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Fourier Analysis of UGAZ (VelocityShares 3X Long Natural )


UGAZ (VelocityShares 3X Long Natural ) appears to have interesting cyclic behaviour every 21 weeks (312.796*cosine), 27 weeks (257.8308*sine), and 12 weeks (185.7413*cosine).

UGAZ (VelocityShares 3X Long Natural ) has an average price of 1,717.62 (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 2/8/2012 to 3/20/2017 for UGAZ (VelocityShares 3X Long Natural ), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
01,717.62   0 
164.05019 1,832.844 (1*2π)/268268 weeks
2275.5924 357.6729 (2*2π)/268134 weeks
3-169.3067 610.8299 (3*2π)/26889 weeks
464.82069 -39.96241 (4*2π)/26867 weeks
5178.0571 284.7437 (5*2π)/26854 weeks
6-40.71119 178.9918 (6*2π)/26845 weeks
7163.5852 -94.01355 (7*2π)/26838 weeks
8280.2722 188.1259 (8*2π)/26834 weeks
9200.1562 225.9366 (9*2π)/26830 weeks
10-8.15424 257.8308 (10*2π)/26827 weeks
1127.58921 40.89826 (11*2π)/26824 weeks
1274.52828 -7.18571 (12*2π)/26822 weeks
13312.796 61.80984 (13*2π)/26821 weeks
14126.6921 236.6847 (14*2π)/26819 weeks
15116.9622 139.898 (15*2π)/26818 weeks
1695.44252 173.9773 (16*2π)/26817 weeks
1762.71187 155.7009 (17*2π)/26816 weeks
1864.99483 128.7865 (18*2π)/26815 weeks
1916.86719 124.886 (19*2π)/26814 weeks
2064.99875 52.17323 (20*2π)/26813 weeks
2178.15802 52.78757 (21*2π)/26813 weeks
22185.7413 87.56709 (22*2π)/26812 weeks
2399.83706 173.7378 (23*2π)/26812 weeks
2473.46439 178.7419 (24*2π)/26811 weeks
2524.75698 121.0306 (25*2π)/26811 weeks
2667.47417 175.3891 (26*2π)/26810 weeks
27-39.75128 123.9904 (27*2π)/26810 weeks
2836.92783 115.4997 (28*2π)/26810 weeks
29-70.60188 121.0054 (29*2π)/2689 weeks
30-16.50141 3.30024 (30*2π)/2689 weeks
3142.21157 47.51733 (31*2π)/2689 weeks
3211.5739 36.53331 (32*2π)/2688 weeks
3384.74937 56.62669 (33*2π)/2688 weeks
34-12.19847 82.10318 (34*2π)/2688 weeks
3541.62131 14.96371 (35*2π)/2688 weeks
3637.34322 36.05508 (36*2π)/2687 weeks
3765.65206 41.27233 (37*2π)/2687 weeks
3846.98438 27.07812 (38*2π)/2687 weeks
39123.7533 47.64893 (39*2π)/2687 weeks
4065.02799 133.0755 (40*2π)/2687 weeks
415.09865 90.38739 (41*2π)/2687 weeks
4230.53284 42.46519 (42*2π)/2686 weeks
4342.19425 72.38059 (43*2π)/2686 weeks
4447.53329 53.76853 (44*2π)/2686 weeks
4538.96804 91.9016 (45*2π)/2686 weeks
4623.82191 52.38683 (46*2π)/2686 weeks
4758.09594 83.153 (47*2π)/2686 weeks
486.71089 99.9248 (48*2π)/2686 weeks
49-18.05018 82.07449 (49*2π)/2685 weeks
50-23.06316 27.30793 (50*2π)/2685 weeks
51-5.70537 16.5133 (51*2π)/2685 weeks
5253.24333 -13.55537 (52*2π)/2685 weeks
5361.55262 71.96537 (53*2π)/2685 weeks
5414.87474 46.23254 (54*2π)/2685 weeks
5540.46393 37.51894 (55*2π)/2685 weeks
5625.97566 60.92805 (56*2π)/2685 weeks
5724.38375 18.51143 (57*2π)/2685 weeks
5862.70872 62.54735 (58*2π)/2685 weeks
5910.82197 41.9974 (59*2π)/2685 weeks
6082.87804 51.31644 (60*2π)/2684 weeks
6128.71926 126.4357 (61*2π)/2684 weeks
62-47.53427 81.49325 (62*2π)/2684 weeks
63-19.75516 17.68167 (63*2π)/2684 weeks
6411.03627 19.67121 (64*2π)/2684 weeks
6515.11054 31.79278 (65*2π)/2684 weeks
6623.27172 41.69799 (66*2π)/2684 weeks
67-3.14022 31.62739 (67*2π)/2684 weeks
6836.04013 28.83378 (68*2π)/2684 weeks
69-6.64118 58.95674 (69*2π)/2684 weeks
704.88928 3.25817 (70*2π)/2684 weeks
7128.67882 38.31569 (71*2π)/2684 weeks
72-.16728 25.87163 (72*2π)/2684 weeks
7330.13403 25.12064 (73*2π)/2684 weeks
741.56058 51.14391 (74*2π)/2684 weeks
75-2.4586 7.55693 (75*2π)/2684 weeks
7629.29919 20.10069 (76*2π)/2684 weeks
776.13336 39.39347 (77*2π)/2683 weeks
788.52758 3.97704 (78*2π)/2683 weeks
7927.74276 31.31213 (79*2π)/2683 weeks
805.58543 14.19503 (80*2π)/2683 weeks
8133.60263 30.3911 (81*2π)/2683 weeks
82-.15621 35.07532 (82*2π)/2683 weeks
837.99392 18.26543 (83*2π)/2683 weeks
849.80302 23.78753 (84*2π)/2683 weeks
85-11.81328 21.5724 (85*2π)/2683 weeks
8614.00133 -16.62018 (86*2π)/2683 weeks
8717.59646 29.84998 (87*2π)/2683 weeks
884.87909 -5.36536 (88*2π)/2683 weeks
8919.53364 11.58825 (89*2π)/2683 weeks
905.56868 3.89813 (90*2π)/2683 weeks
9115.04258 -18.4619 (91*2π)/2683 weeks
9250.10857 1.32261 (92*2π)/2683 weeks
9325.91736 11.47713 (93*2π)/2683 weeks
9444.71727 16.57433 (94*2π)/2683 weeks
9519.50629 26.87562 (95*2π)/2683 weeks
9620.15393 12.23884 (96*2π)/2683 weeks
9729.99222 16.92282 (97*2π)/2683 weeks
9812.49785 12.42771 (98*2π)/2683 weeks
9944.94981 10.93972 (99*2π)/2683 weeks
10012.17004 40.45869 (100*2π)/2683 weeks
10114.61265 11.77911 (101*2π)/2683 weeks
102-1.38207 14.02302 (102*2π)/2683 weeks
10329.85017 -7.84407 (103*2π)/2683 weeks
10422.89807 14.32039 (104*2π)/2683 weeks
10536.41456 14.10248 (105*2π)/2683 weeks
10616.86434 25.49689 (106*2π)/2683 weeks
10713.54727 27.16393 (107*2π)/2683 weeks
1081.57827 4.78438 (108*2π)/2682 weeks
10916.16002 22.39551 (109*2π)/2682 weeks
110-8.98515 -11.65898 (110*2π)/2682 weeks
11135.92626 -3.98054 (111*2π)/2682 weeks
11219.40376 6.21843 (112*2π)/2682 weeks
11334.48868 7.94981 (113*2π)/2682 weeks
11419.31084 31.91409 (114*2π)/2682 weeks
115-7.93991 8.85846 (115*2π)/2682 weeks
11617.58497 -5.15468 (116*2π)/2682 weeks
1177.57787 2.32605 (117*2π)/2682 weeks
11825.02698 -10.73486 (118*2π)/2682 weeks
11924.32983 6.72362 (119*2π)/2682 weeks
12021.09169 -2.55418 (120*2π)/2682 weeks
12134.04483 9.15219 (121*2π)/2682 weeks
12211.48291 20.62895 (122*2π)/2682 weeks
1239.50361 -8.33616 (123*2π)/2682 weeks
12429.89018 8.13429 (124*2π)/2682 weeks
1258.55763 5.78637 (125*2π)/2682 weeks
12618.74951 5.93496 (126*2π)/2682 weeks
1274.94056 1.34634 (127*2π)/2682 weeks
1285.92732 -19.27121 (128*2π)/2682 weeks
12946.8573 -10.30117 (129*2π)/2682 weeks
13015.56774 9.95351 (130*2π)/2682 weeks
13133.64843 -6.75704 (131*2π)/2682 weeks
13227.48139 18.54251 (132*2π)/2682 weeks
1339.58163 13.24295 (133*2π)/2682 weeks
1341.96463   (134*2π)/2682 weeks
1359.58163 -13.24295 (135*2π)/2682 weeks
13627.48139 -18.54251 (136*2π)/2682 weeks
13733.64843 6.75704 (137*2π)/2682 weeks
13815.56774 -9.95351 (138*2π)/2682 weeks
13946.8573 10.30117 (139*2π)/2682 weeks
1405.92732 19.27121 (140*2π)/2682 weeks
1414.94056 -1.34634 (141*2π)/2682 weeks
14218.74951 -5.93496 (142*2π)/2682 weeks
1438.55763 -5.78637 (143*2π)/2682 weeks
14429.89018 -8.13429 (144*2π)/2682 weeks
1459.50361 8.33616 (145*2π)/2682 weeks
14611.48291 -20.62895 (146*2π)/2682 weeks
14734.04483 -9.15219 (147*2π)/2682 weeks
14821.09169 2.55418 (148*2π)/2682 weeks
14924.32983 -6.72362 (149*2π)/2682 weeks
15025.02698 10.73486 (150*2π)/2682 weeks
1517.57787 -2.32605 (151*2π)/2682 weeks
15217.58497 5.15468 (152*2π)/2682 weeks
153-7.93991 -8.85846 (153*2π)/2682 weeks
15419.31084 -31.91409 (154*2π)/2682 weeks
15534.48868 -7.94981 (155*2π)/2682 weeks
15619.40376 -6.21843 (156*2π)/2682 weeks
15735.92626 3.98054 (157*2π)/2682 weeks
158-8.98515 11.65898 (158*2π)/2682 weeks
15916.16002 -22.39551 (159*2π)/2682 weeks
1601.57827 -4.78438 (160*2π)/2682 weeks
16113.54727 -27.16393 (161*2π)/2682 weeks
16216.86434 -25.49689 (162*2π)/2682 weeks
16336.41456 -14.10248 (163*2π)/2682 weeks
16422.89807 -14.32039 (164*2π)/2682 weeks
16529.85017 7.84407 (165*2π)/2682 weeks
166-1.38207 -14.02302 (166*2π)/2682 weeks
16714.61265 -11.77911 (167*2π)/2682 weeks
16812.17004 -40.45869 (168*2π)/2682 weeks
16944.94981 -10.93972 (169*2π)/2682 weeks
17012.49785 -12.42771 (170*2π)/2682 weeks
17129.99222 -16.92282 (171*2π)/2682 weeks
17220.15393 -12.23884 (172*2π)/2682 weeks
17319.50629 -26.87562 (173*2π)/2682 weeks
17444.71727 -16.57433 (174*2π)/2682 weeks
17525.91736 -11.47713 (175*2π)/2682 weeks
17650.10857 -1.32261 (176*2π)/2682 weeks
17715.04258 18.4619 (177*2π)/2682 weeks
1785.56868 -3.89813 (178*2π)/2682 weeks
17919.53364 -11.58825 (179*2π)/2681 weeks
1804.87909 5.36536 (180*2π)/2681 weeks
18117.59646 -29.84998 (181*2π)/2681 weeks
18214.00133 16.62018 (182*2π)/2681 weeks
183-11.81328 -21.5724 (183*2π)/2681 weeks
1849.80302 -23.78753 (184*2π)/2681 weeks
1857.99392 -18.26543 (185*2π)/2681 weeks
186-.15621 -35.07532 (186*2π)/2681 weeks
18733.60263 -30.3911 (187*2π)/2681 weeks
1885.58543 -14.19503 (188*2π)/2681 weeks
18927.74276 -31.31213 (189*2π)/2681 weeks
1908.52758 -3.97704 (190*2π)/2681 weeks
1916.13336 -39.39347 (191*2π)/2681 weeks
19229.29919 -20.10069 (192*2π)/2681 weeks
193-2.4586 -7.55693 (193*2π)/2681 weeks
1941.56058 -51.14391 (194*2π)/2681 weeks
19530.13403 -25.12064 (195*2π)/2681 weeks
196-.16728 -25.87163 (196*2π)/2681 weeks
19728.67882 -38.31569 (197*2π)/2681 weeks
1984.88928 -3.25817 (198*2π)/2681 weeks
199-6.64118 -58.95674 (199*2π)/2681 weeks
20036.04013 -28.83378 (200*2π)/2681 weeks
201-3.14022 -31.62739 (201*2π)/2681 weeks
20223.27172 -41.69799 (202*2π)/2681 weeks
20315.11054 -31.79278 (203*2π)/2681 weeks
20411.03627 -19.67121 (204*2π)/2681 weeks
205-19.75516 -17.68167 (205*2π)/2681 weeks
206-47.53427 -81.49325 (206*2π)/2681 weeks
20728.71926 -126.4357 (207*2π)/2681 weeks
20882.87804 -51.31644 (208*2π)/2681 weeks
20910.82197 -41.9974 (209*2π)/2681 weeks
21062.70872 -62.54735 (210*2π)/2681 weeks
21124.38375 -18.51143 (211*2π)/2681 weeks
21225.97566 -60.92805 (212*2π)/2681 weeks
21340.46393 -37.51894 (213*2π)/2681 weeks
21414.87474 -46.23254 (214*2π)/2681 weeks
21561.55262 -71.96537 (215*2π)/2681 weeks
21653.24333 13.55537 (216*2π)/2681 weeks
217-5.70537 -16.5133 (217*2π)/2681 weeks
218-23.06316 -27.30793 (218*2π)/2681 weeks
219-18.05018 -82.07449 (219*2π)/2681 weeks
2206.71089 -99.9248 (220*2π)/2681 weeks
22158.09594 -83.153 (221*2π)/2681 weeks
22223.82191 -52.38683 (222*2π)/2681 weeks
22338.96804 -91.9016 (223*2π)/2681 weeks
22447.53329 -53.76853 (224*2π)/2681 weeks
22542.19425 -72.38059 (225*2π)/2681 weeks
22630.53284 -42.46519 (226*2π)/2681 weeks
2275.09865 -90.38739 (227*2π)/2681 weeks
22865.02799 -133.0755 (228*2π)/2681 weeks
229123.7533 -47.64893 (229*2π)/2681 weeks
23046.98438 -27.07812 (230*2π)/2681 weeks
23165.65206 -41.27233 (231*2π)/2681 weeks
23237.34322 -36.05508 (232*2π)/2681 weeks
23341.62131 -14.96371 (233*2π)/2681 weeks
234-12.19847 -82.10318 (234*2π)/2681 weeks
23584.74937 -56.62669 (235*2π)/2681 weeks
23611.5739 -36.53331 (236*2π)/2681 weeks
23742.21157 -47.51733 (237*2π)/2681 weeks
238-16.50141 -3.30024 (238*2π)/2681 weeks
239-70.60188 -121.0054 (239*2π)/2681 weeks
24036.92783 -115.4997 (240*2π)/2681 weeks
241-39.75128 -123.9904 (241*2π)/2681 weeks
24267.47417 -175.3891 (242*2π)/2681 weeks
24324.75698 -121.0306 (243*2π)/2681 weeks
24473.46439 -178.7419 (244*2π)/2681 weeks
24599.83706 -173.7378 (245*2π)/2681 weeks
246185.7413 -87.56709 (246*2π)/2681 weeks
24778.15802 -52.78757 (247*2π)/2681 weeks
24864.99875 -52.17323 (248*2π)/2681 weeks
24916.86719 -124.886 (249*2π)/2681 weeks
25064.99483 -128.7865 (250*2π)/2681 weeks
25162.71187 -155.7009 (251*2π)/2681 weeks
25295.44252 -173.9773 (252*2π)/2681 weeks
253116.9622 -139.898 (253*2π)/2681 weeks
254126.6921 -236.6847 (254*2π)/2681 weeks
255312.796 -61.80984 (255*2π)/2681 weeks
25674.52828 7.18571 (256*2π)/2681 weeks
25727.58921 -40.89826 (257*2π)/2681 weeks
258-8.15424 -257.8308 (258*2π)/2681 weeks
259200.1562 -225.9366 (259*2π)/2681 weeks
260280.2722 -188.1259 (260*2π)/2681 weeks
261163.5852 94.01355 (261*2π)/2681 weeks
262-40.71119 -178.9918 (262*2π)/2681 weeks
263178.0571 -284.7437 (263*2π)/2681 weeks
26464.82069 39.96241 (264*2π)/2681 weeks
265-169.3067 -610.8299 (265*2π)/2681 weeks
266275.5924 -357.6729 (266*2π)/2681 weeks

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