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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 20 weeks (295.2164*cosine), 28 weeks (272.0202*sine), and 12 weeks (147.0316*cosine).

UGAZ (VelocityShares 3x Long Natural Gas ETN) has an average price of 1,621.84 (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 7/10/2017 for UGAZ (VelocityShares 3x Long Natural Gas ETN), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
01,621.838   0 
1206.4032 1,850.71 (1*2π)/284284 weeks
2164.5632 302.922 (2*2π)/284142 weeks
3-35.3169 664.296 (3*2π)/28495 weeks
4-92.15425 -1.7326 (4*2π)/28471 weeks
5236.2402 211.5246 (5*2π)/28457 weeks
618.24983 237.9785 (6*2π)/28447 weeks
7-.33178 -34.53257 (7*2π)/28441 weeks
8308.7193 53.43351 (8*2π)/28436 weeks
9194.7339 193.7655 (9*2π)/28432 weeks
10138.5938 272.0202 (10*2π)/28428 weeks
11-48.20958 141.9512 (11*2π)/28426 weeks
1257.34771 39.52972 (12*2π)/28424 weeks
13115.4903 -43.11349 (13*2π)/28422 weeks
14295.2164 130.6377 (14*2π)/28420 weeks
1595.07969 203.4379 (15*2π)/28419 weeks
16114.7376 135.2802 (16*2π)/28418 weeks
1787.92008 163.9093 (17*2π)/28417 weeks
1859.63358 147.537 (18*2π)/28416 weeks
1960.20214 120.8322 (19*2π)/28415 weeks
2024.38825 127.3593 (20*2π)/28414 weeks
2146.13186 47.97223 (21*2π)/28414 weeks
2271.07524 61.26219 (22*2π)/28413 weeks
23147.0316 41.88259 (23*2π)/28412 weeks
24129.594 167.6785 (24*2π)/28412 weeks
2583.45802 154.8645 (25*2π)/28411 weeks
2625.25344 157.892 (26*2π)/28411 weeks
2764.9269 111.1743 (27*2π)/28411 weeks
288.51799 181.3945 (28*2π)/28410 weeks
29-11.59101 79.96706 (29*2π)/28410 weeks
3018.37615 138.0116 (30*2π)/2849 weeks
31-76.93794 75.63773 (31*2π)/2849 weeks
325.12477 3.68395 (32*2π)/2849 weeks
3336.71525 51.37599 (33*2π)/2849 weeks
3413.21745 28.89251 (34*2π)/2848 weeks
3580.05932 56.99167 (35*2π)/2848 weeks
36-9.55182 80.54348 (36*2π)/2848 weeks
3733.10169 10.93627 (37*2π)/2848 weeks
3836.19811 38.14125 (38*2π)/2847 weeks
3959.95236 31.14085 (39*2π)/2847 weeks
4041.68016 39.28934 (40*2π)/2847 weeks
4195.85775 19.07018 (41*2π)/2847 weeks
4297.67878 112.8417 (42*2π)/2847 weeks
4318.7608 108.0797 (43*2π)/2847 weeks
446.9254 55.20664 (44*2π)/2846 weeks
4548.29236 51.45993 (45*2π)/2846 weeks
4630.13321 60.92669 (46*2π)/2846 weeks
4754.90948 61.99823 (47*2π)/2846 weeks
4820.83871 82.15665 (48*2π)/2846 weeks
4934.27314 46.6677 (49*2π)/2846 weeks
5049.6488 89.1693 (50*2π)/2846 weeks
512.76654 90.87051 (51*2π)/2846 weeks
52-19.70056 75.6846 (52*2π)/2845 weeks
53-21.11086 25.38049 (53*2π)/2845 weeks
54-5.15625 17.11072 (54*2π)/2845 weeks
5541.08406 -15.5011 (55*2π)/2845 weeks
5669.14134 59.1653 (56*2π)/2845 weeks
5714.26783 52.98537 (57*2π)/2845 weeks
5831.98126 31.59085 (58*2π)/2845 weeks
5936.50773 54.30596 (59*2π)/2845 weeks
609.60687 34.80363 (60*2π)/2845 weeks
6158.04056 27.25631 (61*2π)/2845 weeks
6225.34801 70.85129 (62*2π)/2845 weeks
6338.82799 18.24452 (63*2π)/2845 weeks
6474.0704 87.47493 (64*2π)/2844 weeks
65-3.52663 116.5714 (65*2π)/2844 weeks
66-47.45275 53.05591 (66*2π)/2844 weeks
67-9.18568 15.46142 (67*2π)/2844 weeks
6813.72709 20.80938 (68*2π)/2844 weeks
6914.30313 29.42053 (69*2π)/2844 weeks
7021.21156 40.90456 (70*2π)/2844 weeks
71-2.94218 29.87232 (71*2π)/2844 weeks
7232.6206 24.33462 (72*2π)/2844 weeks
73.91925 59.10447 (73*2π)/2844 weeks
74-5.539 6.60918 (74*2π)/2844 weeks
7530.90996 27.24774 (75*2π)/2844 weeks
761.67798 35.51496 (76*2π)/2844 weeks
7720.11376 14.92041 (77*2π)/2844 weeks
7821.09348 46.35588 (78*2π)/2844 weeks
79-12.87817 24.90969 (79*2π)/2844 weeks
8017.17381 5.36042 (80*2π)/2844 weeks
8124.1434 32.04454 (81*2π)/2844 weeks
82-4.66534 25.46474 (82*2π)/2843 weeks
8321.57196 5.42615 (83*2π)/2843 weeks
8416.58026 34.1583 (84*2π)/2843 weeks
8512.16058 8.35641 (85*2π)/2843 weeks
8628.54268 34.86655 (86*2π)/2843 weeks
87-1.32654 30.17971 (87*2π)/2843 weeks
887.94595 17.46268 (88*2π)/2843 weeks
899.31746 22.34927 (89*2π)/2843 weeks
90-9.2919 22.48447 (90*2π)/2843 weeks
915.16753 -15.58494 (91*2π)/2843 weeks
9226.29721 23.55769 (92*2π)/2843 weeks
93-3.40417 2.01286 (93*2π)/2843 weeks
9421.46548 5.28789 (94*2π)/2843 weeks
957.5346 9.40103 (95*2π)/2843 weeks
966.42239 -7.40528 (96*2π)/2843 weeks
9736.91492 -17.31001 (97*2π)/2843 weeks
9837.10717 16.90534 (98*2π)/2843 weeks
9931.16152 3.12561 (99*2π)/2843 weeks
10036.18867 26.503 (100*2π)/2843 weeks
10115.59665 19.15699 (101*2π)/2843 weeks
10221.00505 10.20175 (102*2π)/2843 weeks
10326.62258 19.68903 (103*2π)/2843 weeks
10412.89739 7.14202 (104*2π)/2843 weeks
10543.76122 14.52429 (105*2π)/2843 weeks
10610.27139 37.45448 (106*2π)/2843 weeks
10713.16707 10.83807 (107*2π)/2843 weeks
108.43551 16.31637 (108*2π)/2843 weeks
10922.32739 -10.56602 (109*2π)/2843 weeks
11025.47934 15.01824 (110*2π)/2843 weeks
11130.21927 7.21814 (111*2π)/2843 weeks
11221.911 27.74346 (112*2π)/2843 weeks
11317.05115 21.78041 (113*2π)/2843 weeks
114-.64387 18.65261 (114*2π)/2842 weeks
11518.31876 4.62468 (115*2π)/2842 weeks
116-5.81361 18.56577 (116*2π)/2842 weeks
11713.0979 -22.12204 (117*2π)/2842 weeks
11829.85823 7.69273 (118*2π)/2842 weeks
11920.56347 1.4433 (119*2π)/2842 weeks
12033.41485 13.5464 (120*2π)/2842 weeks
12111.53303 30.30935 (121*2π)/2842 weeks
122-6.67487 3.3612 (122*2π)/2842 weeks
12317.57686 -3.4101 (123*2π)/2842 weeks
1246.99026 1.8699 (124*2π)/2842 weeks
12522.61417 -10.7532 (125*2π)/2842 weeks
12624.34902 5.78922 (126*2π)/2842 weeks
12718.07965 -.96273 (127*2π)/2842 weeks
12831.59491 3.65883 (128*2π)/2842 weeks
12918.55458 20.84126 (129*2π)/2842 weeks
1302.0095 .79888 (130*2π)/2842 weeks
13126.99705 -3.57016 (131*2π)/2842 weeks
13214.3181 14.37582 (132*2π)/2842 weeks
13314.78526 -.51186 (133*2π)/2842 weeks
13410.73294 8.42334 (134*2π)/2842 weeks
1353.92878 -3.87884 (135*2π)/2842 weeks
13617.12464 -26.37729 (136*2π)/2842 weeks
13742.41395 5.17961 (137*2π)/2842 weeks
13812.30564 1.43345 (138*2π)/2842 weeks
13935.06321 -1.95373 (139*2π)/2842 weeks
14023.36965 18.10999 (140*2π)/2842 weeks
1418.61161 11.97068 (141*2π)/2842 weeks
1421.90028   (142*2π)/2842 weeks
1438.61161 -11.97068 (143*2π)/2842 weeks
14423.36965 -18.10999 (144*2π)/2842 weeks
14535.06321 1.95373 (145*2π)/2842 weeks
14612.30564 -1.43345 (146*2π)/2842 weeks
14742.41395 -5.17961 (147*2π)/2842 weeks
14817.12464 26.37729 (148*2π)/2842 weeks
1493.92878 3.87884 (149*2π)/2842 weeks
15010.73294 -8.42334 (150*2π)/2842 weeks
15114.78526 .51186 (151*2π)/2842 weeks
15214.3181 -14.37582 (152*2π)/2842 weeks
15326.99705 3.57016 (153*2π)/2842 weeks
1542.0095 -.79888 (154*2π)/2842 weeks
15518.55458 -20.84126 (155*2π)/2842 weeks
15631.59491 -3.65883 (156*2π)/2842 weeks
15718.07965 .96273 (157*2π)/2842 weeks
15824.34902 -5.78922 (158*2π)/2842 weeks
15922.61417 10.7532 (159*2π)/2842 weeks
1606.99026 -1.8699 (160*2π)/2842 weeks
16117.57686 3.4101 (161*2π)/2842 weeks
162-6.67487 -3.3612 (162*2π)/2842 weeks
16311.53303 -30.30935 (163*2π)/2842 weeks
16433.41485 -13.5464 (164*2π)/2842 weeks
16520.56347 -1.4433 (165*2π)/2842 weeks
16629.85823 -7.69273 (166*2π)/2842 weeks
16713.0979 22.12204 (167*2π)/2842 weeks
168-5.81361 -18.56577 (168*2π)/2842 weeks
16918.31876 -4.62468 (169*2π)/2842 weeks
170-.64387 -18.65261 (170*2π)/2842 weeks
17117.05115 -21.78041 (171*2π)/2842 weeks
17221.911 -27.74346 (172*2π)/2842 weeks
17330.21927 -7.21814 (173*2π)/2842 weeks
17425.47934 -15.01824 (174*2π)/2842 weeks
17522.32739 10.56602 (175*2π)/2842 weeks
176.43551 -16.31637 (176*2π)/2842 weeks
17713.16707 -10.83807 (177*2π)/2842 weeks
17810.27139 -37.45448 (178*2π)/2842 weeks
17943.76122 -14.52429 (179*2π)/2842 weeks
18012.89739 -7.14202 (180*2π)/2842 weeks
18126.62258 -19.68903 (181*2π)/2842 weeks
18221.00505 -10.20175 (182*2π)/2842 weeks
18315.59665 -19.15699 (183*2π)/2842 weeks
18436.18867 -26.503 (184*2π)/2842 weeks
18531.16152 -3.12561 (185*2π)/2842 weeks
18637.10717 -16.90534 (186*2π)/2842 weeks
18736.91492 17.31001 (187*2π)/2842 weeks
1886.42239 7.40528 (188*2π)/2842 weeks
1897.5346 -9.40103 (189*2π)/2842 weeks
19021.46548 -5.28789 (190*2π)/2841 weeks
191-3.40417 -2.01286 (191*2π)/2841 weeks
19226.29721 -23.55769 (192*2π)/2841 weeks
1935.16753 15.58494 (193*2π)/2841 weeks
194-9.2919 -22.48447 (194*2π)/2841 weeks
1959.31746 -22.34927 (195*2π)/2841 weeks
1967.94595 -17.46268 (196*2π)/2841 weeks
197-1.32654 -30.17971 (197*2π)/2841 weeks
19828.54268 -34.86655 (198*2π)/2841 weeks
19912.16058 -8.35641 (199*2π)/2841 weeks
20016.58026 -34.1583 (200*2π)/2841 weeks
20121.57196 -5.42615 (201*2π)/2841 weeks
202-4.66534 -25.46474 (202*2π)/2841 weeks
20324.1434 -32.04454 (203*2π)/2841 weeks
20417.17381 -5.36042 (204*2π)/2841 weeks
205-12.87817 -24.90969 (205*2π)/2841 weeks
20621.09348 -46.35588 (206*2π)/2841 weeks
20720.11376 -14.92041 (207*2π)/2841 weeks
2081.67798 -35.51496 (208*2π)/2841 weeks
20930.90996 -27.24774 (209*2π)/2841 weeks
210-5.539 -6.60918 (210*2π)/2841 weeks
211.91925 -59.10447 (211*2π)/2841 weeks
21232.6206 -24.33462 (212*2π)/2841 weeks
213-2.94218 -29.87232 (213*2π)/2841 weeks
21421.21156 -40.90456 (214*2π)/2841 weeks
21514.30313 -29.42053 (215*2π)/2841 weeks
21613.72709 -20.80938 (216*2π)/2841 weeks
217-9.18568 -15.46142 (217*2π)/2841 weeks
218-47.45275 -53.05591 (218*2π)/2841 weeks
219-3.52663 -116.5714 (219*2π)/2841 weeks
22074.0704 -87.47493 (220*2π)/2841 weeks
22138.82799 -18.24452 (221*2π)/2841 weeks
22225.34801 -70.85129 (222*2π)/2841 weeks
22358.04056 -27.25631 (223*2π)/2841 weeks
2249.60687 -34.80363 (224*2π)/2841 weeks
22536.50773 -54.30596 (225*2π)/2841 weeks
22631.98126 -31.59085 (226*2π)/2841 weeks
22714.26783 -52.98537 (227*2π)/2841 weeks
22869.14134 -59.1653 (228*2π)/2841 weeks
22941.08406 15.5011 (229*2π)/2841 weeks
230-5.15625 -17.11072 (230*2π)/2841 weeks
231-21.11086 -25.38049 (231*2π)/2841 weeks
232-19.70056 -75.6846 (232*2π)/2841 weeks
2332.76654 -90.87051 (233*2π)/2841 weeks
23449.6488 -89.1693 (234*2π)/2841 weeks
23534.27314 -46.6677 (235*2π)/2841 weeks
23620.83871 -82.15665 (236*2π)/2841 weeks
23754.90948 -61.99823 (237*2π)/2841 weeks
23830.13321 -60.92669 (238*2π)/2841 weeks
23948.29236 -51.45993 (239*2π)/2841 weeks
2406.9254 -55.20664 (240*2π)/2841 weeks
24118.7608 -108.0797 (241*2π)/2841 weeks
24297.67878 -112.8417 (242*2π)/2841 weeks
24395.85775 -19.07018 (243*2π)/2841 weeks
24441.68016 -39.28934 (244*2π)/2841 weeks
24559.95236 -31.14085 (245*2π)/2841 weeks
24636.19811 -38.14125 (246*2π)/2841 weeks
24733.10169 -10.93627 (247*2π)/2841 weeks
248-9.55182 -80.54348 (248*2π)/2841 weeks
24980.05932 -56.99167 (249*2π)/2841 weeks
25013.21745 -28.89251 (250*2π)/2841 weeks
25136.71525 -51.37599 (251*2π)/2841 weeks
2525.12477 -3.68395 (252*2π)/2841 weeks
253-76.93794 -75.63773 (253*2π)/2841 weeks
25418.37615 -138.0116 (254*2π)/2841 weeks
255-11.59101 -79.96706 (255*2π)/2841 weeks
2568.51799 -181.3945 (256*2π)/2841 weeks
25764.9269 -111.1743 (257*2π)/2841 weeks
25825.25344 -157.892 (258*2π)/2841 weeks
25983.45802 -154.8645 (259*2π)/2841 weeks
260129.594 -167.6785 (260*2π)/2841 weeks
261147.0316 -41.88259 (261*2π)/2841 weeks
26271.07524 -61.26219 (262*2π)/2841 weeks
26346.13186 -47.97223 (263*2π)/2841 weeks
26424.38825 -127.3593 (264*2π)/2841 weeks
26560.20214 -120.8322 (265*2π)/2841 weeks
26659.63358 -147.537 (266*2π)/2841 weeks
26787.92008 -163.9093 (267*2π)/2841 weeks
268114.7376 -135.2802 (268*2π)/2841 weeks
26995.07969 -203.4379 (269*2π)/2841 weeks
270295.2164 -130.6377 (270*2π)/2841 weeks
271115.4903 43.11349 (271*2π)/2841 weeks
27257.34771 -39.52972 (272*2π)/2841 weeks
273-48.20958 -141.9512 (273*2π)/2841 weeks
274138.5938 -272.0202 (274*2π)/2841 weeks
275194.7339 -193.7655 (275*2π)/2841 weeks
276308.7193 -53.43351 (276*2π)/2841 weeks
277-.33178 34.53257 (277*2π)/2841 weeks
27818.24983 -237.9785 (278*2π)/2841 weeks
279236.2402 -211.5246 (279*2π)/2841 weeks
280-92.15425 1.7326 (280*2π)/2841 weeks
281-35.3169 -664.296 (281*2π)/2841 weeks
282164.5632 -302.922 (282*2π)/2841 weeks



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