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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 21 weeks (268.684*cosine), 28 weeks (254.5484*sine), and 19 weeks (145.4472*cosine).

UGAZ (VelocityShares 3x Long Natural Gas ETN) has an average price of 1,487.37 (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 1/8/2018 for UGAZ (VelocityShares 3x Long Natural Gas ETN), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
01,487.37   0 
1412.1961 1,827.068 (1*2π)/310310 weeks
2-6.62511 305.5285 (2*2π)/310155 weeks
3153.4047 626.1754 (3*2π)/310103 weeks
4-226.0503 178.6525 (4*2π)/31078 weeks
5205.7357 44.83872 (5*2π)/31062 weeks
6110.6055 253.0819 (6*2π)/31052 weeks
7-39.18933 141.4218 (7*2π)/31044 weeks
8109.5256 -81.91808 (8*2π)/31039 weeks
9276.2624 118.8357 (9*2π)/31034 weeks
10175.0753 175.4579 (10*2π)/31031 weeks
11112.7407 254.5484 (11*2π)/31028 weeks
12-43.10176 131.0243 (12*2π)/31026 weeks
1348.99603 34.33182 (13*2π)/31024 weeks
1477.28035 -20.9835 (14*2π)/31022 weeks
15268.684 43.1246 (15*2π)/31021 weeks
16145.4472 214.8036 (16*2π)/31019 weeks
1784.50631 124.3848 (17*2π)/31018 weeks
18104.5981 143.4809 (18*2π)/31017 weeks
1969.20213 141.8951 (19*2π)/31016 weeks
2048.15348 124.1727 (20*2π)/31016 weeks
2157.43972 113.7345 (21*2π)/31015 weeks
2214.14638 105.5235 (22*2π)/31014 weeks
2348.31646 42.64295 (23*2π)/31013 weeks
2465.64865 55.39751 (24*2π)/31013 weeks
25123.617 31.0669 (25*2π)/31012 weeks
26138.9781 142.3923 (26*2π)/31012 weeks
2777.44194 139.5107 (27*2π)/31011 weeks
2848.76823 156.1955 (28*2π)/31011 weeks
2926.10129 99.17029 (29*2π)/31011 weeks
3063.07368 144.5405 (30*2π)/31010 weeks
31-30.64603 132.3151 (31*2π)/31010 weeks
3217.90281 73.0636 (32*2π)/31010 weeks
33-7.31294 133.764 (33*2π)/3109 weeks
34-67.50854 48.56393 (34*2π)/3109 weeks
359.78165 3.6902 (35*2π)/3109 weeks
3633.94572 45.40471 (36*2π)/3109 weeks
379.61585 31.41431 (37*2π)/3108 weeks
3868.82877 32.0176 (38*2π)/3108 weeks
3914.5926 90.76007 (39*2π)/3108 weeks
40.97996 13.25403 (40*2π)/3108 weeks
4142.77787 33.26012 (41*2π)/3108 weeks
4237.77391 22.76576 (42*2π)/3107 weeks
4354.06838 40.79887 (43*2π)/3107 weeks
4441.49897 20.88581 (44*2π)/3107 weeks
45102.0031 31.58923 (45*2π)/3107 weeks
4677.17186 109.8659 (46*2π)/3107 weeks
4714.30596 95.97301 (47*2π)/3107 weeks
485.19315 51.25167 (48*2π)/3106 weeks
4941.41103 42.76845 (49*2π)/3106 weeks
5029.47846 60.18641 (50*2π)/3106 weeks
5143.67152 47.71133 (51*2π)/3106 weeks
5235.52318 78.79533 (52*2π)/3106 weeks
5314.08811 51.1194 (53*2π)/3106 weeks
5448.11753 54.52066 (54*2π)/3106 weeks
5526.47545 92.16708 (55*2π)/3106 weeks
56-2.50042 77.42085 (56*2π)/3106 weeks
57-25.4905 61.65904 (57*2π)/3105 weeks
58-14.69858 20.16099 (58*2π)/3105 weeks
59-5.38203 14.11284 (59*2π)/3105 weeks
6034.55998 -14.65656 (60*2π)/3105 weeks
6168.29678 46.10139 (61*2π)/3105 weeks
6216.67573 56.55964 (62*2π)/3105 weeks
6321.81295 29.19465 (63*2π)/3105 weeks
6437.55514 40.56881 (64*2π)/3105 weeks
6514.94971 49.73211 (65*2π)/3105 weeks
6623.9771 14.89864 (66*2π)/3105 weeks
6756.27397 49.2467 (67*2π)/3105 weeks
689.74828 51.43647 (68*2π)/3105 weeks
6951.96841 20.60423 (69*2π)/3104 weeks
7061.43662 89.56129 (70*2π)/3104 weeks
71-6.71274 105.7203 (71*2π)/3104 weeks
72-43.86537 51.50646 (72*2π)/3104 weeks
73-12.68397 14.52356 (73*2π)/3104 weeks
748.92743 16.89242 (74*2π)/3104 weeks
7513.70489 27.79074 (75*2π)/3104 weeks
7619.76069 29.14264 (76*2π)/3104 weeks
774.72539 41.2606 (77*2π)/3104 weeks
788.45595 13.76319 (78*2π)/3104 weeks
7930.94973 40.9781 (79*2π)/3104 weeks
80-13.15375 43.65734 (80*2π)/3104 weeks
815.72467 2.75576 (81*2π)/3104 weeks
8227.08583 29.51907 (82*2π)/3104 weeks
83.91067 31.37301 (83*2π)/3104 weeks
8417.15601 13.15971 (84*2π)/3104 weeks
8523.31063 38.95407 (85*2π)/3104 weeks
86-10.35886 32.2536 (86*2π)/3104 weeks
875.74666 3.58703 (87*2π)/3104 weeks
8825.59982 19.64199 (88*2π)/3104 weeks
897.46643 34.61881 (89*2π)/3103 weeks
90.6746 7.15468 (90*2π)/3103 weeks
9127.37301 15.37329 (91*2π)/3103 weeks
926.30551 27.77619 (92*2π)/3103 weeks
9318.44547 7.14107 (93*2π)/3103 weeks
9423.02408 34.81895 (94*2π)/3103 weeks
95-1.33018 26.60568 (95*2π)/3103 weeks
966.95154 15.56485 (96*2π)/3103 weeks
978.75736 19.28511 (97*2π)/3103 weeks
98-2.94828 23.81728 (98*2π)/3103 weeks
99-8.88702 -6.69071 (99*2π)/3103 weeks
10030.3013 2.51909 (100*2π)/3103 weeks
101-.02093 20.98805 (101*2π)/3103 weeks
10210.71485 -5.62577 (102*2π)/3103 weeks
10316.11764 10.23534 (103*2π)/3103 weeks
1044.97073 4.50674 (104*2π)/3103 weeks
1057.81311 -11.2093 (105*2π)/3103 weeks
10637.31202 -13.28148 (106*2π)/3103 weeks
10733.10472 15.4592 (107*2π)/3103 weeks
10826.99665 2.84459 (108*2π)/3103 weeks
10936.01489 21.01674 (109*2π)/3103 weeks
11015.37745 21.22642 (110*2π)/3103 weeks
11117.01433 10.52073 (111*2π)/3103 weeks
11225.24159 11.44214 (112*2π)/3103 weeks
11313.85602 18.09299 (113*2π)/3103 weeks
11423.43111 -1.04814 (114*2π)/3103 weeks
11536.10121 28.83957 (115*2π)/3103 weeks
1161.95587 25.49072 (116*2π)/3103 weeks
11714.61934 12.31153 (117*2π)/3103 weeks
118-1.62114 11.50636 (118*2π)/3103 weeks
11920.95272 -9.55123 (119*2π)/3103 weeks
12024.42231 13.48016 (120*2π)/3103 weeks
12124.31949 5.31482 (121*2π)/3103 weeks
12225.72321 24.20577 (122*2π)/3103 weeks
12314.40313 18.60305 (123*2π)/3103 weeks
1247.02576 23.53514 (124*2π)/3103 weeks
1252.72564 2.62396 (125*2π)/3102 weeks
12615.78972 17.48438 (126*2π)/3102 weeks
127-11.75206 .96826 (127*2π)/3102 weeks
12823.68558 -16.0381 (128*2π)/3102 weeks
12923.36569 9.11541 (129*2π)/3102 weeks
13020.00641 .68782 (130*2π)/3102 weeks
13130.31429 12.71642 (131*2π)/3102 weeks
13212.56985 27.95841 (132*2π)/3102 weeks
133-7.13805 8.40324 (133*2π)/3102 weeks
13411.87639 -6.77588 (134*2π)/3102 weeks
13510.84309 5.37875 (135*2π)/3102 weeks
13610.83958 -9.87575 (136*2π)/3102 weeks
13725.86123 -.98645 (137*2π)/3102 weeks
13817.16762 5.17293 (138*2π)/3102 weeks
13920.4897 -2.87586 (139*2π)/3102 weeks
14029.17781 8.606 (140*2π)/3102 weeks
14112.45383 18.71271 (141*2π)/3102 weeks
1422.71411 -1.81936 (142*2π)/3102 weeks
14324.64063 -3.09754 (143*2π)/3102 weeks
14414.85562 13.66362 (144*2π)/3102 weeks
14510.99187 -.23268 (145*2π)/3102 weeks
14613.60829 7.50299 (146*2π)/3102 weeks
1474.02382 .12409 (147*2π)/3102 weeks
1484.21997 -15.15094 (148*2π)/3102 weeks
14936.20806 -17.31139 (149*2π)/3102 weeks
15024.2687 13.90876 (150*2π)/3102 weeks
15116.0566 -7.02226 (151*2π)/3102 weeks
15233.00859 5.01929 (152*2π)/3102 weeks
15318.08279 16.71022 (153*2π)/3102 weeks
1547.19208 10.32079 (154*2π)/3102 weeks
1551.63831   (155*2π)/3102 weeks
1567.19208 -10.32079 (156*2π)/3102 weeks
15718.08279 -16.71022 (157*2π)/3102 weeks
15833.00859 -5.01929 (158*2π)/3102 weeks
15916.0566 7.02226 (159*2π)/3102 weeks
16024.2687 -13.90876 (160*2π)/3102 weeks
16136.20806 17.31139 (161*2π)/3102 weeks
1624.21997 15.15094 (162*2π)/3102 weeks
1634.02382 -.12409 (163*2π)/3102 weeks
16413.60829 -7.50299 (164*2π)/3102 weeks
16510.99187 .23268 (165*2π)/3102 weeks
16614.85562 -13.66362 (166*2π)/3102 weeks
16724.64063 3.09754 (167*2π)/3102 weeks
1682.71411 1.81936 (168*2π)/3102 weeks
16912.45383 -18.71271 (169*2π)/3102 weeks
17029.17781 -8.606 (170*2π)/3102 weeks
17120.4897 2.87586 (171*2π)/3102 weeks
17217.16762 -5.17293 (172*2π)/3102 weeks
17325.86123 .98645 (173*2π)/3102 weeks
17410.83958 9.87575 (174*2π)/3102 weeks
17510.84309 -5.37875 (175*2π)/3102 weeks
17611.87639 6.77588 (176*2π)/3102 weeks
177-7.13805 -8.40324 (177*2π)/3102 weeks
17812.56985 -27.95841 (178*2π)/3102 weeks
17930.31429 -12.71642 (179*2π)/3102 weeks
18020.00641 -.68782 (180*2π)/3102 weeks
18123.36569 -9.11541 (181*2π)/3102 weeks
18223.68558 16.0381 (182*2π)/3102 weeks
183-11.75206 -.96826 (183*2π)/3102 weeks
18415.78972 -17.48438 (184*2π)/3102 weeks
1852.72564 -2.62396 (185*2π)/3102 weeks
1867.02576 -23.53514 (186*2π)/3102 weeks
18714.40313 -18.60305 (187*2π)/3102 weeks
18825.72321 -24.20577 (188*2π)/3102 weeks
18924.31949 -5.31482 (189*2π)/3102 weeks
19024.42231 -13.48016 (190*2π)/3102 weeks
19120.95272 9.55123 (191*2π)/3102 weeks
192-1.62114 -11.50636 (192*2π)/3102 weeks
19314.61934 -12.31153 (193*2π)/3102 weeks
1941.95587 -25.49072 (194*2π)/3102 weeks
19536.10121 -28.83957 (195*2π)/3102 weeks
19623.43111 1.04814 (196*2π)/3102 weeks
19713.85602 -18.09299 (197*2π)/3102 weeks
19825.24159 -11.44214 (198*2π)/3102 weeks
19917.01433 -10.52073 (199*2π)/3102 weeks
20015.37745 -21.22642 (200*2π)/3102 weeks
20136.01489 -21.01674 (201*2π)/3102 weeks
20226.99665 -2.84459 (202*2π)/3102 weeks
20333.10472 -15.4592 (203*2π)/3102 weeks
20437.31202 13.28148 (204*2π)/3102 weeks
2057.81311 11.2093 (205*2π)/3102 weeks
2064.97073 -4.50674 (206*2π)/3102 weeks
20716.11764 -10.23534 (207*2π)/3101 weeks
20810.71485 5.62577 (208*2π)/3101 weeks
209-.02093 -20.98805 (209*2π)/3101 weeks
21030.3013 -2.51909 (210*2π)/3101 weeks
211-8.88702 6.69071 (211*2π)/3101 weeks
212-2.94828 -23.81728 (212*2π)/3101 weeks
2138.75736 -19.28511 (213*2π)/3101 weeks
2146.95154 -15.56485 (214*2π)/3101 weeks
215-1.33018 -26.60568 (215*2π)/3101 weeks
21623.02408 -34.81895 (216*2π)/3101 weeks
21718.44547 -7.14107 (217*2π)/3101 weeks
2186.30551 -27.77619 (218*2π)/3101 weeks
21927.37301 -15.37329 (219*2π)/3101 weeks
220.6746 -7.15468 (220*2π)/3101 weeks
2217.46643 -34.61881 (221*2π)/3101 weeks
22225.59982 -19.64199 (222*2π)/3101 weeks
2235.74666 -3.58703 (223*2π)/3101 weeks
224-10.35886 -32.2536 (224*2π)/3101 weeks
22523.31063 -38.95407 (225*2π)/3101 weeks
22617.15601 -13.15971 (226*2π)/3101 weeks
227.91067 -31.37301 (227*2π)/3101 weeks
22827.08583 -29.51907 (228*2π)/3101 weeks
2295.72467 -2.75576 (229*2π)/3101 weeks
230-13.15375 -43.65734 (230*2π)/3101 weeks
23130.94973 -40.9781 (231*2π)/3101 weeks
2328.45595 -13.76319 (232*2π)/3101 weeks
2334.72539 -41.2606 (233*2π)/3101 weeks
23419.76069 -29.14264 (234*2π)/3101 weeks
23513.70489 -27.79074 (235*2π)/3101 weeks
2368.92743 -16.89242 (236*2π)/3101 weeks
237-12.68397 -14.52356 (237*2π)/3101 weeks
238-43.86537 -51.50646 (238*2π)/3101 weeks
239-6.71274 -105.7203 (239*2π)/3101 weeks
24061.43662 -89.56129 (240*2π)/3101 weeks
24151.96841 -20.60423 (241*2π)/3101 weeks
2429.74828 -51.43647 (242*2π)/3101 weeks
24356.27397 -49.2467 (243*2π)/3101 weeks
24423.9771 -14.89864 (244*2π)/3101 weeks
24514.94971 -49.73211 (245*2π)/3101 weeks
24637.55514 -40.56881 (246*2π)/3101 weeks
24721.81295 -29.19465 (247*2π)/3101 weeks
24816.67573 -56.55964 (248*2π)/3101 weeks
24968.29678 -46.10139 (249*2π)/3101 weeks
25034.55998 14.65656 (250*2π)/3101 weeks
251-5.38203 -14.11284 (251*2π)/3101 weeks
252-14.69858 -20.16099 (252*2π)/3101 weeks
253-25.4905 -61.65904 (253*2π)/3101 weeks
254-2.50042 -77.42085 (254*2π)/3101 weeks
25526.47545 -92.16708 (255*2π)/3101 weeks
25648.11753 -54.52066 (256*2π)/3101 weeks
25714.08811 -51.1194 (257*2π)/3101 weeks
25835.52318 -78.79533 (258*2π)/3101 weeks
25943.67152 -47.71133 (259*2π)/3101 weeks
26029.47846 -60.18641 (260*2π)/3101 weeks
26141.41103 -42.76845 (261*2π)/3101 weeks
2625.19315 -51.25167 (262*2π)/3101 weeks
26314.30596 -95.97301 (263*2π)/3101 weeks
26477.17186 -109.8659 (264*2π)/3101 weeks
265102.0031 -31.58923 (265*2π)/3101 weeks
26641.49897 -20.88581 (266*2π)/3101 weeks
26754.06838 -40.79887 (267*2π)/3101 weeks
26837.77391 -22.76576 (268*2π)/3101 weeks
26942.77787 -33.26012 (269*2π)/3101 weeks
270.97996 -13.25403 (270*2π)/3101 weeks
27114.5926 -90.76007 (271*2π)/3101 weeks
27268.82877 -32.0176 (272*2π)/3101 weeks
2739.61585 -31.41431 (273*2π)/3101 weeks
27433.94572 -45.40471 (274*2π)/3101 weeks
2759.78165 -3.6902 (275*2π)/3101 weeks
276-67.50854 -48.56393 (276*2π)/3101 weeks
277-7.31294 -133.764 (277*2π)/3101 weeks
27817.90281 -73.0636 (278*2π)/3101 weeks
279-30.64603 -132.3151 (279*2π)/3101 weeks
28063.07368 -144.5405 (280*2π)/3101 weeks
28126.10129 -99.17029 (281*2π)/3101 weeks
28248.76823 -156.1955 (282*2π)/3101 weeks
28377.44194 -139.5107 (283*2π)/3101 weeks
284138.9781 -142.3923 (284*2π)/3101 weeks
285123.617 -31.0669 (285*2π)/3101 weeks
28665.64865 -55.39751 (286*2π)/3101 weeks
28748.31646 -42.64295 (287*2π)/3101 weeks
28814.14638 -105.5235 (288*2π)/3101 weeks
28957.43972 -113.7345 (289*2π)/3101 weeks
29048.15348 -124.1727 (290*2π)/3101 weeks
29169.20213 -141.8951 (291*2π)/3101 weeks
292104.5981 -143.4809 (292*2π)/3101 weeks
29384.50631 -124.3848 (293*2π)/3101 weeks
294145.4472 -214.8036 (294*2π)/3101 weeks
295268.684 -43.1246 (295*2π)/3101 weeks
29677.28035 20.9835 (296*2π)/3101 weeks
29748.99603 -34.33182 (297*2π)/3101 weeks
298-43.10176 -131.0243 (298*2π)/3101 weeks
299112.7407 -254.5484 (299*2π)/3101 weeks
300175.0753 -175.4579 (300*2π)/3101 weeks
301276.2624 -118.8357 (301*2π)/3101 weeks
302109.5256 81.91808 (302*2π)/3101 weeks
303-39.18933 -141.4218 (303*2π)/3101 weeks
304110.6055 -253.0819 (304*2π)/3101 weeks
305205.7357 -44.83872 (305*2π)/3101 weeks
306-226.0503 -178.6525 (306*2π)/3101 weeks
307153.4047 -626.1754 (307*2π)/3101 weeks
308-6.62511 -305.5285 (308*2π)/3101 weeks



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