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Fourier Analysis of DGAZ (VelocityShares 3X Inverse Natur)


DGAZ (VelocityShares 3X Inverse Natur) appears to have interesting cyclic behaviour every 21 weeks (15.0158*cosine), 27 weeks (14.7824*sine), and 19 weeks (9.7311*cosine).

DGAZ (VelocityShares 3X Inverse Natur) has an average price of 75.48 (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 3/20/2017 for DGAZ (VelocityShares 3X Inverse Natur), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
075.48022   0 
162.86428 20.25631 (1*2π)/268268 weeks
216.99095 31.05306 (2*2π)/268134 weeks
322.72422 40.34645 (3*2π)/26889 weeks
421.77861 48.26691 (4*2π)/26867 weeks
514.96566 28.35876 (5*2π)/26854 weeks
65.43223 26.12617 (6*2π)/26845 weeks
7-5.7838 33.10958 (7*2π)/26838 weeks
8-9.48368 23.71156 (8*2π)/26834 weeks
9-8.47944 18.64001 (9*2π)/26830 weeks
10-5.73417 14.78237 (10*2π)/26827 weeks
11-5.5028 13.73281 (11*2π)/26824 weeks
12-9.56398 10.64775 (12*2π)/26822 weeks
13-15.01578 6.56165 (13*2π)/26821 weeks
14-9.73113 3.9926 (14*2π)/26819 weeks
15-5.94023 1.85017 (15*2π)/26818 weeks
16-4.89437 -2.2123 (16*2π)/26817 weeks
17-5.70086 -2.43023 (17*2π)/26816 weeks
18-3.90328 1.04327 (18*2π)/26815 weeks
19-.79088 -.07459 (19*2π)/26814 weeks
20-1.27784 -1.97187 (20*2π)/26813 weeks
21-3.86849 -1.32723 (21*2π)/26813 weeks
22-6.99366 .9135 (22*2π)/26812 weeks
23-1.24603 -.87364 (23*2π)/26812 weeks
242.35955 -4.37482 (24*2π)/26811 weeks
251.67541 -5.1203 (25*2π)/26811 weeks
261.85575 -4.66108 (26*2π)/26810 weeks
275.09343 -.96244 (27*2π)/26810 weeks
286.72019 -.95982 (28*2π)/26810 weeks
297.99462 -1.41718 (29*2π)/2689 weeks
306.24 2.617 (30*2π)/2689 weeks
315.56681 5.05099 (31*2π)/2689 weeks
324.9153 4.61484 (32*2π)/2688 weeks
331.66976 4.66645 (33*2π)/2688 weeks
342.16613 4.96586 (34*2π)/2688 weeks
351.57335 7.50361 (35*2π)/2688 weeks
36.41885 7.49011 (36*2π)/2687 weeks
37-1.43381 4.78851 (37*2π)/2687 weeks
38-2.97423 5.6982 (38*2π)/2687 weeks
39-4.31502 4.12047 (39*2π)/2687 weeks
40-3.29852 .73918 (40*2π)/2687 weeks
41-2.62133 .51988 (41*2π)/2687 weeks
42-2.61811 .74984 (42*2π)/2686 weeks
43-1.6714 -1.80139 (43*2π)/2686 weeks
44-.98387 -3.53411 (44*2π)/2686 weeks
45-.71679 -3.06472 (45*2π)/2686 weeks
46-.19739 -1.24929 (46*2π)/2686 weeks
472.06904 -.76238 (47*2π)/2686 weeks
484.27729 -2.17477 (48*2π)/2686 weeks
492.44591 -1.59125 (49*2π)/2685 weeks
502.9083 1.14445 (50*2π)/2685 weeks
513.58632 2.61785 (51*2π)/2685 weeks
522.86578 2.6738 (52*2π)/2685 weeks
531.45157 .54136 (53*2π)/2685 weeks
54-.06658 1.59293 (54*2π)/2685 weeks
55.64151 1.92239 (55*2π)/2685 weeks
561.13742 1.34737 (56*2π)/2685 weeks
57.17812 .68477 (57*2π)/2685 weeks
58-1.08382 -.34384 (58*2π)/2685 weeks
59.35965 .43923 (59*2π)/2685 weeks
60.29255 -.61319 (60*2π)/2684 weeks
611.1956 -2.04724 (61*2π)/2684 weeks
622.71204 -1.36186 (62*2π)/2684 weeks
632.03331 1.25336 (63*2π)/2684 weeks
642.34749 1.55438 (64*2π)/2684 weeks
652.28717 .09176 (65*2π)/2684 weeks
661.41393 1.26799 (66*2π)/2684 weeks
671.52545 1.68799 (67*2π)/2684 weeks
681.57652 .71737 (68*2π)/2684 weeks
691.23704 .28381 (69*2π)/2684 weeks
70-.57523 1.26717 (70*2π)/2684 weeks
71.02588 1.47265 (71*2π)/2684 weeks
721.52806 .47716 (72*2π)/2684 weeks
731.04004 -.75647 (73*2π)/2684 weeks
74.5677 -.98995 (74*2π)/2684 weeks
75.88379 .2587 (75*2π)/2684 weeks
761.63106 -.29127 (76*2π)/2684 weeks
771.52695 -1.5803 (77*2π)/2683 weeks
781.32234 -.34839 (78*2π)/2683 weeks
792.00604 .57191 (79*2π)/2683 weeks
803.06782 .7695 (80*2π)/2683 weeks
812.90045 .11343 (81*2π)/2683 weeks
822.1865 .27464 (82*2π)/2683 weeks
831.75691 1.41346 (83*2π)/2683 weeks
842.12484 1.89741 (84*2π)/2683 weeks
852.29904 2.04724 (85*2π)/2683 weeks
861.90267 2.29848 (86*2π)/2683 weeks
87.68469 1.41924 (87*2π)/2683 weeks
88.20256 1.88959 (88*2π)/2683 weeks
89.16339 2.08569 (89*2π)/2683 weeks
90.78128 2.32592 (90*2π)/2683 weeks
91.9584 1.8897 (91*2π)/2683 weeks
92-.39689 1.17234 (92*2π)/2683 weeks
93-1.00037 .52577 (93*2π)/2683 weeks
94-1.29473 .34719 (94*2π)/2683 weeks
95-.31328 .18352 (95*2π)/2683 weeks
96.35151 -.56141 (96*2π)/2683 weeks
97.00365 -.51904 (97*2π)/2683 weeks
98.14354 -.28659 (98*2π)/2683 weeks
99-.05791 -.26305 (99*2π)/2683 weeks
100.44063 -.42858 (100*2π)/2683 weeks
101.94598 -.21098 (101*2π)/2683 weeks
1021.0107 -.43804 (102*2π)/2683 weeks
103.50503 -.53391 (103*2π)/2683 weeks
104.61879 -.6646 (104*2π)/2683 weeks
105.46396 -.49637 (105*2π)/2683 weeks
1061.51836 -.78905 (106*2π)/2683 weeks
1072.07286 -1.02348 (107*2π)/2683 weeks
1081.96079 -.87478 (108*2π)/2682 weeks
1091.67249 -.57223 (109*2π)/2682 weeks
1102.12298 .3132 (110*2π)/2682 weeks
1111.92788 .36072 (111*2π)/2682 weeks
1121.84692 .04286 (112*2π)/2682 weeks
1131.37833 -.10281 (113*2π)/2682 weeks
1141.40356 -.02106 (114*2π)/2682 weeks
1152.09701 .43307 (115*2π)/2682 weeks
1161.9965 .77728 (116*2π)/2682 weeks
1171.33694 .81566 (117*2π)/2682 weeks
118.56551 .81214 (118*2π)/2682 weeks
119.47141 .96519 (119*2π)/2682 weeks
120.74172 .40338 (120*2π)/2682 weeks
121.24132 -.37049 (121*2π)/2682 weeks
122.56897 -.16566 (122*2π)/2682 weeks
123.98544 .01168 (123*2π)/2682 weeks
1241.25901 -.09217 (124*2π)/2682 weeks
1251.63163 -.58231 (125*2π)/2682 weeks
126.97577 -.28062 (126*2π)/2682 weeks
1271.60712 .67408 (127*2π)/2682 weeks
1281.80378 .49097 (128*2π)/2682 weeks
129.75818 .20736 (129*2π)/2682 weeks
130.95801 -.5232 (130*2π)/2682 weeks
131.74417 -.33278 (131*2π)/2682 weeks
132.86789 .16965 (132*2π)/2682 weeks
1331.80604 -.2881 (133*2π)/2682 weeks
1342.37522   (134*2π)/2682 weeks
1351.80604 .2881 (135*2π)/2682 weeks
136.86789 -.16965 (136*2π)/2682 weeks
137.74417 .33278 (137*2π)/2682 weeks
138.95801 .5232 (138*2π)/2682 weeks
139.75818 -.20736 (139*2π)/2682 weeks
1401.80378 -.49097 (140*2π)/2682 weeks
1411.60712 -.67408 (141*2π)/2682 weeks
142.97577 .28062 (142*2π)/2682 weeks
1431.63163 .58231 (143*2π)/2682 weeks
1441.25901 .09217 (144*2π)/2682 weeks
145.98544 -.01168 (145*2π)/2682 weeks
146.56897 .16566 (146*2π)/2682 weeks
147.24132 .37049 (147*2π)/2682 weeks
148.74172 -.40338 (148*2π)/2682 weeks
149.47141 -.96519 (149*2π)/2682 weeks
150.56551 -.81214 (150*2π)/2682 weeks
1511.33694 -.81566 (151*2π)/2682 weeks
1521.9965 -.77728 (152*2π)/2682 weeks
1532.09701 -.43307 (153*2π)/2682 weeks
1541.40356 .02106 (154*2π)/2682 weeks
1551.37833 .10281 (155*2π)/2682 weeks
1561.84692 -.04286 (156*2π)/2682 weeks
1571.92788 -.36072 (157*2π)/2682 weeks
1582.12298 -.3132 (158*2π)/2682 weeks
1591.67249 .57223 (159*2π)/2682 weeks
1601.96079 .87478 (160*2π)/2682 weeks
1612.07286 1.02348 (161*2π)/2682 weeks
1621.51836 .78905 (162*2π)/2682 weeks
163.46396 .49637 (163*2π)/2682 weeks
164.61879 .6646 (164*2π)/2682 weeks
165.50503 .53391 (165*2π)/2682 weeks
1661.0107 .43804 (166*2π)/2682 weeks
167.94598 .21098 (167*2π)/2682 weeks
168.44063 .42858 (168*2π)/2682 weeks
169-.05791 .26305 (169*2π)/2682 weeks
170.14354 .28659 (170*2π)/2682 weeks
171.00365 .51904 (171*2π)/2682 weeks
172.35151 .56141 (172*2π)/2682 weeks
173-.31328 -.18352 (173*2π)/2682 weeks
174-1.29473 -.34719 (174*2π)/2682 weeks
175-1.00037 -.52577 (175*2π)/2682 weeks
176-.39689 -1.17234 (176*2π)/2682 weeks
177.9584 -1.8897 (177*2π)/2682 weeks
178.78128 -2.32592 (178*2π)/2682 weeks
179.16339 -2.08569 (179*2π)/2681 weeks
180.20256 -1.88959 (180*2π)/2681 weeks
181.68469 -1.41924 (181*2π)/2681 weeks
1821.90267 -2.29848 (182*2π)/2681 weeks
1832.29904 -2.04724 (183*2π)/2681 weeks
1842.12484 -1.89741 (184*2π)/2681 weeks
1851.75691 -1.41346 (185*2π)/2681 weeks
1862.1865 -.27464 (186*2π)/2681 weeks
1872.90045 -.11343 (187*2π)/2681 weeks
1883.06782 -.7695 (188*2π)/2681 weeks
1892.00604 -.57191 (189*2π)/2681 weeks
1901.32234 .34839 (190*2π)/2681 weeks
1911.52695 1.5803 (191*2π)/2681 weeks
1921.63106 .29127 (192*2π)/2681 weeks
193.88379 -.2587 (193*2π)/2681 weeks
194.5677 .98995 (194*2π)/2681 weeks
1951.04004 .75647 (195*2π)/2681 weeks
1961.52806 -.47716 (196*2π)/2681 weeks
197.02588 -1.47265 (197*2π)/2681 weeks
198-.57523 -1.26717 (198*2π)/2681 weeks
1991.23704 -.28381 (199*2π)/2681 weeks
2001.57652 -.71737 (200*2π)/2681 weeks
2011.52545 -1.68799 (201*2π)/2681 weeks
2021.41393 -1.26799 (202*2π)/2681 weeks
2032.28717 -.09176 (203*2π)/2681 weeks
2042.34749 -1.55438 (204*2π)/2681 weeks
2052.03331 -1.25336 (205*2π)/2681 weeks
2062.71204 1.36186 (206*2π)/2681 weeks
2071.1956 2.04724 (207*2π)/2681 weeks
208.29255 .61319 (208*2π)/2681 weeks
209.35965 -.43923 (209*2π)/2681 weeks
210-1.08382 .34384 (210*2π)/2681 weeks
211.17812 -.68477 (211*2π)/2681 weeks
2121.13742 -1.34737 (212*2π)/2681 weeks
213.64151 -1.92239 (213*2π)/2681 weeks
214-.06658 -1.59293 (214*2π)/2681 weeks
2151.45157 -.54136 (215*2π)/2681 weeks
2162.86578 -2.6738 (216*2π)/2681 weeks
2173.58632 -2.61785 (217*2π)/2681 weeks
2182.9083 -1.14445 (218*2π)/2681 weeks
2192.44591 1.59125 (219*2π)/2681 weeks
2204.27729 2.17477 (220*2π)/2681 weeks
2212.06904 .76238 (221*2π)/2681 weeks
222-.19739 1.24929 (222*2π)/2681 weeks
223-.71679 3.06472 (223*2π)/2681 weeks
224-.98387 3.53411 (224*2π)/2681 weeks
225-1.6714 1.80139 (225*2π)/2681 weeks
226-2.61811 -.74984 (226*2π)/2681 weeks
227-2.62133 -.51988 (227*2π)/2681 weeks
228-3.29852 -.73918 (228*2π)/2681 weeks
229-4.31502 -4.12047 (229*2π)/2681 weeks
230-2.97423 -5.6982 (230*2π)/2681 weeks
231-1.43381 -4.78851 (231*2π)/2681 weeks
232.41885 -7.49011 (232*2π)/2681 weeks
2331.57335 -7.50361 (233*2π)/2681 weeks
2342.16613 -4.96586 (234*2π)/2681 weeks
2351.66976 -4.66645 (235*2π)/2681 weeks
2364.9153 -4.61484 (236*2π)/2681 weeks
2375.56681 -5.05099 (237*2π)/2681 weeks
2386.24 -2.617 (238*2π)/2681 weeks
2397.99462 1.41718 (239*2π)/2681 weeks
2406.72019 .95982 (240*2π)/2681 weeks
2415.09343 .96244 (241*2π)/2681 weeks
2421.85575 4.66108 (242*2π)/2681 weeks
2431.67541 5.1203 (243*2π)/2681 weeks
2442.35955 4.37482 (244*2π)/2681 weeks
245-1.24603 .87364 (245*2π)/2681 weeks
246-6.99366 -.9135 (246*2π)/2681 weeks
247-3.86849 1.32723 (247*2π)/2681 weeks
248-1.27784 1.97187 (248*2π)/2681 weeks
249-.79088 .07459 (249*2π)/2681 weeks
250-3.90328 -1.04327 (250*2π)/2681 weeks
251-5.70086 2.43023 (251*2π)/2681 weeks
252-4.89437 2.2123 (252*2π)/2681 weeks
253-5.94023 -1.85017 (253*2π)/2681 weeks
254-9.73113 -3.9926 (254*2π)/2681 weeks
255-15.01578 -6.56165 (255*2π)/2681 weeks
256-9.56398 -10.64775 (256*2π)/2681 weeks
257-5.5028 -13.73281 (257*2π)/2681 weeks
258-5.73417 -14.78237 (258*2π)/2681 weeks
259-8.47944 -18.64001 (259*2π)/2681 weeks
260-9.48368 -23.71156 (260*2π)/2681 weeks
261-5.7838 -33.10958 (261*2π)/2681 weeks
2625.43223 -26.12617 (262*2π)/2681 weeks
26314.96566 -28.35876 (263*2π)/2681 weeks
26421.77861 -48.26691 (264*2π)/2681 weeks
26522.72422 -40.34645 (265*2π)/2681 weeks
26616.99095 -31.05306 (266*2π)/2681 weeks

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