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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 (2568.959*cosine), 27 weeks (2264.099*sine), and 12 weeks (1462.609*cosine).

UGAZ (VelocityShares 3x Long Natural Gas ETN) has an average price of 14,226.77 (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 4/16/2018 for UGAZ (VelocityShares 3x Long Natural Gas ETN), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
014,226.77   0 
15,052.308 17,959.78 (1*2π)/324324 weeks
2-830.0753 3,398.707 (2*2π)/324162 weeks
32,181.013 5,676.649 (3*2π)/324108 weeks
4-2,324.461 2,847.656 (4*2π)/32481 weeks
51,261.292 -137.4132 (5*2π)/32465 weeks
61,563.275 2,327.818 (6*2π)/32454 weeks
7-45.73676 1,907.126 (7*2π)/32446 weeks
828.37621 -328.7248 (8*2π)/32441 weeks
92,610.806 139.8796 (9*2π)/32436 weeks
101,903.25 1,728.707 (10*2π)/32432 weeks
111,622.579 1,985.179 (11*2π)/32429 weeks
1285.4659 2,264.099 (12*2π)/32427 weeks
13-103.701 525.7075 (13*2π)/32425 weeks
14533.2209 332.8967 (14*2π)/32423 weeks
151,338.648 -450.5766 (15*2π)/32422 weeks
162,568.959 1,213.016 (16*2π)/32420 weeks
17950.3484 1,898.224 (17*2π)/32419 weeks
18911.3924 1,151.557 (18*2π)/32418 weeks
19928.605 1,428.556 (19*2π)/32417 weeks
20632.5779 1,351.65 (20*2π)/32416 weeks
21448.1387 1,168.077 (21*2π)/32415 weeks
22540.7561 1,109.852 (22*2π)/32415 weeks
23127.7691 1,016.506 (23*2π)/32414 weeks
24433.1123 419.1265 (24*2π)/32414 weeks
25629.9472 556.2468 (25*2π)/32413 weeks
261,048.428 273.2414 (26*2π)/32412 weeks
271,462.609 1,221.048 (27*2π)/32412 weeks
28762.8419 1,385.071 (28*2π)/32412 weeks
29615.2111 1,476.08 (29*2π)/32411 weeks
30146.0735 1,150.877 (30*2π)/32411 weeks
31647.6342 1,101.043 (31*2π)/32410 weeks
3215.39552 1,571.745 (32*2π)/32410 weeks
33-165.1168 737.4216 (33*2π)/32410 weeks
34278.2981 1,066.917 (34*2π)/32410 weeks
35-546.4807 1,058.845 (35*2π)/3249 weeks
36-357.6433 106.4341 (36*2π)/3249 weeks
37300.6353 187.5931 (37*2π)/3249 weeks
38219.4442 503.6418 (38*2π)/3249 weeks
39200.3042 165.8896 (39*2π)/3248 weeks
40695.1445 564.7798 (40*2π)/3248 weeks
41-42.59865 758.0765 (41*2π)/3248 weeks
42149.7329 83.08126 (42*2π)/3248 weeks
43384.5006 353.4311 (43*2π)/3248 weeks
44394.7755 216.6214 (44*2π)/3247 weeks
45510.903 409.0847 (45*2π)/3247 weeks
46406.215 201.7959 (46*2π)/3247 weeks
47966.7929 286.882 (47*2π)/3247 weeks
48799.2706 1,028.539 (48*2π)/3247 weeks
49185.3624 967.1381 (49*2π)/3247 weeks
5032.44857 563.5568 (50*2π)/3246 weeks
51339.792 366.7061 (51*2π)/3246 weeks
52346.1145 599.8688 (52*2π)/3246 weeks
53339.5614 441.2054 (53*2π)/3246 weeks
54458.4048 678.1931 (54*2π)/3246 weeks
55126.4928 640.8796 (55*2π)/3246 weeks
56337.2236 415.1539 (56*2π)/3246 weeks
57447.2693 765.1986 (57*2π)/3246 weeks
5863.79387 833.3327 (58*2π)/3246 weeks
59-88.63756 707.7834 (59*2π)/3245 weeks
60-282.252 402.0434 (60*2π)/3245 weeks
61-44.58399 184.2368 (61*2π)/3245 weeks
62-19.0724 20.40734 (62*2π)/3245 weeks
63525.6927 -62.76593 (63*2π)/3245 weeks
64550.297 570.6521 (64*2π)/3245 weeks
65127.7882 474.3926 (65*2π)/3245 weeks
66245.5164 273.3457 (66*2π)/3245 weeks
67359.7193 412.6032 (67*2π)/3245 weeks
68129.8579 460.9742 (68*2π)/3245 weeks
69241.3314 139.553 (69*2π)/3245 weeks
70545.6797 456.791 (70*2π)/3245 weeks
71112.9438 526.9709 (71*2π)/3245 weeks
72424.9543 168.7022 (72*2π)/3245 weeks
73654.4077 757.9122 (73*2π)/3244 weeks
7468.76333 1,045.386 (74*2π)/3244 weeks
75-401.3361 647.4028 (75*2π)/3244 weeks
76-222.1358 169.9708 (76*2π)/3244 weeks
7730.6127 146.7111 (77*2π)/3244 weeks
78146.6801 237.5281 (78*2π)/3244 weeks
79143.2729 248.9561 (79*2π)/3244 weeks
80164.8495 383.1881 (80*2π)/3244 weeks
81-25.23586 261.9067 (81*2π)/3244 weeks
82250.608 168.9296 (82*2π)/3244 weeks
83147.6509 520.9225 (83*2π)/3244 weeks
84-164.8281 225.1763 (84*2π)/3244 weeks
85191.4234 63.39581 (85*2π)/3244 weeks
86200.1551 350.3577 (86*2π)/3244 weeks
87-3.80432 227.3354 (87*2π)/3244 weeks
88210.5255 153.3726 (88*2π)/3244 weeks
89180.5825 409.4677 (89*2π)/3244 weeks
90-111.2909 266.3081 (90*2π)/3244 weeks
9175.41318 33.29116 (91*2π)/3244 weeks
92244.1452 195.0257 (92*2π)/3244 weeks
9376.36557 333.5376 (93*2π)/3243 weeks
94-8.47355 84.97306 (94*2π)/3243 weeks
95252.0163 116.7415 (95*2π)/3243 weeks
9697.569 291.4092 (96*2π)/3243 weeks
97115.3076 70.73373 (97*2π)/3243 weeks
98269.9085 274.2258 (98*2π)/3243 weeks
9918.58844 317.2731 (99*2π)/3243 weeks
10032.79858 151.3106 (100*2π)/3243 weeks
10181.88818 174.0637 (101*2π)/3243 weeks
10248.18191 229.8537 (102*2π)/3243 weeks
103-128.73 109.9188 (103*2π)/3243 weeks
104129.76 -134.1454 (104*2π)/3243 weeks
105216.3906 218.1766 (105*2π)/3243 weeks
106-42.65432 50.12288 (106*2π)/3243 weeks
107179.3523 1.25693 (107*2π)/3243 weeks
108108.6432 108.462 (108*2π)/3243 weeks
10945.1717 8.39997 (109*2π)/3243 weeks
110121.214 -150.2572 (110*2π)/3243 weeks
111400.0001 -63.13147 (111*2π)/3243 weeks
112276.9592 153.2801 (112*2π)/3243 weeks
113285.3432 27.4383 (113*2π)/3243 weeks
114333.5835 218.5661 (114*2π)/3243 weeks
115146.2733 200.7981 (115*2π)/3243 weeks
116164.0795 103.6709 (116*2π)/3243 weeks
117239.8221 105.5477 (117*2π)/3243 weeks
118151.981 186.676 (118*2π)/3243 weeks
119182.3467 .3577 (119*2π)/3243 weeks
120381.1618 209.3031 (120*2π)/3243 weeks
12169.26674 313.5376 (121*2π)/3243 weeks
122102.4792 92.44918 (122*2π)/3243 weeks
12348.71729 180.0889 (123*2π)/3243 weeks
12472.18356 -83.08166 (124*2π)/3243 weeks
125296.2226 64.04681 (125*2π)/3243 weeks
126179.9098 85.02399 (126*2π)/3243 weeks
127304.0157 130.572 (127*2π)/3243 weeks
128154.1753 227.7623 (128*2π)/3243 weeks
129147.49 197.9789 (129*2π)/3243 weeks
130.95869 175.8822 (130*2π)/3242 weeks
131118.5821 11.31367 (131*2π)/3242 weeks
13264.27045 208.2434 (132*2π)/3242 weeks
133-70.10229 -101.9391 (133*2π)/3242 weeks
134280.3923 -92.47729 (134*2π)/3242 weeks
135197.2353 88.41074 (135*2π)/3242 weeks
136212.6154 4.77705 (136*2π)/3242 weeks
137290.3817 138.1756 (137*2π)/3242 weeks
138112.3993 266.9983 (138*2π)/3242 weeks
139-65.84715 82.16228 (139*2π)/3242 weeks
140105.7224 -69.16929 (140*2π)/3242 weeks
141120.1306 51.17282 (141*2π)/3242 weeks
14281.86932 -77.75115 (142*2π)/3242 weeks
143245.0724 -39.84935 (143*2π)/3242 weeks
144187.3916 56.35644 (144*2π)/3242 weeks
145167.2363 -16.95365 (145*2π)/3242 weeks
146275.1956 28.01259 (146*2π)/3242 weeks
147196.8888 176.7066 (147*2π)/3242 weeks
14818.65471 84.91931 (148*2π)/3242 weeks
149150.7018 -83.12177 (149*2π)/3242 weeks
150239.4178 85.11477 (150*2π)/3242 weeks
15173.79125 68.71277 (151*2π)/3242 weeks
152155.0504 12.52082 (152*2π)/3242 weeks
15378.316 66.69532 (153*2π)/3242 weeks
15435.24714 -32.9179 (154*2π)/3242 weeks
155102.9019 -211.4461 (155*2π)/3242 weeks
156391.6447 -67.70332 (156*2π)/3242 weeks
157165.0433 114.247 (157*2π)/3242 weeks
158195.8766 -82.19419 (158*2π)/3242 weeks
159309.4913 76.74402 (159*2π)/3242 weeks
160160.4557 157.7967 (160*2π)/3242 weeks
16167.19921 95.7326 (161*2π)/3242 weeks
16216.67935   (162*2π)/3242 weeks
16367.19921 -95.7326 (163*2π)/3242 weeks
164160.4557 -157.7967 (164*2π)/3242 weeks
165309.4913 -76.74402 (165*2π)/3242 weeks
166195.8766 82.19419 (166*2π)/3242 weeks
167165.0433 -114.247 (167*2π)/3242 weeks
168391.6447 67.70332 (168*2π)/3242 weeks
169102.9019 211.4461 (169*2π)/3242 weeks
17035.24714 32.9179 (170*2π)/3242 weeks
17178.316 -66.69532 (171*2π)/3242 weeks
172155.0504 -12.52082 (172*2π)/3242 weeks
17373.79125 -68.71277 (173*2π)/3242 weeks
174239.4178 -85.11477 (174*2π)/3242 weeks
175150.7018 83.12177 (175*2π)/3242 weeks
17618.65471 -84.91931 (176*2π)/3242 weeks
177196.8888 -176.7066 (177*2π)/3242 weeks
178275.1956 -28.01259 (178*2π)/3242 weeks
179167.2363 16.95365 (179*2π)/3242 weeks
180187.3916 -56.35644 (180*2π)/3242 weeks
181245.0724 39.84935 (181*2π)/3242 weeks
18281.86932 77.75115 (182*2π)/3242 weeks
183120.1306 -51.17282 (183*2π)/3242 weeks
184105.7224 69.16929 (184*2π)/3242 weeks
185-65.84715 -82.16228 (185*2π)/3242 weeks
186112.3993 -266.9983 (186*2π)/3242 weeks
187290.3817 -138.1756 (187*2π)/3242 weeks
188212.6154 -4.77705 (188*2π)/3242 weeks
189197.2353 -88.41074 (189*2π)/3242 weeks
190280.3923 92.47729 (190*2π)/3242 weeks
191-70.10229 101.9391 (191*2π)/3242 weeks
19264.27045 -208.2434 (192*2π)/3242 weeks
193118.5821 -11.31367 (193*2π)/3242 weeks
194.95869 -175.8822 (194*2π)/3242 weeks
195147.49 -197.9789 (195*2π)/3242 weeks
196154.1753 -227.7623 (196*2π)/3242 weeks
197304.0157 -130.572 (197*2π)/3242 weeks
198179.9098 -85.02399 (198*2π)/3242 weeks
199296.2226 -64.04681 (199*2π)/3242 weeks
20072.18356 83.08166 (200*2π)/3242 weeks
20148.71729 -180.0889 (201*2π)/3242 weeks
202102.4792 -92.44918 (202*2π)/3242 weeks
20369.26674 -313.5376 (203*2π)/3242 weeks
204381.1618 -209.3031 (204*2π)/3242 weeks
205182.3467 -.3577 (205*2π)/3242 weeks
206151.981 -186.676 (206*2π)/3242 weeks
207239.8221 -105.5477 (207*2π)/3242 weeks
208164.0795 -103.6709 (208*2π)/3242 weeks
209146.2733 -200.7981 (209*2π)/3242 weeks
210333.5835 -218.5661 (210*2π)/3242 weeks
211285.3432 -27.4383 (211*2π)/3242 weeks
212276.9592 -153.2801 (212*2π)/3242 weeks
213400.0001 63.13147 (213*2π)/3242 weeks
214121.214 150.2572 (214*2π)/3242 weeks
21545.1717 -8.39997 (215*2π)/3242 weeks
216108.6432 -108.462 (216*2π)/3242 weeks
217179.3523 -1.25693 (217*2π)/3241 weeks
218-42.65432 -50.12288 (218*2π)/3241 weeks
219216.3906 -218.1766 (219*2π)/3241 weeks
220129.76 134.1454 (220*2π)/3241 weeks
221-128.73 -109.9188 (221*2π)/3241 weeks
22248.18191 -229.8537 (222*2π)/3241 weeks
22381.88818 -174.0637 (223*2π)/3241 weeks
22432.79858 -151.3106 (224*2π)/3241 weeks
22518.58844 -317.2731 (225*2π)/3241 weeks
226269.9085 -274.2258 (226*2π)/3241 weeks
227115.3076 -70.73373 (227*2π)/3241 weeks
22897.569 -291.4092 (228*2π)/3241 weeks
229252.0163 -116.7415 (229*2π)/3241 weeks
230-8.47355 -84.97306 (230*2π)/3241 weeks
23176.36557 -333.5376 (231*2π)/3241 weeks
232244.1452 -195.0257 (232*2π)/3241 weeks
23375.41318 -33.29116 (233*2π)/3241 weeks
234-111.2909 -266.3081 (234*2π)/3241 weeks
235180.5825 -409.4677 (235*2π)/3241 weeks
236210.5255 -153.3726 (236*2π)/3241 weeks
237-3.80432 -227.3354 (237*2π)/3241 weeks
238200.1551 -350.3577 (238*2π)/3241 weeks
239191.4234 -63.39581 (239*2π)/3241 weeks
240-164.8281 -225.1763 (240*2π)/3241 weeks
241147.6509 -520.9225 (241*2π)/3241 weeks
242250.608 -168.9296 (242*2π)/3241 weeks
243-25.23586 -261.9067 (243*2π)/3241 weeks
244164.8495 -383.1881 (244*2π)/3241 weeks
245143.2729 -248.9561 (245*2π)/3241 weeks
246146.6801 -237.5281 (246*2π)/3241 weeks
24730.6127 -146.7111 (247*2π)/3241 weeks
248-222.1358 -169.9708 (248*2π)/3241 weeks
249-401.3361 -647.4028 (249*2π)/3241 weeks
25068.76333 -1,045.386 (250*2π)/3241 weeks
251654.4077 -757.9122 (251*2π)/3241 weeks
252424.9543 -168.7022 (252*2π)/3241 weeks
253112.9438 -526.9709 (253*2π)/3241 weeks
254545.6797 -456.791 (254*2π)/3241 weeks
255241.3314 -139.553 (255*2π)/3241 weeks
256129.8579 -460.9742 (256*2π)/3241 weeks
257359.7193 -412.6032 (257*2π)/3241 weeks
258245.5164 -273.3457 (258*2π)/3241 weeks
259127.7882 -474.3926 (259*2π)/3241 weeks
260550.297 -570.6521 (260*2π)/3241 weeks
261525.6927 62.76593 (261*2π)/3241 weeks
262-19.0724 -20.40734 (262*2π)/3241 weeks
263-44.58399 -184.2368 (263*2π)/3241 weeks
264-282.252 -402.0434 (264*2π)/3241 weeks
265-88.63756 -707.7834 (265*2π)/3241 weeks
26663.79387 -833.3327 (266*2π)/3241 weeks
267447.2693 -765.1986 (267*2π)/3241 weeks
268337.2236 -415.1539 (268*2π)/3241 weeks
269126.4928 -640.8796 (269*2π)/3241 weeks
270458.4048 -678.1931 (270*2π)/3241 weeks
271339.5614 -441.2054 (271*2π)/3241 weeks
272346.1145 -599.8688 (272*2π)/3241 weeks
273339.792 -366.7061 (273*2π)/3241 weeks
27432.44857 -563.5568 (274*2π)/3241 weeks
275185.3624 -967.1381 (275*2π)/3241 weeks
276799.2706 -1,028.539 (276*2π)/3241 weeks
277966.7929 -286.882 (277*2π)/3241 weeks
278406.215 -201.7959 (278*2π)/3241 weeks
279510.903 -409.0847 (279*2π)/3241 weeks
280394.7755 -216.6214 (280*2π)/3241 weeks
281384.5006 -353.4311 (281*2π)/3241 weeks
282149.7329 -83.08126 (282*2π)/3241 weeks
283-42.59865 -758.0765 (283*2π)/3241 weeks
284695.1445 -564.7798 (284*2π)/3241 weeks
285200.3042 -165.8896 (285*2π)/3241 weeks
286219.4442 -503.6418 (286*2π)/3241 weeks
287300.6353 -187.5931 (287*2π)/3241 weeks
288-357.6433 -106.4341 (288*2π)/3241 weeks
289-546.4807 -1,058.845 (289*2π)/3241 weeks
290278.2981 -1,066.917 (290*2π)/3241 weeks
291-165.1168 -737.4216 (291*2π)/3241 weeks
29215.39552 -1,571.745 (292*2π)/3241 weeks
293647.6342 -1,101.043 (293*2π)/3241 weeks
294146.0735 -1,150.877 (294*2π)/3241 weeks
295615.2111 -1,476.08 (295*2π)/3241 weeks
296762.8419 -1,385.071 (296*2π)/3241 weeks
2971,462.609 -1,221.048 (297*2π)/3241 weeks
2981,048.428 -273.2414 (298*2π)/3241 weeks
299629.9472 -556.2468 (299*2π)/3241 weeks
300433.1123 -419.1265 (300*2π)/3241 weeks
301127.7691 -1,016.506 (301*2π)/3241 weeks
302540.7561 -1,109.852 (302*2π)/3241 weeks
303448.1387 -1,168.077 (303*2π)/3241 weeks
304632.5779 -1,351.65 (304*2π)/3241 weeks
305928.605 -1,428.556 (305*2π)/3241 weeks
306911.3924 -1,151.557 (306*2π)/3241 weeks
307950.3484 -1,898.224 (307*2π)/3241 weeks
3082,568.959 -1,213.016 (308*2π)/3241 weeks
3091,338.648 450.5766 (309*2π)/3241 weeks
310533.2209 -332.8967 (310*2π)/3241 weeks
311-103.701 -525.7075 (311*2π)/3241 weeks
31285.4659 -2,264.099 (312*2π)/3241 weeks
3131,622.579 -1,985.179 (313*2π)/3241 weeks
3141,903.25 -1,728.707 (314*2π)/3241 weeks
3152,610.806 -139.8796 (315*2π)/3241 weeks
31628.37621 328.7248 (316*2π)/3241 weeks
317-45.73676 -1,907.126 (317*2π)/3241 weeks
3181,563.275 -2,327.818 (318*2π)/3241 weeks
3191,261.292 137.4132 (319*2π)/3241 weeks
320-2,324.461 -2,847.656 (320*2π)/3241 weeks
3212,181.013 -5,676.649 (321*2π)/3241 weeks
322-830.0753 -3,398.707 (322*2π)/3241 weeks



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