Back to list of Stocks    See Also: Seasonal Analysis of DGAZGenetic Algorithms Stock Portfolio Generator, and Best Months to Buy/Sell Stocks

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


DGAZ (VelocityShares 3x Inv Natural Gas ETN) appears to have interesting cyclic behaviour every 30 weeks (16.4797*sine), 27 weeks (12.7654*sine), and 21 weeks (11.9004*cosine).

DGAZ (VelocityShares 3x Inv Natural Gas ETN) has an average price of 70.45 (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 10/9/2017 for DGAZ (VelocityShares 3x Inv Natural Gas ETN), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
070.44599   0 
152.14293 17.01799 (1*2π)/297297 weeks
219.45088 43.18521 (2*2π)/297149 weeks
334.21675 34.88535 (3*2π)/29799 weeks
427.98288 28.08039 (4*2π)/29774 weeks
51.73031 29.02714 (5*2π)/29759 weeks
67.30045 32.77709 (6*2π)/29750 weeks
78.5378 27.44407 (7*2π)/29742 weeks
8-6.45423 25.72578 (8*2π)/29737 weeks
9-9.11622 19.62612 (9*2π)/29733 weeks
10-8.02659 16.47967 (10*2π)/29730 weeks
11-5.36024 12.7654 (11*2π)/29727 weeks
12-5.81241 11.28802 (12*2π)/29725 weeks
13-10.20627 11.15049 (13*2π)/29723 weeks
14-11.90036 11.01275 (14*2π)/29721 weeks
15-9.05247 2.83053 (15*2π)/29720 weeks
16-8.77378 1.21387 (16*2π)/29719 weeks
17-7.11884 2.62571 (17*2π)/29717 weeks
18-2.7028 .05301 (18*2π)/29717 weeks
19-3.37691 -2.77635 (19*2π)/29716 weeks
20-3.55175 .59925 (20*2π)/29715 weeks
21-.66522 -.50229 (21*2π)/29714 weeks
22-2.43622 -1.70562 (22*2π)/29714 weeks
23-3.49226 1.35297 (23*2π)/29713 weeks
24-1.24985 2.69927 (24*2π)/29712 weeks
25-1.1801 -4.98833 (25*2π)/29712 weeks
26-3.06778 -4.60233 (26*2π)/29711 weeks
27.67847 -1.90489 (27*2π)/29711 weeks
282.84416 -3.57498 (28*2π)/29711 weeks
292.82661 -4.92467 (29*2π)/29710 weeks
304.28588 -.91366 (30*2π)/29710 weeks
316.15471 -1.04587 (31*2π)/29710 weeks
326.37075 -1.75161 (32*2π)/2979 weeks
336.01427 2.75157 (33*2π)/2979 weeks
346.14031 3.88107 (34*2π)/2979 weeks
353.9841 4.02055 (35*2π)/2978 weeks
363.50102 5.85877 (36*2π)/2978 weeks
372.9584 3.70766 (37*2π)/2978 weeks
382.71078 3.8504 (38*2π)/2978 weeks
39.5301 6.03155 (39*2π)/2978 weeks
40-.21004 6.76336 (40*2π)/2977 weeks
41-1.36606 4.27139 (41*2π)/2977 weeks
42-2.35482 5.31965 (42*2π)/2977 weeks
43-3.27307 3.86427 (43*2π)/2977 weeks
44-3.77398 .72547 (44*2π)/2977 weeks
45-2.57413 .45002 (45*2π)/2977 weeks
46-2.16552 .12348 (46*2π)/2976 weeks
47-3.434 -.47941 (47*2π)/2976 weeks
48-1.71607 -.97257 (48*2π)/2976 weeks
49.22623 -2.69195 (49*2π)/2976 weeks
50-.06117 -3.22873 (50*2π)/2976 weeks
51-.27943 -1.31565 (51*2π)/2976 weeks
522.15791 -.99625 (52*2π)/2976 weeks
532.90195 -2.9397 (53*2π)/2976 weeks
541.66233 -.35365 (54*2π)/2976 weeks
553.99967 .52796 (55*2π)/2975 weeks
563.4677 .24699 (56*2π)/2975 weeks
571.72091 1.74182 (57*2π)/2975 weeks
58.94418 3.03154 (58*2π)/2975 weeks
592.11722 1.26349 (59*2π)/2975 weeks
60.16525 .87661 (60*2π)/2975 weeks
61.48415 1.60259 (61*2π)/2975 weeks
621.01474 .9492 (62*2π)/2975 weeks
63-.18538 .55613 (63*2π)/2975 weeks
64-1.10395 .65476 (64*2π)/2975 weeks
65.75758 -.21002 (65*2π)/2975 weeks
66-.16371 -.44225 (66*2π)/2975 weeks
67-.02146 -.94437 (67*2π)/2974 weeks
681.81646 -1.42379 (68*2π)/2974 weeks
693.14173 -.78043 (69*2π)/2974 weeks
701.47993 .7033 (70*2π)/2974 weeks
711.85072 1.49662 (71*2π)/2974 weeks
721.95238 .03019 (72*2π)/2974 weeks
731.35748 1.2812 (73*2π)/2974 weeks
741.6229 1.19445 (74*2π)/2974 weeks
75.69979 .54242 (75*2π)/2974 weeks
76.56172 1.16295 (76*2π)/2974 weeks
771.55542 1.82335 (77*2π)/2974 weeks
78.47765 -.01412 (78*2π)/2974 weeks
79-.65858 .22795 (79*2π)/2974 weeks
80.80536 .94604 (80*2π)/2974 weeks
811.15991 -.49892 (81*2π)/2974 weeks
82.47117 -.9307 (82*2π)/2974 weeks
83.94843 .28394 (83*2π)/2974 weeks
841.25726 -.57582 (84*2π)/2974 weeks
85.49144 -.69967 (85*2π)/2973 weeks
862.09382 .23864 (86*2π)/2973 weeks
872.53828 -.53621 (87*2π)/2973 weeks
881.7557 -.49908 (88*2π)/2973 weeks
891.83822 .92002 (89*2π)/2973 weeks
902.73541 .70386 (90*2π)/2973 weeks
912.26256 .19911 (91*2π)/2973 weeks
921.51515 1.22164 (92*2π)/2973 weeks
932.02464 1.70919 (93*2π)/2973 weeks
942.13338 1.56047 (94*2π)/2973 weeks
951.56705 1.78003 (95*2π)/2973 weeks
96.38735 2.21039 (96*2π)/2973 weeks
971.13376 2.04767 (97*2π)/2973 weeks
98.83652 1.31138 (98*2π)/2973 weeks
99.13717 1.04744 (99*2π)/2973 weeks
100-.03234 2.01193 (100*2π)/2973 weeks
101.64988 2.18113 (101*2π)/2973 weeks
102-.24846 1.11573 (102*2π)/2973 weeks
103-.93519 .58759 (103*2π)/2973 weeks
104-.96391 .67745 (104*2π)/2973 weeks
105-.02057 -.09331 (105*2π)/2973 weeks
106-.23042 -.68519 (106*2π)/2973 weeks
107.08251 -.0364 (107*2π)/2973 weeks
108.46763 -.34259 (108*2π)/2973 weeks
109.38696 -.42801 (109*2π)/2973 weeks
110.02166 -.72478 (110*2π)/2973 weeks
111.27802 -.58423 (111*2π)/2973 weeks
112.73159 -.19203 (112*2π)/2973 weeks
113.86321 -.4682 (113*2π)/2973 weeks
114.38283 -.41906 (114*2π)/2973 weeks
115.56674 -.51212 (115*2π)/2973 weeks
116.83848 -.4769 (116*2π)/2973 weeks
117.92159 -1.43186 (117*2π)/2973 weeks
118.88663 -1.06643 (118*2π)/2973 weeks
1191.51172 -.41958 (119*2π)/2972 weeks
1201.90741 -.42693 (120*2π)/2972 weeks
1211.68372 -.64468 (121*2π)/2972 weeks
1221.76132 .28297 (122*2π)/2972 weeks
1231.70496 .28847 (123*2π)/2972 weeks
1241.50557 -.08298 (124*2π)/2972 weeks
1251.01806 .09134 (125*2π)/2972 weeks
1261.28478 .19489 (126*2π)/2972 weeks
1271.77042 -.0472 (127*2π)/2972 weeks
1281.55947 .51355 (128*2π)/2972 weeks
1291.36192 1.11201 (129*2π)/2972 weeks
1301.21236 1.03607 (130*2π)/2972 weeks
131.60381 .59752 (131*2π)/2972 weeks
132.26638 .86565 (132*2π)/2972 weeks
133.6819 .496 (133*2π)/2972 weeks
134.18259 -.11784 (134*2π)/2972 weeks
135.74085 .05076 (135*2π)/2972 weeks
1361.21928 -.18652 (136*2π)/2972 weeks
1371.09849 -.46879 (137*2π)/2972 weeks
138.83325 -.45692 (138*2π)/2972 weeks
1391.49792 .08369 (139*2π)/2972 weeks
1401.41797 -.62183 (140*2π)/2972 weeks
141.97905 .3982 (141*2π)/2972 weeks
1421.44853 .67823 (142*2π)/2972 weeks
143.68144 .16383 (143*2π)/2972 weeks
144.75483 -.48551 (144*2π)/2972 weeks
145.67658 -.08285 (145*2π)/2972 weeks
1461.26934 .06667 (146*2π)/2972 weeks
1471.27505 -.89608 (147*2π)/2972 weeks
1481.34374 -.54849 (148*2π)/2972 weeks
1491.34374 .54849 (149*2π)/2972 weeks
1501.27505 .89608 (150*2π)/2972 weeks
1511.26934 -.06667 (151*2π)/2972 weeks
152.67658 .08285 (152*2π)/2972 weeks
153.75483 .48551 (153*2π)/2972 weeks
154.68144 -.16383 (154*2π)/2972 weeks
1551.44853 -.67823 (155*2π)/2972 weeks
156.97905 -.3982 (156*2π)/2972 weeks
1571.41797 .62183 (157*2π)/2972 weeks
1581.49792 -.08369 (158*2π)/2972 weeks
159.83325 .45692 (159*2π)/2972 weeks
1601.09849 .46879 (160*2π)/2972 weeks
1611.21928 .18652 (161*2π)/2972 weeks
162.74085 -.05076 (162*2π)/2972 weeks
163.18259 .11784 (163*2π)/2972 weeks
164.6819 -.496 (164*2π)/2972 weeks
165.26638 -.86565 (165*2π)/2972 weeks
166.60381 -.59752 (166*2π)/2972 weeks
1671.21236 -1.03607 (167*2π)/2972 weeks
1681.36192 -1.11201 (168*2π)/2972 weeks
1691.55947 -.51355 (169*2π)/2972 weeks
1701.77042 .0472 (170*2π)/2972 weeks
1711.28478 -.19489 (171*2π)/2972 weeks
1721.01806 -.09134 (172*2π)/2972 weeks
1731.50557 .08298 (173*2π)/2972 weeks
1741.70496 -.28847 (174*2π)/2972 weeks
1751.76132 -.28297 (175*2π)/2972 weeks
1761.68372 .64468 (176*2π)/2972 weeks
1771.90741 .42693 (177*2π)/2972 weeks
1781.51172 .41958 (178*2π)/2972 weeks
179.88663 1.06643 (179*2π)/2972 weeks
180.92159 1.43186 (180*2π)/2972 weeks
181.83848 .4769 (181*2π)/2972 weeks
182.56674 .51212 (182*2π)/2972 weeks
183.38283 .41906 (183*2π)/2972 weeks
184.86321 .4682 (184*2π)/2972 weeks
185.73159 .19203 (185*2π)/2972 weeks
186.27802 .58423 (186*2π)/2972 weeks
187.02166 .72478 (187*2π)/2972 weeks
188.38696 .42801 (188*2π)/2972 weeks
189.46763 .34259 (189*2π)/2972 weeks
190.08251 .0364 (190*2π)/2972 weeks
191-.23042 .68519 (191*2π)/2972 weeks
192-.02057 .09331 (192*2π)/2972 weeks
193-.96391 -.67745 (193*2π)/2972 weeks
194-.93519 -.58759 (194*2π)/2972 weeks
195-.24846 -1.11573 (195*2π)/2972 weeks
196.64988 -2.18113 (196*2π)/2972 weeks
197-.03234 -2.01193 (197*2π)/2972 weeks
198.13717 -1.04744 (198*2π)/2972 weeks
199.83652 -1.31138 (199*2π)/2971 weeks
2001.13376 -2.04767 (200*2π)/2971 weeks
201.38735 -2.21039 (201*2π)/2971 weeks
2021.56705 -1.78003 (202*2π)/2971 weeks
2032.13338 -1.56047 (203*2π)/2971 weeks
2042.02464 -1.70919 (204*2π)/2971 weeks
2051.51515 -1.22164 (205*2π)/2971 weeks
2062.26256 -.19911 (206*2π)/2971 weeks
2072.73541 -.70386 (207*2π)/2971 weeks
2081.83822 -.92002 (208*2π)/2971 weeks
2091.7557 .49908 (209*2π)/2971 weeks
2102.53828 .53621 (210*2π)/2971 weeks
2112.09382 -.23864 (211*2π)/2971 weeks
212.49144 .69967 (212*2π)/2971 weeks
2131.25726 .57582 (213*2π)/2971 weeks
214.94843 -.28394 (214*2π)/2971 weeks
215.47117 .9307 (215*2π)/2971 weeks
2161.15991 .49892 (216*2π)/2971 weeks
217.80536 -.94604 (217*2π)/2971 weeks
218-.65858 -.22795 (218*2π)/2971 weeks
219.47765 .01412 (219*2π)/2971 weeks
2201.55542 -1.82335 (220*2π)/2971 weeks
221.56172 -1.16295 (221*2π)/2971 weeks
222.69979 -.54242 (222*2π)/2971 weeks
2231.6229 -1.19445 (223*2π)/2971 weeks
2241.35748 -1.2812 (224*2π)/2971 weeks
2251.95238 -.03019 (225*2π)/2971 weeks
2261.85072 -1.49662 (226*2π)/2971 weeks
2271.47993 -.7033 (227*2π)/2971 weeks
2283.14173 .78043 (228*2π)/2971 weeks
2291.81646 1.42379 (229*2π)/2971 weeks
230-.02146 .94437 (230*2π)/2971 weeks
231-.16371 .44225 (231*2π)/2971 weeks
232.75758 .21002 (232*2π)/2971 weeks
233-1.10395 -.65476 (233*2π)/2971 weeks
234-.18538 -.55613 (234*2π)/2971 weeks
2351.01474 -.9492 (235*2π)/2971 weeks
236.48415 -1.60259 (236*2π)/2971 weeks
237.16525 -.87661 (237*2π)/2971 weeks
2382.11722 -1.26349 (238*2π)/2971 weeks
239.94418 -3.03154 (239*2π)/2971 weeks
2401.72091 -1.74182 (240*2π)/2971 weeks
2413.4677 -.24699 (241*2π)/2971 weeks
2423.99967 -.52796 (242*2π)/2971 weeks
2431.66233 .35365 (243*2π)/2971 weeks
2442.90195 2.9397 (244*2π)/2971 weeks
2452.15791 .99625 (245*2π)/2971 weeks
246-.27943 1.31565 (246*2π)/2971 weeks
247-.06117 3.22873 (247*2π)/2971 weeks
248.22623 2.69195 (248*2π)/2971 weeks
249-1.71607 .97257 (249*2π)/2971 weeks
250-3.434 .47941 (250*2π)/2971 weeks
251-2.16552 -.12348 (251*2π)/2971 weeks
252-2.57413 -.45002 (252*2π)/2971 weeks
253-3.77398 -.72547 (253*2π)/2971 weeks
254-3.27307 -3.86427 (254*2π)/2971 weeks
255-2.35482 -5.31965 (255*2π)/2971 weeks
256-1.36606 -4.27139 (256*2π)/2971 weeks
257-.21004 -6.76336 (257*2π)/2971 weeks
258.5301 -6.03155 (258*2π)/2971 weeks
2592.71078 -3.8504 (259*2π)/2971 weeks
2602.9584 -3.70766 (260*2π)/2971 weeks
2613.50102 -5.85877 (261*2π)/2971 weeks
2623.9841 -4.02055 (262*2π)/2971 weeks
2636.14031 -3.88107 (263*2π)/2971 weeks
2646.01427 -2.75157 (264*2π)/2971 weeks
2656.37075 1.75161 (265*2π)/2971 weeks
2666.15471 1.04587 (266*2π)/2971 weeks
2674.28588 .91366 (267*2π)/2971 weeks
2682.82661 4.92467 (268*2π)/2971 weeks
2692.84416 3.57498 (269*2π)/2971 weeks
270.67847 1.90489 (270*2π)/2971 weeks
271-3.06778 4.60233 (271*2π)/2971 weeks
272-1.1801 4.98833 (272*2π)/2971 weeks
273-1.24985 -2.69927 (273*2π)/2971 weeks
274-3.49226 -1.35297 (274*2π)/2971 weeks
275-2.43622 1.70562 (275*2π)/2971 weeks
276-.66522 .50229 (276*2π)/2971 weeks
277-3.55175 -.59925 (277*2π)/2971 weeks
278-3.37691 2.77635 (278*2π)/2971 weeks
279-2.7028 -.05301 (279*2π)/2971 weeks
280-7.11884 -2.62571 (280*2π)/2971 weeks
281-8.77378 -1.21387 (281*2π)/2971 weeks
282-9.05247 -2.83053 (282*2π)/2971 weeks
283-11.90036 -11.01275 (283*2π)/2971 weeks
284-10.20627 -11.15049 (284*2π)/2971 weeks
285-5.81241 -11.28802 (285*2π)/2971 weeks
286-5.36024 -12.7654 (286*2π)/2971 weeks
287-8.02659 -16.47967 (287*2π)/2971 weeks
288-9.11622 -19.62612 (288*2π)/2971 weeks
289-6.45423 -25.72578 (289*2π)/2971 weeks
2908.5378 -27.44407 (290*2π)/2971 weeks
2917.30045 -32.77709 (291*2π)/2971 weeks
2921.73031 -29.02714 (292*2π)/2971 weeks
29327.98288 -28.08039 (293*2π)/2971 weeks
29434.21675 -34.88535 (294*2π)/2971 weeks
29519.45088 -43.18521 (295*2π)/2971 weeks



Back to list of Stocks