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Fourier Analysis of UGAZ (VelocityShares 3x Long Natural Gas ETN)


UGAZ (VelocityShares 3x Long Natural Gas ETN) appears to have interesting cyclic behaviour every 27 weeks (246.8796*sine), 20 weeks (226.4639*cosine), and 20 weeks (205.3835*sine).

UGAZ (VelocityShares 3x Long Natural Gas ETN) has an average price of 1,551.36 (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 10/9/2017 for UGAZ (VelocityShares 3x Long Natural Gas ETN), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
01,551.36   0 
1313.1739 1,845.612 (1*2π)/297297 weeks
274.24506 292.2942 (2*2π)/297149 weeks
367.10954 660.7095 (3*2π)/29799 weeks
4-181.5853 79.3698 (4*2π)/29774 weeks
5242.3929 126.6124 (5*2π)/29759 weeks
664.44351 253.8636 (6*2π)/29750 weeks
7-49.85971 62.59818 (7*2π)/29742 weeks
8230.6225 -52.25975 (8*2π)/29737 weeks
9231.3486 182.9018 (9*2π)/29733 weeks
10180.1973 206.9693 (10*2π)/29730 weeks
119.25838 246.8796 (11*2π)/29727 weeks
12-.05052 48.41196 (12*2π)/29725 weeks
1357.1339 26.91778 (13*2π)/29723 weeks
14210.7343 -35.38383 (14*2π)/29721 weeks
15226.4639 205.3835 (15*2π)/29720 weeks
1676.77512 154.5542 (16*2π)/29719 weeks
17113.2547 140.3803 (17*2π)/29717 weeks
1876.13677 152.8856 (18*2π)/29717 weeks
1952.31631 136.367 (19*2π)/29716 weeks
2059.07679 117.2747 (20*2π)/29715 weeks
2118.16343 116.8481 (21*2π)/29714 weeks
2247.14986 45.62697 (22*2π)/29714 weeks
2367.97646 58.78328 (23*2π)/29713 weeks
24134.4071 36.2938 (24*2π)/29712 weeks
25134.8747 156.0851 (25*2π)/29712 weeks
2680.24094 146.3004 (26*2π)/29711 weeks
2737.09983 160.8324 (27*2π)/29711 weeks
2843.82665 98.95496 (28*2π)/29711 weeks
2943.02197 170.8686 (29*2π)/29710 weeks
30-33.86509 102.8182 (30*2π)/29710 weeks
3133.29807 101.6498 (31*2π)/29710 weeks
32-52.02031 123.8899 (32*2π)/2979 weeks
33-38.9545 11.54192 (33*2π)/2979 weeks
3435.55149 24.72527 (34*2π)/2979 weeks
3517.54675 53.06525 (35*2π)/2978 weeks
3641.25413 13.23501 (36*2π)/2978 weeks
3755.11616 91.16058 (37*2π)/2978 weeks
38-16.1885 40.86167 (38*2π)/2978 weeks
3945.73755 23.54964 (39*2π)/2978 weeks
4034.55226 29.74564 (40*2π)/2977 weeks
4159.33032 37.17873 (41*2π)/2977 weeks
4240.1511 29.83729 (42*2π)/2977 weeks
43100.3571 25.27403 (43*2π)/2977 weeks
4487.15475 112.2096 (44*2π)/2977 weeks
4516.64948 102.0188 (45*2π)/2977 weeks
466.30885 53.44224 (46*2π)/2976 weeks
4745.12957 47.0237 (47*2π)/2976 weeks
4829.71722 61.1013 (48*2π)/2976 weeks
4949.9534 53.82144 (49*2π)/2976 weeks
5028.76513 82.73724 (50*2π)/2976 weeks
5122.4309 46.87531 (51*2π)/2976 weeks
5253.28741 70.51749 (52*2π)/2976 weeks
5313.05568 94.45494 (53*2π)/2976 weeks
54-7.65363 77.91396 (54*2π)/2976 weeks
55-30.7808 43.87222 (55*2π)/2975 weeks
56-3.76984 20.48212 (56*2π)/2975 weeks
573.82368 -5.33679 (57*2π)/2975 weeks
5871.55523 10.15597 (58*2π)/2975 weeks
5937.50099 69.01471 (59*2π)/2975 weeks
6015.34206 36.95579 (60*2π)/2975 weeks
6137.25763 34.87675 (61*2π)/2975 weeks
6225.63322 55.24056 (62*2π)/2975 weeks
6314.81118 22.14858 (63*2π)/2975 weeks
6460.35403 38.74843 (64*2π)/2975 weeks
6515.57824 61.82676 (65*2π)/2975 weeks
6646.32974 18.3852 (66*2π)/2975 weeks
6767.69785 88.92875 (67*2π)/2974 weeks
68-5.17082 110.864 (68*2π)/2974 weeks
69-45.51731 52.2668 (69*2π)/2974 weeks
70-10.94198 14.86793 (70*2π)/2974 weeks
7111.32416 18.52211 (71*2π)/2974 weeks
7213.75066 28.82984 (72*2π)/2974 weeks
7321.69324 34.25349 (73*2π)/2974 weeks
74-.79736 37.57119 (74*2π)/2974 weeks
7520.67509 14.47856 (75*2π)/2974 weeks
7620.59554 55.12924 (76*2π)/2974 weeks
77-17.99015 24.59403 (77*2π)/2974 weeks
7823.84612 9.44346 (78*2π)/2974 weeks
7916.32792 40.36243 (79*2π)/2974 weeks
803.34298 17.13878 (80*2π)/2974 weeks
8128.17161 25.88604 (81*2π)/2974 weeks
821.77454 46.32534 (82*2π)/2974 weeks
83-5.69065 9.66251 (83*2π)/2974 weeks
8424.3341 12.09326 (84*2π)/2974 weeks
8516.28034 35.61489 (85*2π)/2973 weeks
86-4.11366 14.88467 (86*2π)/2973 weeks
8725.98036 10.0889 (87*2π)/2973 weeks
8810.59033 31.79216 (88*2π)/2973 weeks
8915.51785 7.2945 (89*2π)/2973 weeks
9025.65775 35.13219 (90*2π)/2973 weeks
91-1.36601 28.4105 (91*2π)/2973 weeks
927.40839 16.58738 (92*2π)/2973 weeks
939.05462 20.82343 (93*2π)/2973 weeks
94-5.90238 23.80574 (94*2π)/2973 weeks
95-3.34763 -11.80307 (95*2π)/2973 weeks
9631.14174 13.27927 (96*2π)/2973 weeks
97-5.03394 12.71073 (97*2π)/2973 weeks
9818.32393 -1.68394 (98*2π)/2973 weeks
9911.81446 11.82448 (99*2π)/2973 weeks
1004.94336 -.32132 (100*2π)/2973 weeks
10118.42385 -18.87899 (101*2π)/2973 weeks
10245.10255 2.94456 (102*2π)/2973 weeks
10323.73359 11.78908 (103*2π)/2973 weeks
10439.60173 9.89919 (104*2π)/2973 weeks
10523.35645 27.59533 (105*2π)/2973 weeks
10616.04286 13.53026 (106*2π)/2973 weeks
10723.50478 9.54225 (107*2π)/2973 weeks
10820.23239 21.15678 (108*2π)/2973 weeks
10917.32561 1.25922 (109*2π)/2973 weeks
11041.5796 22.8084 (110*2π)/2973 weeks
1115.06417 31.62885 (111*2π)/2973 weeks
11214.45578 11.50514 (112*2π)/2973 weeks
113-.63082 13.91687 (113*2π)/2973 weeks
11421.78647 -9.94523 (114*2π)/2973 weeks
11525.10445 14.33961 (115*2π)/2973 weeks
11627.25423 6.07426 (116*2π)/2973 weeks
11724.17983 26.4471 (117*2π)/2973 weeks
11816.07957 19.65925 (118*2π)/2973 weeks
1193.15924 22.58842 (119*2π)/2972 weeks
12010.36164 .7155 (120*2π)/2972 weeks
1217.00088 22.71749 (121*2π)/2972 weeks
122-4.69218 -14.55076 (122*2π)/2972 weeks
12332.41524 -3.96884 (123*2π)/2972 weeks
12418.1148 7.34232 (124*2π)/2972 weeks
12528.70774 3.23063 (125*2π)/2972 weeks
12626.35172 24.40314 (126*2π)/2972 weeks
127-2.04064 21.9564 (127*2π)/2972 weeks
1282.25224 -6.94668 (128*2π)/2972 weeks
12916.64256 3.38154 (129*2π)/2972 weeks
1306.66846 -5.2076 (130*2π)/2972 weeks
13126.05004 -5.95534 (131*2π)/2972 weeks
13220.45104 6.12977 (132*2π)/2972 weeks
13319.22796 -2.46297 (133*2π)/2972 weeks
13430.76025 6.22735 (134*2π)/2972 weeks
13515.36032 19.85779 (135*2π)/2972 weeks
1362.42379 -.68542 (136*2π)/2972 weeks
13725.85555 -3.34953 (137*2π)/2972 weeks
13814.71225 14.02942 (138*2π)/2972 weeks
13912.85046 -.56387 (139*2π)/2972 weeks
14012.46058 8.24515 (140*2π)/2972 weeks
1414.13558 -1.74097 (141*2π)/2972 weeks
1428.69277 -21.21288 (142*2π)/2972 weeks
14342.69791 -7.35468 (143*2π)/2972 weeks
14415.62461 10.7125 (144*2π)/2972 weeks
14526.08313 -8.52026 (145*2π)/2972 weeks
14630.28701 13.5157 (146*2π)/2972 weeks
14712.47443 15.25365 (147*2π)/2972 weeks
1484.2288 6.95833 (148*2π)/2972 weeks
1494.2288 -6.95833 (149*2π)/2972 weeks
15012.47443 -15.25365 (150*2π)/2972 weeks
15130.28701 -13.5157 (151*2π)/2972 weeks
15226.08313 8.52026 (152*2π)/2972 weeks
15315.62461 -10.7125 (153*2π)/2972 weeks
15442.69791 7.35468 (154*2π)/2972 weeks
1558.69277 21.21288 (155*2π)/2972 weeks
1564.13558 1.74097 (156*2π)/2972 weeks
15712.46058 -8.24515 (157*2π)/2972 weeks
15812.85046 .56387 (158*2π)/2972 weeks
15914.71225 -14.02942 (159*2π)/2972 weeks
16025.85555 3.34953 (160*2π)/2972 weeks
1612.42379 .68542 (161*2π)/2972 weeks
16215.36032 -19.85779 (162*2π)/2972 weeks
16330.76025 -6.22735 (163*2π)/2972 weeks
16419.22796 2.46297 (164*2π)/2972 weeks
16520.45104 -6.12977 (165*2π)/2972 weeks
16626.05004 5.95534 (166*2π)/2972 weeks
1676.66846 5.2076 (167*2π)/2972 weeks
16816.64256 -3.38154 (168*2π)/2972 weeks
1692.25224 6.94668 (169*2π)/2972 weeks
170-2.04064 -21.9564 (170*2π)/2972 weeks
17126.35172 -24.40314 (171*2π)/2972 weeks
17228.70774 -3.23063 (172*2π)/2972 weeks
17318.1148 -7.34232 (173*2π)/2972 weeks
17432.41524 3.96884 (174*2π)/2972 weeks
175-4.69218 14.55076 (175*2π)/2972 weeks
1767.00088 -22.71749 (176*2π)/2972 weeks
17710.36164 -.7155 (177*2π)/2972 weeks
1783.15924 -22.58842 (178*2π)/2972 weeks
17916.07957 -19.65925 (179*2π)/2972 weeks
18024.17983 -26.4471 (180*2π)/2972 weeks
18127.25423 -6.07426 (181*2π)/2972 weeks
18225.10445 -14.33961 (182*2π)/2972 weeks
18321.78647 9.94523 (183*2π)/2972 weeks
184-.63082 -13.91687 (184*2π)/2972 weeks
18514.45578 -11.50514 (185*2π)/2972 weeks
1865.06417 -31.62885 (186*2π)/2972 weeks
18741.5796 -22.8084 (187*2π)/2972 weeks
18817.32561 -1.25922 (188*2π)/2972 weeks
18920.23239 -21.15678 (189*2π)/2972 weeks
19023.50478 -9.54225 (190*2π)/2972 weeks
19116.04286 -13.53026 (191*2π)/2972 weeks
19223.35645 -27.59533 (192*2π)/2972 weeks
19339.60173 -9.89919 (193*2π)/2972 weeks
19423.73359 -11.78908 (194*2π)/2972 weeks
19545.10255 -2.94456 (195*2π)/2972 weeks
19618.42385 18.87899 (196*2π)/2972 weeks
1974.94336 .32132 (197*2π)/2972 weeks
19811.81446 -11.82448 (198*2π)/2972 weeks
19918.32393 1.68394 (199*2π)/2971 weeks
200-5.03394 -12.71073 (200*2π)/2971 weeks
20131.14174 -13.27927 (201*2π)/2971 weeks
202-3.34763 11.80307 (202*2π)/2971 weeks
203-5.90238 -23.80574 (203*2π)/2971 weeks
2049.05462 -20.82343 (204*2π)/2971 weeks
2057.40839 -16.58738 (205*2π)/2971 weeks
206-1.36601 -28.4105 (206*2π)/2971 weeks
20725.65775 -35.13219 (207*2π)/2971 weeks
20815.51785 -7.2945 (208*2π)/2971 weeks
20910.59033 -31.79216 (209*2π)/2971 weeks
21025.98036 -10.0889 (210*2π)/2971 weeks
211-4.11366 -14.88467 (211*2π)/2971 weeks
21216.28034 -35.61489 (212*2π)/2971 weeks
21324.3341 -12.09326 (213*2π)/2971 weeks
214-5.69065 -9.66251 (214*2π)/2971 weeks
2151.77454 -46.32534 (215*2π)/2971 weeks
21628.17161 -25.88604 (216*2π)/2971 weeks
2173.34298 -17.13878 (217*2π)/2971 weeks
21816.32792 -40.36243 (218*2π)/2971 weeks
21923.84612 -9.44346 (219*2π)/2971 weeks
220-17.99015 -24.59403 (220*2π)/2971 weeks
22120.59554 -55.12924 (221*2π)/2971 weeks
22220.67509 -14.47856 (222*2π)/2971 weeks
223-.79736 -37.57119 (223*2π)/2971 weeks
22421.69324 -34.25349 (224*2π)/2971 weeks
22513.75066 -28.82984 (225*2π)/2971 weeks
22611.32416 -18.52211 (226*2π)/2971 weeks
227-10.94198 -14.86793 (227*2π)/2971 weeks
228-45.51731 -52.2668 (228*2π)/2971 weeks
229-5.17082 -110.864 (229*2π)/2971 weeks
23067.69785 -88.92875 (230*2π)/2971 weeks
23146.32974 -18.3852 (231*2π)/2971 weeks
23215.57824 -61.82676 (232*2π)/2971 weeks
23360.35403 -38.74843 (233*2π)/2971 weeks
23414.81118 -22.14858 (234*2π)/2971 weeks
23525.63322 -55.24056 (235*2π)/2971 weeks
23637.25763 -34.87675 (236*2π)/2971 weeks
23715.34206 -36.95579 (237*2π)/2971 weeks
23837.50099 -69.01471 (238*2π)/2971 weeks
23971.55523 -10.15597 (239*2π)/2971 weeks
2403.82368 5.33679 (240*2π)/2971 weeks
241-3.76984 -20.48212 (241*2π)/2971 weeks
242-30.7808 -43.87222 (242*2π)/2971 weeks
243-7.65363 -77.91396 (243*2π)/2971 weeks
24413.05568 -94.45494 (244*2π)/2971 weeks
24553.28741 -70.51749 (245*2π)/2971 weeks
24622.4309 -46.87531 (246*2π)/2971 weeks
24728.76513 -82.73724 (247*2π)/2971 weeks
24849.9534 -53.82144 (248*2π)/2971 weeks
24929.71722 -61.1013 (249*2π)/2971 weeks
25045.12957 -47.0237 (250*2π)/2971 weeks
2516.30885 -53.44224 (251*2π)/2971 weeks
25216.64948 -102.0188 (252*2π)/2971 weeks
25387.15475 -112.2096 (253*2π)/2971 weeks
254100.3571 -25.27403 (254*2π)/2971 weeks
25540.1511 -29.83729 (255*2π)/2971 weeks
25659.33032 -37.17873 (256*2π)/2971 weeks
25734.55226 -29.74564 (257*2π)/2971 weeks
25845.73755 -23.54964 (258*2π)/2971 weeks
259-16.1885 -40.86167 (259*2π)/2971 weeks
26055.11616 -91.16058 (260*2π)/2971 weeks
26141.25413 -13.23501 (261*2π)/2971 weeks
26217.54675 -53.06525 (262*2π)/2971 weeks
26335.55149 -24.72527 (263*2π)/2971 weeks
264-38.9545 -11.54192 (264*2π)/2971 weeks
265-52.02031 -123.8899 (265*2π)/2971 weeks
26633.29807 -101.6498 (266*2π)/2971 weeks
267-33.86509 -102.8182 (267*2π)/2971 weeks
26843.02197 -170.8686 (268*2π)/2971 weeks
26943.82665 -98.95496 (269*2π)/2971 weeks
27037.09983 -160.8324 (270*2π)/2971 weeks
27180.24094 -146.3004 (271*2π)/2971 weeks
272134.8747 -156.0851 (272*2π)/2971 weeks
273134.4071 -36.2938 (273*2π)/2971 weeks
27467.97646 -58.78328 (274*2π)/2971 weeks
27547.14986 -45.62697 (275*2π)/2971 weeks
27618.16343 -116.8481 (276*2π)/2971 weeks
27759.07679 -117.2747 (277*2π)/2971 weeks
27852.31631 -136.367 (278*2π)/2971 weeks
27976.13677 -152.8856 (279*2π)/2971 weeks
280113.2547 -140.3803 (280*2π)/2971 weeks
28176.77512 -154.5542 (281*2π)/2971 weeks
282226.4639 -205.3835 (282*2π)/2971 weeks
283210.7343 35.38383 (283*2π)/2971 weeks
28457.1339 -26.91778 (284*2π)/2971 weeks
285-.05052 -48.41196 (285*2π)/2971 weeks
2869.25838 -246.8796 (286*2π)/2971 weeks
287180.1973 -206.9693 (287*2π)/2971 weeks
288231.3486 -182.9018 (288*2π)/2971 weeks
289230.6225 52.25975 (289*2π)/2971 weeks
290-49.85971 -62.59818 (290*2π)/2971 weeks
29164.44351 -253.8636 (291*2π)/2971 weeks
292242.3929 -126.6124 (292*2π)/2971 weeks
293-181.5853 -79.3698 (293*2π)/2971 weeks
29467.10954 -660.7095 (294*2π)/2971 weeks
29574.24506 -292.2942 (295*2π)/2971 weeks



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