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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 24 weeks (14.7586*sine), 26 weeks (13.631*sine), and 28 weeks (13.494*sine).

DGAZ (VelocityShares 3x Inv Natural Gas ETN) has an average price of 72.5 (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 DGAZ (VelocityShares 3x Inv Natural Gas ETN), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
072.49697   0 
156.38227 17.94465 (1*2π)/284284 weeks
216.55368 38.62741 (2*2π)/284142 weeks
329.63128 39.79683 (3*2π)/28495 weeks
429.4518 37.22465 (4*2π)/28471 weeks
56.62241 24.09876 (5*2π)/28457 weeks
62.21417 30.56536 (6*2π)/28447 weeks
74.15508 34.5593 (7*2π)/28441 weeks
8-6.07137 24.79557 (8*2π)/28436 weeks
9-7.60843 17.37581 (9*2π)/28432 weeks
10-8.57117 13.49395 (10*2π)/28428 weeks
11-7.31077 13.631 (11*2π)/28426 weeks
12-7.3561 14.75858 (12*2π)/28424 weeks
13-8.36066 11.11743 (13*2π)/28422 weeks
14-12.4275 3.38144 (14*2π)/28420 weeks
15-9.52288 2.9495 (15*2π)/28419 weeks
16-5.74523 2.17261 (16*2π)/28418 weeks
17-4.079 -2.09123 (17*2π)/28417 weeks
18-5.48562 -2.41916 (18*2π)/28416 weeks
19-3.32388 1.03748 (19*2π)/28415 weeks
20-1.00062 -1.00426 (20*2π)/28414 weeks
21-2.89698 -1.6287 (21*2π)/28414 weeks
22-3.75876 1.32085 (22*2π)/28413 weeks
23-2.10892 3.05512 (23*2π)/28412 weeks
24-.25628 -4.42504 (24*2π)/28412 weeks
25-1.91894 -6.00138 (25*2π)/28411 weeks
26-.29429 -2.71747 (26*2π)/28411 weeks
272.61397 -2.74288 (27*2π)/28411 weeks
285.10553 -4.70456 (28*2π)/28410 weeks
293.85158 -2.13377 (29*2π)/28410 weeks
305.1855 -.12316 (30*2π)/2849 weeks
318.47666 .66437 (31*2π)/2849 weeks
326.21013 2.36464 (32*2π)/2849 weeks
334.76278 4.74211 (33*2π)/2849 weeks
344.6923 4.60739 (34*2π)/2848 weeks
351.58548 4.24795 (35*2π)/2848 weeks
362.01122 4.77898 (36*2π)/2848 weeks
372.02824 7.1292 (37*2π)/2848 weeks
38.99639 6.65254 (38*2π)/2847 weeks
39-1.73648 4.79976 (39*2π)/2847 weeks
40-1.7607 5.65821 (40*2π)/2847 weeks
41-3.18362 3.99336 (41*2π)/2847 weeks
42-4.18731 .92413 (42*2π)/2847 weeks
43-2.71178 .4911 (43*2π)/2847 weeks
44-2.24786 .14213 (44*2π)/2846 weeks
45-3.58018 -.77702 (45*2π)/2846 weeks
46-2.10981 -1.06126 (46*2π)/2846 weeks
47.45355 -2.07 (47*2π)/2846 weeks
481.15307 -3.19984 (48*2π)/2846 weeks
49-.08435 -2.71414 (49*2π)/2846 weeks
50.98425 -.92763 (50*2π)/2846 weeks
514.19442 -1.21041 (51*2π)/2846 weeks
522.64597 -1.72473 (52*2π)/2845 weeks
532.67044 .952 (53*2π)/2845 weeks
543.54091 2.23991 (54*2π)/2845 weeks
552.74221 1.96094 (55*2π)/2845 weeks
56.46964 .56414 (56*2π)/2845 weeks
57.19934 2.27137 (57*2π)/2845 weeks
581.10439 1.44453 (58*2π)/2845 weeks
59.5321 .6191 (59*2π)/2845 weeks
60-.40925 1.23585 (60*2π)/2845 weeks
61-.60134 1.31988 (61*2π)/2845 weeks
62.68055 -.56678 (62*2π)/2845 weeks
63-.19884 -.23999 (63*2π)/2845 weeks
64.04017 -.82972 (64*2π)/2844 weeks
651.91743 -1.5112 (65*2π)/2844 weeks
663.36634 -.74154 (66*2π)/2844 weeks
671.57106 .55445 (67*2π)/2844 weeks
681.56644 1.57113 (68*2π)/2844 weeks
692.36138 .35369 (69*2π)/2844 weeks
701.29148 1.11929 (70*2π)/2844 weeks
711.41704 1.58211 (71*2π)/2844 weeks
721.36792 .55688 (72*2π)/2844 weeks
73.75827 .35479 (73*2π)/2844 weeks
74-.13264 1.97476 (74*2π)/2844 weeks
75.90352 1.17361 (75*2π)/2844 weeks
76.9306 -.69719 (76*2π)/2844 weeks
77-.26413 -.3165 (77*2π)/2844 weeks
78.30516 .28861 (78*2π)/2844 weeks
791.69933 -.03752 (79*2π)/2844 weeks
80.86026 -.52992 (80*2π)/2844 weeks
81.85302 .05676 (81*2π)/2844 weeks
822.64548 -.50303 (82*2π)/2843 weeks
832.13791 -.95044 (83*2π)/2843 weeks
841.592 -.16981 (84*2π)/2843 weeks
852.27106 1.04248 (85*2π)/2843 weeks
862.92342 .54823 (86*2π)/2843 weeks
872.36192 .19473 (87*2π)/2843 weeks
881.62854 1.19368 (88*2π)/2843 weeks
892.01974 1.76831 (89*2π)/2843 weeks
902.22837 1.79375 (90*2π)/2843 weeks
911.77437 1.93769 (91*2π)/2843 weeks
92.33211 1.70571 (92*2π)/2843 weeks
93.59855 2.24245 (93*2π)/2843 weeks
94.89964 1.90308 (94*2π)/2843 weeks
951.02796 1.13159 (95*2π)/2843 weeks
96.04326 1.02786 (96*2π)/2843 weeks
97-.76167 2.03773 (97*2π)/2843 weeks
98-.70658 1.57611 (98*2π)/2843 weeks
99-.40761 .69015 (99*2π)/2843 weeks
100-.71039 -.4261 (100*2π)/2843 weeks
101-.65999 -.13432 (101*2π)/2843 weeks
102.35053 -.12841 (102*2π)/2843 weeks
103.23222 -.52442 (103*2π)/2843 weeks
104.16186 -.36978 (104*2π)/2843 weeks
105-.12447 -.37744 (105*2π)/2843 weeks
106.35294 -.39603 (106*2π)/2843 weeks
107.89288 -.20195 (107*2π)/2843 weeks
108.88896 -.47971 (108*2π)/2843 weeks
109.41374 -.37312 (109*2π)/2843 weeks
110.59546 -.49119 (110*2π)/2843 weeks
111.81995 -.38045 (111*2π)/2843 weeks
1121.26565 -1.33948 (112*2π)/2843 weeks
1131.2036 -1.30072 (113*2π)/2843 weeks
1141.39587 -.55414 (114*2π)/2842 weeks
1151.78788 -.15128 (115*2π)/2842 weeks
1162.16638 -.43905 (116*2π)/2842 weeks
1171.61431 .17292 (117*2π)/2842 weeks
1181.37109 .44342 (118*2π)/2842 weeks
1191.65524 .48974 (119*2π)/2842 weeks
1201.56705 .00183 (120*2π)/2842 weeks
1211.46912 -.12392 (121*2π)/2842 weeks
1221.91649 .54833 (122*2π)/2842 weeks
1231.89624 .86946 (123*2π)/2842 weeks
1241.30728 .81722 (124*2π)/2842 weeks
125.57961 .87828 (125*2π)/2842 weeks
126.65762 .99912 (126*2π)/2842 weeks
127.74682 .27378 (127*2π)/2842 weeks
128.12449 -.01125 (128*2π)/2842 weeks
129.83942 -.04092 (129*2π)/2842 weeks
1301.22665 -.31817 (130*2π)/2842 weeks
1311.09701 -.52143 (131*2π)/2842 weeks
132.86246 -.54189 (132*2π)/2842 weeks
1331.42507 .1576 (133*2π)/2842 weeks
1341.74231 -.53659 (134*2π)/2842 weeks
135.94776 .09434 (135*2π)/2842 weeks
1361.04326 .85035 (136*2π)/2842 weeks
137.62942 .1868 (137*2π)/2842 weeks
1381.17631 -.33017 (138*2π)/2842 weeks
139.86612 -.5429 (139*2π)/2842 weeks
140.60229 -.03506 (140*2π)/2842 weeks
1411.62915 -.19158 (141*2π)/2842 weeks
1422.22775   (142*2π)/2842 weeks
1431.62915 .19158 (143*2π)/2842 weeks
144.60229 .03506 (144*2π)/2842 weeks
145.86612 .5429 (145*2π)/2842 weeks
1461.17631 .33017 (146*2π)/2842 weeks
147.62942 -.1868 (147*2π)/2842 weeks
1481.04326 -.85035 (148*2π)/2842 weeks
149.94776 -.09434 (149*2π)/2842 weeks
1501.74231 .53659 (150*2π)/2842 weeks
1511.42507 -.1576 (151*2π)/2842 weeks
152.86246 .54189 (152*2π)/2842 weeks
1531.09701 .52143 (153*2π)/2842 weeks
1541.22665 .31817 (154*2π)/2842 weeks
155.83942 .04092 (155*2π)/2842 weeks
156.12449 .01125 (156*2π)/2842 weeks
157.74682 -.27378 (157*2π)/2842 weeks
158.65762 -.99912 (158*2π)/2842 weeks
159.57961 -.87828 (159*2π)/2842 weeks
1601.30728 -.81722 (160*2π)/2842 weeks
1611.89624 -.86946 (161*2π)/2842 weeks
1621.91649 -.54833 (162*2π)/2842 weeks
1631.46912 .12392 (163*2π)/2842 weeks
1641.56705 -.00183 (164*2π)/2842 weeks
1651.65524 -.48974 (165*2π)/2842 weeks
1661.37109 -.44342 (166*2π)/2842 weeks
1671.61431 -.17292 (167*2π)/2842 weeks
1682.16638 .43905 (168*2π)/2842 weeks
1691.78788 .15128 (169*2π)/2842 weeks
1701.39587 .55414 (170*2π)/2842 weeks
1711.2036 1.30072 (171*2π)/2842 weeks
1721.26565 1.33948 (172*2π)/2842 weeks
173.81995 .38045 (173*2π)/2842 weeks
174.59546 .49119 (174*2π)/2842 weeks
175.41374 .37312 (175*2π)/2842 weeks
176.88896 .47971 (176*2π)/2842 weeks
177.89288 .20195 (177*2π)/2842 weeks
178.35294 .39603 (178*2π)/2842 weeks
179-.12447 .37744 (179*2π)/2842 weeks
180.16186 .36978 (180*2π)/2842 weeks
181.23222 .52442 (181*2π)/2842 weeks
182.35053 .12841 (182*2π)/2842 weeks
183-.65999 .13432 (183*2π)/2842 weeks
184-.71039 .4261 (184*2π)/2842 weeks
185-.40761 -.69015 (185*2π)/2842 weeks
186-.70658 -1.57611 (186*2π)/2842 weeks
187-.76167 -2.03773 (187*2π)/2842 weeks
188.04326 -1.02786 (188*2π)/2842 weeks
1891.02796 -1.13159 (189*2π)/2842 weeks
190.89964 -1.90308 (190*2π)/2841 weeks
191.59855 -2.24245 (191*2π)/2841 weeks
192.33211 -1.70571 (192*2π)/2841 weeks
1931.77437 -1.93769 (193*2π)/2841 weeks
1942.22837 -1.79375 (194*2π)/2841 weeks
1952.01974 -1.76831 (195*2π)/2841 weeks
1961.62854 -1.19368 (196*2π)/2841 weeks
1972.36192 -.19473 (197*2π)/2841 weeks
1982.92342 -.54823 (198*2π)/2841 weeks
1992.27106 -1.04248 (199*2π)/2841 weeks
2001.592 .16981 (200*2π)/2841 weeks
2012.13791 .95044 (201*2π)/2841 weeks
2022.64548 .50303 (202*2π)/2841 weeks
203.85302 -.05676 (203*2π)/2841 weeks
204.86026 .52992 (204*2π)/2841 weeks
2051.69933 .03752 (205*2π)/2841 weeks
206.30516 -.28861 (206*2π)/2841 weeks
207-.26413 .3165 (207*2π)/2841 weeks
208.9306 .69719 (208*2π)/2841 weeks
209.90352 -1.17361 (209*2π)/2841 weeks
210-.13264 -1.97476 (210*2π)/2841 weeks
211.75827 -.35479 (211*2π)/2841 weeks
2121.36792 -.55688 (212*2π)/2841 weeks
2131.41704 -1.58211 (213*2π)/2841 weeks
2141.29148 -1.11929 (214*2π)/2841 weeks
2152.36138 -.35369 (215*2π)/2841 weeks
2161.56644 -1.57113 (216*2π)/2841 weeks
2171.57106 -.55445 (217*2π)/2841 weeks
2183.36634 .74154 (218*2π)/2841 weeks
2191.91743 1.5112 (219*2π)/2841 weeks
220.04017 .82972 (220*2π)/2841 weeks
221-.19884 .23999 (221*2π)/2841 weeks
222.68055 .56678 (222*2π)/2841 weeks
223-.60134 -1.31988 (223*2π)/2841 weeks
224-.40925 -1.23585 (224*2π)/2841 weeks
225.5321 -.6191 (225*2π)/2841 weeks
2261.10439 -1.44453 (226*2π)/2841 weeks
227.19934 -2.27137 (227*2π)/2841 weeks
228.46964 -.56414 (228*2π)/2841 weeks
2292.74221 -1.96094 (229*2π)/2841 weeks
2303.54091 -2.23991 (230*2π)/2841 weeks
2312.67044 -.952 (231*2π)/2841 weeks
2322.64597 1.72473 (232*2π)/2841 weeks
2334.19442 1.21041 (233*2π)/2841 weeks
234.98425 .92763 (234*2π)/2841 weeks
235-.08435 2.71414 (235*2π)/2841 weeks
2361.15307 3.19984 (236*2π)/2841 weeks
237.45355 2.07 (237*2π)/2841 weeks
238-2.10981 1.06126 (238*2π)/2841 weeks
239-3.58018 .77702 (239*2π)/2841 weeks
240-2.24786 -.14213 (240*2π)/2841 weeks
241-2.71178 -.4911 (241*2π)/2841 weeks
242-4.18731 -.92413 (242*2π)/2841 weeks
243-3.18362 -3.99336 (243*2π)/2841 weeks
244-1.7607 -5.65821 (244*2π)/2841 weeks
245-1.73648 -4.79976 (245*2π)/2841 weeks
246.99639 -6.65254 (246*2π)/2841 weeks
2472.02824 -7.1292 (247*2π)/2841 weeks
2482.01122 -4.77898 (248*2π)/2841 weeks
2491.58548 -4.24795 (249*2π)/2841 weeks
2504.6923 -4.60739 (250*2π)/2841 weeks
2514.76278 -4.74211 (251*2π)/2841 weeks
2526.21013 -2.36464 (252*2π)/2841 weeks
2538.47666 -.66437 (253*2π)/2841 weeks
2545.1855 .12316 (254*2π)/2841 weeks
2553.85158 2.13377 (255*2π)/2841 weeks
2565.10553 4.70456 (256*2π)/2841 weeks
2572.61397 2.74288 (257*2π)/2841 weeks
258-.29429 2.71747 (258*2π)/2841 weeks
259-1.91894 6.00138 (259*2π)/2841 weeks
260-.25628 4.42504 (260*2π)/2841 weeks
261-2.10892 -3.05512 (261*2π)/2841 weeks
262-3.75876 -1.32085 (262*2π)/2841 weeks
263-2.89698 1.6287 (263*2π)/2841 weeks
264-1.00062 1.00426 (264*2π)/2841 weeks
265-3.32388 -1.03748 (265*2π)/2841 weeks
266-5.48562 2.41916 (266*2π)/2841 weeks
267-4.079 2.09123 (267*2π)/2841 weeks
268-5.74523 -2.17261 (268*2π)/2841 weeks
269-9.52288 -2.9495 (269*2π)/2841 weeks
270-12.4275 -3.38144 (270*2π)/2841 weeks
271-8.36066 -11.11743 (271*2π)/2841 weeks
272-7.3561 -14.75858 (272*2π)/2841 weeks
273-7.31077 -13.631 (273*2π)/2841 weeks
274-8.57117 -13.49395 (274*2π)/2841 weeks
275-7.60843 -17.37581 (275*2π)/2841 weeks
276-6.07137 -24.79557 (276*2π)/2841 weeks
2774.15508 -34.5593 (277*2π)/2841 weeks
2782.21417 -30.56536 (278*2π)/2841 weeks
2796.62241 -24.09876 (279*2π)/2841 weeks
28029.4518 -37.22465 (280*2π)/2841 weeks
28129.63128 -39.79683 (281*2π)/2841 weeks
28216.55368 -38.62741 (282*2π)/2841 weeks



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