912.6337 (101*2π)/3103 weeks
1024,416.311 1,776.387 (102*2π)/3103 weeks
1033,516.937 3,266.583 (103*2π)/3103 weeks
1041,800.965 2,434.839 (104*2π)/3103 weeks
1052,118.95 468.0061 (105*2π)/3103 weeks
1064,219.715 192.8245 (106*2π)/3103 weeks
1075,033.625 2,066.822 (107*2π)/3103 weeks
1083,680.166 3,493.991 (108*2π)/3103 weeks
1091,760.506 2,791.046 (109*2π)/3103 weeks
1101,461.693 808.7961 (110*2π)/3103 weeks
1113,218.219 -435.977 (111*2π)/3103 weeks
1125,093.393 776.8185 (112*2π)/3103 weeks
1134,298.825 2,821.958 (113*2π)/3103 weeks
1142,584.565 2,590.668 (114*2π)/3103 weeks
1152,294.657 1,286.596 (115*2π)/3103 weeks
1162,996.175 1,063.246 (116*2π)/3103 weeks
1172,919.3 850.1013 (117*2π)/3103 weeks
1183,482.462 689.338 (118*2π)/3103 weeks
1193,929.78 1,032.079 (119*2π)/3103 weeks
1203,708.957 1,816.222 (120*2π)/3103 weeks
1213,080.969 1,624.208 (121*2π)/3103 weeks
1222,848.56 1,593.644 (122*2π)/3103 weeks
1232,459.923 998.7338 (123*2π)/3103 weeks
1242,758.38 246.3034 (124*2π)/3103 weeks
1253,837.352 132.1002 (125*2π)/3102 weeks
1264,264.874 1,017.589 (126*2π)/3102 weeks
1273,874.135 1,963.009 (127*2π)/3102 weeks
1282,463.251 2,067.38 (128*2π)/3102 weeks
1291,771.051 598.4059 (129*2π)/3102 weeks
1303,098.837 -644.2772 (130*2π)/3102 weeks
1314,355.2 367.4973 (131*2π)/3102 weeks
1323,896.138 1,527.022 (132*2π)/3102 weeks
1332,613.806 1,361.676 (133*2π)/3102 weeks
1342,853.277 106.382 (134*2π)/3102 weeks
1353,911.17 479.39 (135*2π)/3102 weeks
1363,499.557 1,537.728 (136*2π)/3102 weeks
1372,074.74 1,136.908 (137*2π)/3102 weeks
1382,216.92 -452.4713 (138*2π)/3102 weeks
1393,849.176 -1,199.742 (139*2π)/3102 weeks
1405,320.527 561.4155 (140*2π)/3102 weeks
1414,127.936 2,469.497 (141*2π)/3102 weeks
1421,609.678 2,348.185 (142*2π)/3102 weeks
143740.8387 -533.2 (143*2π)/3102 weeks
1443,006.021 -2,055.348 (144*2π)/3102 weeks
1455,163.83 -1,058.29 (145*2π)/3102 weeks
1465,458.999 1,272.509 (146*2π)/3102 weeks
1473,355.908 2,774.903 (147*2π)/3102 weeks
1481,056.036 1,422.416 (148*2π)/3102 weeks
1491,359.301 -1,059.668 (149*2π)/3102 weeks
1503,386.798 -2,004.728 (150*2π)/3102 weeks
1515,045.394 -573.6567 (151*2π)/3102 weeks
1524,462.17 1,152.775 (152*2π)/3102 weeks
1533,094.999 1,246.671 (153*2π)/3102 weeks
1542,495.587 685.4464 (154*2π)/3102 weeks
1552,305.848   (155*2π)/3102 weeks
1562,495.587 -685.4464 (156*2π)/3102 weeks
1573,094.999 -1,246.671 (157*2π)/3102 weeks
1584,462.17 -1,152.775 (158*2π)/3102 weeks
1595,045.394 573.6567 (159*2π)/3102 weeks
1603,386.798 2,004.728 (160*2π)/3102 weeks
1611,359.301 1,059.668 (161*2π)/3102 weeks
1621,056.036 -1,422.416 (162*2π)/3102 weeks
1633,355.908 -2,774.903 (163*2π)/3102 weeks
1645,458.999 -1,272.509 (164*2π)/3102 weeks
1655,163.83 1,058.29 (165*2π)/3102 weeks
1663,006.021 2,055.348 (166*2π)/3102 weeks
167740.8387 533.2 (167*2π)/3102 weeks
1681,609.678 -2,348.185 (168*2π)/3102 weeks
1694,127.936 -2,469.497 (169*2π)/3102 weeks
1705,320.527 -561.4155 (170*2π)/3102 weeks
1713,849.176 1,199.742 (171*2π)/3102 weeks
1722,216.92 452.4713 (172*2π)/3102 weeks
1732,074.74 -1,136.908 (173*2π)/3102 weeks
1743,499.557 -1,537.728 (174*2π)/3102 weeks
1753,911.17 -479.39 (175*2π)/3102 weeks
1762,853.277 -106.382 (176*2π)/3102 weeks
1772,613.806 -1,361.676 (177*2π)/3102 weeks
1783,896.138 -1,527.022 (178*2π)/3102 weeks
1794,355.2 -367.4973 (179*2π)/3102 weeks
1803,098.837 644.2772 (180*2π)/3102 weeks
1811,771.051 -598.4059 (181*2π)/3102 weeks
1822,463.251 -2,067.38 (182*2π)/3102 weeks
1833,874.135 -1,963.009 (183*2π)/3102 weeks
1844,264.874 -1,017.589 (184*2π)/3102 weeks
1853,837.352 -132.1002 (185*2π)/3102 weeks
1862,758.38 -246.3034 (186*2π)/3102 weeks
1872,459.923 -998.7338 (187*2π)/3102 weeks
1882,848.56 -1,593.644 (188*2π)/3102 weeks
1893,080.969 -1,624.208 (189*2π)/3102 weeks
1903,708.957 -1,816.222 (190*2π)/3102 weeks
1913,929.78 -1,032.079 (191*2π)/3102 weeks
1923,482.462 -689.338 (192*2π)/3102 weeks
1932,919.3 -850.1013 (193*2π)/3102 weeks
1942,996.175 -1,063.246 (194*2π)/3102 weeks
1952,294.657 -1,286.596 (195*2π)/3102 weeks
1962,584.565 -2,590.668 (196*2π)/3102 weeks
1974,298.825 -2,821.958 (197*2π)/3102 weeks
1985,093.393 -776.8185 (198*2π)/3102 weeks
1993,218.219 435.977 (199*2π)/3102 weeks
2001,461.693 -808.7961 (200*2π)/3102 weeks
2011,760.506 -2,791.046 (201*2π)/3102 weeks
2023,680.166 -3,493.991 (202*2π)/3102 weeks
2035,033.625 -2,066.822 (203*2π)/3102 weeks
2044,219.715 -192.8245 (204*2π)/3102 weeks
2052,118.95 -468.0061 (205*2π)/3102 weeks
2061,800.965 -2,434.839 (206*2π)/3102 weeks
2073,516.937 -3,266.583 (207*2π)/3101 weeks
2084,416.311 -1,776.387 (208*2π)/3101 weeks
2093,252.499 -912.6337 (209*2π)/3101 weeks
2102,078.972 -1,745.139 (210*2π)/3101 weeks
2112,694.773 -3,458.813 (211*2π)/3101 weeks
2124,746.268 -3,067.212 (212*2π)/3101 weeks
2134,826.491 -608.9919 (213*2π)/3101 weeks
2141,972.397 -98.92381 (214*2π)/3101 weeks
215843.9555 -2,727.531 (215*2π)/3101 weeks
2162,583.405 -4,755.873 (216*2π)/3101 weeks
2175,488.36 -4,002.765 (217*2π)/3101 weeks
2185,455.92 -808.1376 (218*2π)/3101 weeks
2192,790.728 -118.194 (219*2π)/3101 weeks
2201,244.904 -1,689.884 (220*2π)/3101 weeks
2211,419.996 -3,818.035 (221*2π)/3101 weeks
2223,598.971 -4,811.002 (222*2π)/3101 weeks
2235,205.8 -3,239.625 (223*2π)/3101 weeks
2244,466.578 -1,416.75 (224*2π)/3101 weeks
2252,871.48 -1,351.074 (225*2π)/3101 weeks
2262,177.037 -2,198.45 (226*2π)/3101 weeks
2271,864.097 -3,436.267 (227*2π)/3101 weeks
2283,118.946 -4,225.363 (228*2π)/3101 weeks
2294,233.396 -3,922.626 (229*2π)/3101 weeks
2304,300.684 -2,497.539 (230*2π)/3101 weeks
2313,169.744 -2,314.543 (231*2π)/3101 weeks
2323,082.068 -2,884.592 (232*2π)/3101 weeks
2333,004.324 -2,799.586 (233*2π)/3101 weeks
2342,083.688 -3,002.319 (234*2π)/3101 weeks
2352,442.154 -4,714.518 (235*2π)/3101 weeks
2364,002.259 -4,901.672 (236*2π)/3101 weeks
2375,183.652 -3,528.403 (237*2π)/3101 weeks
2384,080.834 -1,683.656 (238*2π)/3101 weeks
2391,777.87 -1,860.743 (239*2π)/3101 weeks
240967.0965 -4,776.74 (240*2π)/3101 weeks
2413,578.923 -5,804.936 (241*2π)/3101 weeks
2424,447.73 -4,081.368 (242*2π)/3101 weeks
2433,813.668 -3,614.969 (243*2π)/3101 weeks
2443,387.99 -3,759.266 (244*2π)/3101 weeks
2453,278.042 -3,539.118 (245*2π)/3101 weeks
2462,878.308 -3,943.003 (246*2π)/3101 weeks
2472,867.084 -3,995.876 (247*2π)/3101 weeks
2481,928.168 -4,464.46 (248*2π)/3101 weeks
2492,498.662 -6,322.097 (249*2π)/3101 weeks
2505,093.961 -6,766.391 (250*2π)/3101 weeks
2516,482.676 -3,148.413 (251*2π)/3101 weeks
2522,649.161 -1,130.103 (252*2π)/3101 weeks
253-66.08746 -3,941.658 (253*2π)/3101 weeks
254485.4204 -7,343.502 (254*2π)/3101 weeks
2553,980.361 -9,027.266 (255*2π)/3101 weeks
2567,307.864 -6,346.448 (256*2π)/3101 weeks
2575,891.462 -1,968.756 (257*2π)/3101 weeks
2581,265.991 -1,939.278 (258*2π)/3101 weeks
259-648.8273 -5,828.589 (259*2π)/3101 weeks
2601,645.333 -9,154.69 (260*2π)/3101 weeks
2615,760.671 -8,555.295 (261*2π)/3101 weeks
2625,874.637 -4,813.283 (262*2π)/3101 weeks
2633,195.49 -3,937.995 (263*2π)/3101 weeks
2641,338.148 -5,816.409 (264*2π)/3101 weeks
2652,648.981 -8,044.213 (265*2π)/3101 weeks
2664,570.555 -6,984.927 (266*2π)/3101 weeks
2673,188.571 -5,269.789 (267*2π)/3101 weeks
2681,125.834 -7,156.813 (268*2π)/3101 weeks
2692,389.914 -9,401.166 (269*2π)/3101 weeks
2705,098.762 -10,182.04 (270*2π)/3101 weeks
2717,485.549 -6,641.664 (271*2π)/3101 weeks
2724,227.359 -2,465.133 (272*2π)/3101 weeks
273-2,929.219 -4,825.99 (273*2π)/3101 weeks
274-2,269.266 -13,691.88 (274*2π)/3101 weeks
2756,151.537 -15,712.07 (275*2π)/3101 weeks
27610,690.79 -9,191.21 (276*2π)/3101 weeks
2776,253.585 -2,854.179 (277*2π)/3101 weeks
278-357.7524 -4,641.708 (278*2π)/3101 weeks
279-2,702.86 -9,936.271 (279*2π)/3101 weeks
28028.16508 -15,311.67 (280*2π)/3101 weeks
2816,150.969 -16,128.39 (281*2π)/3101 weeks
2829,259.244 -11,142.68 (282*2π)/3101 weeks
2835,520.53 -6,123.336 (283*2π)/3101 weeks
284601.9272 -9,032.897 (284*2π)/3101 weeks
285608.3635 -11,917.98 (285*2π)/3101 weeks
286679.8571 -13,579.57 (286*2π)/3101 weeks
287539.1749 -16,706.65 (287*2π)/3101 weeks
2885,463.697 -20,169.36 (288*2π)/3101 weeks
28910,683.4 -14,780.18 (289*2π)/3101 weeks
2906,298.135 -8,984.034 (290*2π)/3101 weeks
291-1,223.052 -10,749.77 (291*2π)/3101 weeks
292-3,081.331 -17,843.33 (292*2π)/3101 weeks
293-914.7322 -23,998.14 (293*2π)/3101 weeks
2945,320.422 -26,551.01 (294*2π)/3101 weeks
29511,161.93 -23,365.77 (295*2π)/3101 weeks
2969,442.657 -16,220.38 (296*2π)/3101 weeks
297328.0695 -16,746.45 (297*2π)/3101 weeks
298-3,362.997 -24,031.93 (298*2π)/3101 weeks
299-2,237.225 -32,591.71 (299*2π)/3101 weeks
3002,112.202 -37,059.73 (300*2π)/3101 weeks
3014,129.768 -40,364.32 (301*2π)/3101 weeks
30210,175.12 -47,153.55 (302*2π)/3101 weeks
30319,324.06 -41,156.42 (303*2π)/3101 weeks
3049,601.364 -31,782.63 (304*2π)/3101 weeks
305-18,000.45 -39,371.3 (305*2π)/3101 weeks
306-41,586.64 -88,087.23 (306*2π)/3101 weeks
307-20,660.99 -172,833.3 (307*2π)/3101 weeks
30887,078.02 -251,490 (308*2π)/3101 weeks



Back to list of Stocks