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Fourier Analysis of DGAZ (VelocityShares 3x Inv Natural Gas ETN)


DGAZ (VelocityShares 3x Inv Natural Gas ETN) appears to have interesting cyclic behaviour every 31 weeks (15.6935*sine), 21 weeks (13.1642*cosine), and 19 weeks (8.2069*cosine).

DGAZ (VelocityShares 3x Inv Natural Gas ETN) has an average price of 68.76 (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 DGAZ (VelocityShares 3x Inv Natural Gas ETN), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
068.76181   0 
148.93258 16.5951 (1*2π)/310310 weeks
224.09522 45.67012 (2*2π)/310155 weeks
336.01801 28.03796 (3*2π)/310103 weeks
422.99623 23.16098 (4*2π)/31078 weeks
53.70635 35.91929 (5*2π)/31062 weeks
612.49743 28.72614 (6*2π)/31052 weeks
75.64761 22.20259 (7*2π)/31044 weeks
8-3.73451 29.72938 (8*2π)/31039 weeks
9-6.62444 21.95379 (9*2π)/31034 weeks
10-6.1871 15.69346 (10*2π)/31031 weeks
11-7.2047 11.58396 (11*2π)/31028 weeks
12-6.51951 12.18373 (12*2π)/31026 weeks
13-5.77018 12.92332 (13*2π)/31024 weeks
14-7.71167 8.81388 (14*2π)/31022 weeks
15-13.16417 5.54785 (15*2π)/31021 weeks
16-8.2069 2.96171 (16*2π)/31019 weeks
17-6.8335 -.12058 (17*2π)/31018 weeks
18-8.09908 .43632 (18*2π)/31017 weeks
19-3.61995 1.3034 (19*2π)/31016 weeks
20-1.90351 -2.29493 (20*2π)/31016 weeks
21-3.67436 -.1322 (21*2π)/31015 weeks
22-.68088 -.25809 (22*2π)/31014 weeks
23-2.19246 -1.94199 (23*2π)/31013 weeks
24-3.44024 1.16612 (24*2π)/31013 weeks
25-.80034 2.07116 (25*2π)/31012 weeks
26-2.45151 -5.25322 (26*2π)/31012 weeks
27-3.5441 -3.17733 (27*2π)/31011 weeks
281.493 -2.31095 (28*2π)/31011 weeks
291.78641 -4.44686 (29*2π)/31011 weeks
301.25208 -3.8155 (30*2π)/31010 weeks
315.20687 -1.6699 (31*2π)/31010 weeks
324.72226 -2.48889 (32*2π)/31010 weeks
334.15718 -.87409 (33*2π)/3109 weeks
347.30779 1.68437 (34*2π)/3109 weeks
355.62461 2.29372 (35*2π)/3109 weeks
364.23205 4.4278 (36*2π)/3109 weeks
374.04248 4.05786 (37*2π)/3108 weeks
381.33023 4.96066 (38*2π)/3108 weeks
392.47739 4.79932 (39*2π)/3108 weeks
403.32327 5.13774 (40*2π)/3108 weeks
41.64721 5.14636 (41*2π)/3108 weeks
42-1.27733 6.18025 (42*2π)/3107 weeks
43-1.05678 4.22752 (43*2π)/3107 weeks
44-2.77858 4.89618 (44*2π)/3107 weeks
45-3.45639 3.803 (45*2π)/3107 weeks
46-3.41185 .74924 (46*2π)/3107 weeks
47-2.42317 .55143 (47*2π)/3107 weeks
48-2.04738 .23441 (48*2π)/3106 weeks
49-3.20187 -.12319 (49*2π)/3106 weeks
50-1.37345 -.94477 (50*2π)/3106 weeks
51-.28176 -2.94281 (51*2π)/3106 weeks
52-.74197 -2.4486 (52*2π)/3106 weeks
53.68943 -.59523 (53*2π)/3106 weeks
542.33834 -2.14841 (54*2π)/3106 weeks
551.09163 -2.5943 (55*2π)/3106 weeks
562.96521 .26651 (56*2π)/3106 weeks
573.57477 -1.28554 (57*2π)/3105 weeks
582.36661 .5087 (58*2π)/3105 weeks
593.10196 2.17604 (59*2π)/3105 weeks
602.54297 1.66314 (60*2π)/3105 weeks
61.05858 .95716 (61*2π)/3105 weeks
621.01593 2.40255 (62*2π)/3105 weeks
63.97779 .79565 (63*2π)/3105 weeks
64.11563 1.10481 (64*2π)/3105 weeks
65.77679 1.53429 (65*2π)/3105 weeks
66.32627 .54828 (66*2π)/3105 weeks
67-1.01397 -.11133 (67*2π)/3105 weeks
68.71014 .06011 (68*2π)/3105 weeks
69-.012 -.57119 (69*2π)/3104 weeks
70.02689 -1.05841 (70*2π)/3104 weeks
711.79965 -1.34908 (71*2π)/3104 weeks
723.02238 -.80884 (72*2π)/3104 weeks
731.54224 .81945 (73*2π)/3104 weeks
742.15204 1.27722 (74*2π)/3104 weeks
751.59096 -.10476 (75*2π)/3104 weeks
761.65944 1.27059 (76*2π)/3104 weeks
771.60477 .79631 (77*2π)/3104 weeks
78.59293 .96403 (78*2π)/3104 weeks
791.28643 1.12156 (79*2π)/3104 weeks
801.6302 .34318 (80*2π)/3104 weeks
81-.47969 .80534 (81*2π)/3104 weeks
82.47226 1.13157 (82*2π)/3104 weeks
831.00035 -.70741 (83*2π)/3104 weeks
84-.30983 -.27838 (84*2π)/3104 weeks
85.60164 .25922 (85*2π)/3104 weeks
861.46949 -.75154 (86*2π)/3104 weeks
87.55544 -.27478 (87*2π)/3104 weeks
881.31997 -.30328 (88*2π)/3104 weeks
89.9784 -1.48262 (89*2π)/3103 weeks
901.25769 .07938 (90*2π)/3103 weeks
912.38384 -.06692 (91*2π)/3103 weeks
921.94112 -.65262 (92*2π)/3103 weeks
931.42473 .64636 (93*2π)/3103 weeks
942.41579 .77984 (94*2π)/3103 weeks
952.05951 .18703 (95*2π)/3103 weeks
961.3224 1.24416 (96*2π)/3103 weeks
971.9383 1.63442 (97*2π)/3103 weeks
981.91384 1.39136 (98*2π)/3103 weeks
991.35772 1.78362 (99*2π)/3103 weeks
100.71812 2.47115 (100*2π)/3103 weeks
1011.17102 1.51978 (101*2π)/3103 weeks
102.30099 1.28399 (102*2π)/3103 weeks
103.05066 1.73113 (103*2π)/3103 weeks
104.90509 1.83027 (104*2π)/3103 weeks
105.54682 .97687 (105*2π)/3103 weeks
106-.84081 1.55486 (106*2π)/3103 weeks
107-.74899 1.44047 (107*2π)/3103 weeks
108-.42348 .58992 (108*2π)/3103 weeks
109-.9729 -.17722 (109*2π)/3103 weeks
110-.43872 .21463 (110*2π)/3103 weeks
111.25138 -.45037 (111*2π)/3103 weeks
112-.08966 -.1901 (112*2π)/3103 weeks
113.34541 -.05542 (113*2π)/3103 weeks
114.46259 -.16606 (114*2π)/3103 weeks
115.31103 -.76606 (115*2π)/3103 weeks
116.34623 -.6997 (116*2π)/3103 weeks
117.60739 -.1804 (117*2π)/3103 weeks
118.84354 -.4074 (118*2π)/3103 weeks
119.36443 -.41421 (119*2π)/3103 weeks
120.54386 -.48949 (120*2π)/3103 weeks
121.81983 -.52656 (121*2π)/3103 weeks
122.60097 -1.3372 (122*2π)/3103 weeks
123.81632 -.75772 (123*2π)/3103 weeks
1241.67979 -.51264 (124*2π)/3103 weeks
1251.7214 -.7014 (125*2π)/3102 weeks
1261.35404 -.42764 (126*2π)/3102 weeks
1271.99915 .06852 (127*2π)/3102 weeks
1281.55791 .05094 (128*2π)/3102 weeks
1291.12358 .19595 (129*2π)/3102 weeks
1301.36969 .48731 (130*2π)/3102 weeks
1311.43031 -.01334 (131*2π)/3102 weeks
1321.27835 -.11708 (132*2π)/3102 weeks
1331.8176 .32919 (133*2π)/3102 weeks
1341.6643 .47799 (134*2π)/3102 weeks
1351.01508 .81053 (135*2π)/3102 weeks
136.8189 1.08596 (136*2π)/3102 weeks
137.70792 .53535 (137*2π)/3102 weeks
138.04732 .5161 (138*2π)/3102 weeks
139.42324 .6041 (139*2π)/3102 weeks
140.20064 -.1667 (140*2π)/3102 weeks
141.58801 .12569 (141*2π)/3102 weeks
1421.15783 -.02782 (142*2π)/3102 weeks
1431.07847 -.37843 (143*2π)/3102 weeks
144.80554 -.34351 (144*2π)/3102 weeks
1451.52752 .02813 (145*2π)/3102 weeks
1461.14046 -.53811 (146*2π)/3102 weeks
1471.21188 .58058 (147*2π)/3102 weeks
1481.58696 .31682 (148*2π)/3102 weeks
149.5868 .26374 (149*2π)/3102 weeks
150.46156 -.18522 (150*2π)/3102 weeks
1511.00652 .06882 (151*2π)/3102 weeks
1521.20545 -.44968 (152*2π)/3102 weeks
153.52077 -.38995 (153*2π)/3102 weeks
1541.42894 -.10677 (154*2π)/3102 weeks
1552.08315   (155*2π)/3102 weeks
1561.42894 .10677 (156*2π)/3102 weeks
157.52077 .38995 (157*2π)/3102 weeks
1581.20545 .44968 (158*2π)/3102 weeks
1591.00652 -.06882 (159*2π)/3102 weeks
160.46156 .18522 (160*2π)/3102 weeks
161.5868 -.26374 (161*2π)/3102 weeks
1621.58696 -.31682 (162*2π)/3102 weeks
1631.21188 -.58058 (163*2π)/3102 weeks
1641.14046 .53811 (164*2π)/3102 weeks
1651.52752 -.02813 (165*2π)/3102 weeks
166.80554 .34351 (166*2π)/3102 weeks
1671.07847 .37843 (167*2π)/3102 weeks
1681.15783 .02782 (168*2π)/3102 weeks
169.58801 -.12569 (169*2π)/3102 weeks
170.20064 .1667 (170*2π)/3102 weeks
171.42324 -.6041 (171*2π)/3102 weeks
172.04732 -.5161 (172*2π)/3102 weeks
173.70792 -.53535 (173*2π)/3102 weeks
174.8189 -1.08596 (174*2π)/3102 weeks
1751.01508 -.81053 (175*2π)/3102 weeks
1761.6643 -.47799 (176*2π)/3102 weeks
1771.8176 -.32919 (177*2π)/3102 weeks
1781.27835 .11708 (178*2π)/3102 weeks
1791.43031 .01334 (179*2π)/3102 weeks
1801.36969 -.48731 (180*2π)/3102 weeks
1811.12358 -.19595 (181*2π)/3102 weeks
1821.55791 -.05094 (182*2π)/3102 weeks
1831.99915 -.06852 (183*2π)/3102 weeks
1841.35404 .42764 (184*2π)/3102 weeks
1851.7214 .7014 (185*2π)/3102 weeks
1861.67979 .51264 (186*2π)/3102 weeks
187.81632 .75772 (187*2π)/3102 weeks
188.60097 1.3372 (188*2π)/3102 weeks
189.81983 .52656 (189*2π)/3102 weeks
190.54386 .48949 (190*2π)/3102 weeks
191.36443 .41421 (191*2π)/3102 weeks
192.84354 .4074 (192*2π)/3102 weeks
193.60739 .1804 (193*2π)/3102 weeks
194.34623 .6997 (194*2π)/3102 weeks
195.31103 .76606 (195*2π)/3102 weeks
196.46259 .16606 (196*2π)/3102 weeks
197.34541 .05542 (197*2π)/3102 weeks
198-.08966 .1901 (198*2π)/3102 weeks
199.25138 .45037 (199*2π)/3102 weeks
200-.43872 -.21463 (200*2π)/3102 weeks
201-.9729 .17722 (201*2π)/3102 weeks
202-.42348 -.58992 (202*2π)/3102 weeks
203-.74899 -1.44047 (203*2π)/3102 weeks
204-.84081 -1.55486 (204*2π)/3102 weeks
205.54682 -.97687 (205*2π)/3102 weeks
206.90509 -1.83027 (206*2π)/3102 weeks
207.05066 -1.73113 (207*2π)/3101 weeks
208.30099 -1.28399 (208*2π)/3101 weeks
2091.17102 -1.51978 (209*2π)/3101 weeks
210.71812 -2.47115 (210*2π)/3101 weeks
2111.35772 -1.78362 (211*2π)/3101 weeks
2121.91384 -1.39136 (212*2π)/3101 weeks
2131.9383 -1.63442 (213*2π)/3101 weeks
2141.3224 -1.24416 (214*2π)/3101 weeks
2152.05951 -.18703 (215*2π)/3101 weeks
2162.41579 -.77984 (216*2π)/3101 weeks
2171.42473 -.64636 (217*2π)/3101 weeks
2181.94112 .65262 (218*2π)/3101 weeks
2192.38384 .06692 (219*2π)/3101 weeks
2201.25769 -.07938 (220*2π)/3101 weeks
221.9784 1.48262 (221*2π)/3101 weeks
2221.31997 .30328 (222*2π)/3101 weeks
223.55544 .27478 (223*2π)/3101 weeks
2241.46949 .75154 (224*2π)/3101 weeks
225.60164 -.25922 (225*2π)/3101 weeks
226-.30983 .27838 (226*2π)/3101 weeks
2271.00035 .70741 (227*2π)/3101 weeks
228.47226 -1.13157 (228*2π)/3101 weeks
229-.47969 -.80534 (229*2π)/3101 weeks
2301.6302 -.34318 (230*2π)/3101 weeks
2311.28643 -1.12156 (231*2π)/3101 weeks
232.59293 -.96403 (232*2π)/3101 weeks
2331.60477 -.79631 (233*2π)/3101 weeks
2341.65944 -1.27059 (234*2π)/3101 weeks
2351.59096 .10476 (235*2π)/3101 weeks
2362.15204 -1.27722 (236*2π)/3101 weeks
2371.54224 -.81945 (237*2π)/3101 weeks
2383.02238 .80884 (238*2π)/3101 weeks
2391.79965 1.34908 (239*2π)/3101 weeks
240.02689 1.05841 (240*2π)/3101 weeks
241-.012 .57119 (241*2π)/3101 weeks
242.71014 -.06011 (242*2π)/3101 weeks
243-1.01397 .11133 (243*2π)/3101 weeks
244.32627 -.54828 (244*2π)/3101 weeks
245.77679 -1.53429 (245*2π)/3101 weeks
246.11563 -1.10481 (246*2π)/3101 weeks
247.97779 -.79565 (247*2π)/3101 weeks
2481.01593 -2.40255 (248*2π)/3101 weeks
249.05858 -.95716 (249*2π)/3101 weeks
2502.54297 -1.66314 (250*2π)/3101 weeks
2513.10196 -2.17604 (251*2π)/3101 weeks
2522.36661 -.5087 (252*2π)/3101 weeks
2533.57477 1.28554 (253*2π)/3101 weeks
2542.96521 -.26651 (254*2π)/3101 weeks
2551.09163 2.5943 (255*2π)/3101 weeks
2562.33834 2.14841 (256*2π)/3101 weeks
257.68943 .59523 (257*2π)/3101 weeks
258-.74197 2.4486 (258*2π)/3101 weeks
259-.28176 2.94281 (259*2π)/3101 weeks
260-1.37345 .94477 (260*2π)/3101 weeks
261-3.20187 .12319 (261*2π)/3101 weeks
262-2.04738 -.23441 (262*2π)/3101 weeks
263-2.42317 -.55143 (263*2π)/3101 weeks
264-3.41185 -.74924 (264*2π)/3101 weeks
265-3.45639 -3.803 (265*2π)/3101 weeks
266-2.77858 -4.89618 (266*2π)/3101 weeks
267-1.05678 -4.22752 (267*2π)/3101 weeks
268-1.27733 -6.18025 (268*2π)/3101 weeks
269.64721 -5.14636 (269*2π)/3101 weeks
2703.32327 -5.13774 (270*2π)/3101 weeks
2712.47739 -4.79932 (271*2π)/3101 weeks
2721.33023 -4.96066 (272*2π)/3101 weeks
2734.04248 -4.05786 (273*2π)/3101 weeks
2744.23205 -4.4278 (274*2π)/3101 weeks
2755.62461 -2.29372 (275*2π)/3101 weeks
2767.30779 -1.68437 (276*2π)/3101 weeks
2774.15718 .87409 (277*2π)/3101 weeks
2784.72226 2.48889 (278*2π)/3101 weeks
2795.20687 1.6699 (279*2π)/3101 weeks
2801.25208 3.8155 (280*2π)/3101 weeks
2811.78641 4.44686 (281*2π)/3101 weeks
2821.493 2.31095 (282*2π)/3101 weeks
283-3.5441 3.17733 (283*2π)/3101 weeks
284-2.45151 5.25322 (284*2π)/3101 weeks
285-.80034 -2.07116 (285*2π)/3101 weeks
286-3.44024 -1.16612 (286*2π)/3101 weeks
287-2.19246 1.94199 (287*2π)/3101 weeks
288-.68088 .25809 (288*2π)/3101 weeks
289-3.67436 .1322 (289*2π)/3101 weeks
290-1.90351 2.29493 (290*2π)/3101 weeks
291-3.61995 -1.3034 (291*2π)/3101 weeks
292-8.09908 -.43632 (292*2π)/3101 weeks
293-6.8335 .12058 (293*2π)/3101 weeks
294-8.2069 -2.96171 (294*2π)/3101 weeks
295-13.16417 -5.54785 (295*2π)/3101 weeks
296-7.71167 -8.81388 (296*2π)/3101 weeks
297-5.77018 -12.92332 (297*2π)/3101 weeks
298-6.51951 -12.18373 (298*2π)/3101 weeks
299-7.2047 -11.58396 (299*2π)/3101 weeks
300-6.1871 -15.69346 (300*2π)/3101 weeks
301-6.62444 -21.95379 (301*2π)/3101 weeks
302-3.73451 -29.72938 (302*2π)/3101 weeks
3035.64761 -22.20259 (303*2π)/3101 weeks
30412.49743 -28.72614 (304*2π)/3101 weeks
3053.70635 -35.91929 (305*2π)/3101 weeks
30622.99623 -23.16098 (306*2π)/3101 weeks
30736.01801 -28.03796 (307*2π)/3101 weeks
30824.09522 -45.67012 (308*2π)/3101 weeks



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