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Fourier Analysis of UGAZ (VelocityShares 3X Long Natural )


UGAZ (VelocityShares 3X Long Natural ) appears to have interesting cyclic behaviour every 20 weeks (269.1583*cosine), 20 weeks (230.2329*sine), and 22 weeks (186.8449*cosine).

UGAZ (VelocityShares 3X Long Natural ) has an average price of 1,783.38 (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 1/9/2017 for UGAZ (VelocityShares 3X Long Natural ), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
01,783.375   0 
1-28.99728 1,804.631 (1*2π)/258258 weeks
2336.3358 418.3743 (2*2π)/258129 weeks
3-243.386 539.0774 (3*2π)/25886 weeks
4169.2317 -13.20971 (4*2π)/25865 weeks
5129.2221 303.3987 (5*2π)/25852 weeks
6-60.2533 104.5244 (6*2π)/25843 weeks
7283.9667 -45.49599 (7*2π)/25837 weeks
8233.1658 216.3801 (8*2π)/25832 weeks
9171.6025 287.8056 (9*2π)/25829 weeks
10-52.89589 153.8155 (10*2π)/25826 weeks
1166.606 44.47425 (11*2π)/25823 weeks
12186.8449 -56.59564 (12*2π)/25822 weeks
13269.1583 230.2329 (13*2π)/25820 weeks
1491.02149 164.2484 (14*2π)/25818 weeks
15123.4397 174.3846 (15*2π)/25817 weeks
1677.16296 168.3747 (16*2π)/25816 weeks
1759.16621 134.9062 (17*2π)/25815 weeks
1841.36878 147.4563 (18*2π)/25814 weeks
1942.08673 54.50732 (19*2π)/25814 weeks
2077.87031 66.63803 (20*2π)/25813 weeks
21176.3818 59.25664 (21*2π)/25812 weeks
22116.4857 185.3198 (22*2π)/25812 weeks
2382.98851 181.4975 (23*2π)/25811 weeks
2421.46861 132.0291 (24*2π)/25811 weeks
2572.74759 178.6316 (25*2π)/25810 weeks
26-41.31765 127.479 (26*2π)/25810 weeks
2737.56268 125.1412 (27*2π)/25810 weeks
28-79.93781 112.028 (28*2π)/2589 weeks
29-2.61989 2.76177 (29*2π)/2589 weeks
3039.4539 57.2587 (30*2π)/2589 weeks
3120.63872 23.69984 (31*2π)/2588 weeks
3278.52289 90.3642 (32*2π)/2588 weeks
33-19.09524 48.10455 (33*2π)/2588 weeks
3453.71522 34.54232 (34*2π)/2588 weeks
3547.71975 27.26606 (35*2π)/2587 weeks
3657.24877 53.42455 (36*2π)/2587 weeks
3780.08498 12.85931 (37*2π)/2587 weeks
38121.592 108.8262 (38*2π)/2587 weeks
3924.35227 122.2495 (39*2π)/2587 weeks
408.55061 58.9555 (40*2π)/2586 weeks
4154.22281 62.57525 (41*2π)/2586 weeks
4235.39132 59.37231 (42*2π)/2586 weeks
4357.46338 85.04929 (43*2π)/2586 weeks
4415.02649 67.78508 (44*2π)/2586 weeks
4559.85838 69.27086 (45*2π)/2586 weeks
4617.23816 109.4728 (46*2π)/2586 weeks
47-11.90684 88.5165 (47*2π)/2585 weeks
48-30.02679 35.04433 (48*2π)/2585 weeks
49-5.34039 20.49165 (49*2π)/2585 weeks
5048.93046 -16.3456 (50*2π)/2585 weeks
5165.88256 73.55892 (51*2π)/2585 weeks
5215.59644 47.28448 (52*2π)/2585 weeks
5343.0506 40.23148 (53*2π)/2585 weeks
5422.6873 62.05485 (54*2π)/2585 weeks
5534.41747 16.51683 (55*2π)/2585 weeks
5655.07007 75.31696 (56*2π)/2585 weeks
5721.34571 28.0595 (57*2π)/2585 weeks
5887.08012 80.8867 (58*2π)/2584 weeks
59.98012 129.6908 (59*2π)/2584 weeks
60-51.67122 54.41013 (60*2π)/2584 weeks
61-5.20834 17.21567 (61*2π)/2584 weeks
6218.0034 27.46507 (62*2π)/2584 weeks
6319.44676 31.2989 (63*2π)/2584 weeks
649.17952 50.6362 (64*2π)/2584 weeks
6514.8605 15.44045 (65*2π)/2584 weeks
6624.97977 62.68101 (66*2π)/2584 weeks
67-17.93059 19.83313 (67*2π)/2584 weeks
6833.76311 22.89871 (68*2π)/2584 weeks
692.92128 40.64838 (69*2π)/2584 weeks
7023.87364 17.3287 (70*2π)/2584 weeks
7115.76734 54.15113 (71*2π)/2584 weeks
72-10.06005 15.15302 (72*2π)/2584 weeks
7328.4772 14.87369 (73*2π)/2584 weeks
7411.90799 41.97112 (74*2π)/2583 weeks
754.60613 5.75791 (75*2π)/2583 weeks
7630.25684 30.52097 (76*2π)/2583 weeks
775.3507 15.25414 (77*2π)/2583 weeks
7834.49263 32.60391 (78*2π)/2583 weeks
79-1.14287 34.33193 (79*2π)/2583 weeks
809.14686 19.45341 (80*2π)/2583 weeks
819.30404 26.18932 (81*2π)/2583 weeks
82-15.98975 14.61757 (82*2π)/2583 weeks
8328.28819 -10.83281 (83*2π)/2583 weeks
842.85964 27.77854 (84*2π)/2583 weeks
8517.21143 -5.08067 (85*2π)/2583 weeks
8613.55663 13.54564 (86*2π)/2583 weeks
875.88196 -3.13563 (87*2π)/2583 weeks
8834.58844 -21.82009 (88*2π)/2583 weeks
8941.88913 18.07235 (89*2π)/2583 weeks
9036.38551 3.4103 (90*2π)/2583 weeks
9134.43604 31.59221 (91*2π)/2583 weeks
9217.91362 16.50471 (92*2π)/2583 weeks
9327.84711 11.17393 (93*2π)/2583 weeks
9418.11356 22.7857 (94*2π)/2583 weeks
9534.61565 -.07506 (95*2π)/2583 weeks
9628.53728 44.29691 (96*2π)/2583 weeks
978.00193 12.57331 (97*2π)/2583 weeks
984.03788 21.42842 (98*2π)/2583 weeks
9923.4228 -11.98836 (99*2π)/2583 weeks
10026.21033 16.25478 (100*2π)/2583 weeks
10136.80457 11.88576 (101*2π)/2583 weeks
10218.06747 27.27032 (102*2π)/2583 weeks
10314.26268 28.1427 (103*2π)/2583 weeks
1042.54597 4.06988 (104*2π)/2582 weeks
10513.80686 24.87705 (105*2π)/2582 weeks
106-4.34717 -17.75627 (106*2π)/2582 weeks
10736.69164 2.14093 (107*2π)/2582 weeks
10821.04085 3.09359 (108*2π)/2582 weeks
10936.78073 14.50024 (109*2π)/2582 weeks
1109.41374 32.7305 (110*2π)/2582 weeks
111-3.88164 -2.9481 (111*2π)/2582 weeks
11219.73322 2.6879 (112*2π)/2582 weeks
1138.62564 -7.95193 (113*2π)/2582 weeks
11431.21613 -1.74917 (114*2π)/2582 weeks
11519.25552 4.46006 (115*2π)/2582 weeks
11630.91231 -1.53717 (116*2π)/2582 weeks
11726.38386 21.39984 (117*2π)/2582 weeks
1181.56463 4.71673 (118*2π)/2582 weeks
11929.60684 -4.20331 (119*2π)/2582 weeks
12013.32221 14.51721 (120*2π)/2582 weeks
12119.02618 1.02344 (121*2π)/2582 weeks
1227.10509 5.97891 (122*2π)/2582 weeks
1233.50924 -12.38867 (123*2π)/2582 weeks
12443.38195 -21.18047 (124*2π)/2582 weeks
12521.48916 14.80556 (125*2π)/2582 weeks
12631.45103 -9.28688 (126*2π)/2582 weeks
12730.57373 18.47053 (127*2π)/2582 weeks
12810.37834 14.16377 (128*2π)/2582 weeks
1292.08791   (129*2π)/2582 weeks
13010.37834 -14.16377 (130*2π)/2582 weeks
13130.57373 -18.47053 (131*2π)/2582 weeks
13231.45103 9.28688 (132*2π)/2582 weeks
13321.48916 -14.80556 (133*2π)/2582 weeks
13443.38195 21.18047 (134*2π)/2582 weeks
1353.50924 12.38867 (135*2π)/2582 weeks
1367.10509 -5.97891 (136*2π)/2582 weeks
13719.02618 -1.02344 (137*2π)/2582 weeks
13813.32221 -14.51721 (138*2π)/2582 weeks
13929.60684 4.20331 (139*2π)/2582 weeks
1401.56463 -4.71673 (140*2π)/2582 weeks
14126.38386 -21.39984 (141*2π)/2582 weeks
14230.91231 1.53717 (142*2π)/2582 weeks
14319.25552 -4.46006 (143*2π)/2582 weeks
14431.21613 1.74917 (144*2π)/2582 weeks
1458.62564 7.95193 (145*2π)/2582 weeks
14619.73322 -2.6879 (146*2π)/2582 weeks
147-3.88164 2.9481 (147*2π)/2582 weeks
1489.41374 -32.7305 (148*2π)/2582 weeks
14936.78073 -14.50024 (149*2π)/2582 weeks
15021.04085 -3.09359 (150*2π)/2582 weeks
15136.69164 -2.14093 (151*2π)/2582 weeks
152-4.34717 17.75627 (152*2π)/2582 weeks
15313.80686 -24.87705 (153*2π)/2582 weeks
1542.54597 -4.06988 (154*2π)/2582 weeks
15514.26268 -28.1427 (155*2π)/2582 weeks
15618.06747 -27.27032 (156*2π)/2582 weeks
15736.80457 -11.88576 (157*2π)/2582 weeks
15826.21033 -16.25478 (158*2π)/2582 weeks
15923.4228 11.98836 (159*2π)/2582 weeks
1604.03788 -21.42842 (160*2π)/2582 weeks
1618.00193 -12.57331 (161*2π)/2582 weeks
16228.53728 -44.29691 (162*2π)/2582 weeks
16334.61565 .07506 (163*2π)/2582 weeks
16418.11356 -22.7857 (164*2π)/2582 weeks
16527.84711 -11.17393 (165*2π)/2582 weeks
16617.91362 -16.50471 (166*2π)/2582 weeks
16734.43604 -31.59221 (167*2π)/2582 weeks
16836.38551 -3.4103 (168*2π)/2582 weeks
16941.88913 -18.07235 (169*2π)/2582 weeks
17034.58844 21.82009 (170*2π)/2582 weeks
1715.88196 3.13563 (171*2π)/2582 weeks
17213.55663 -13.54564 (172*2π)/2582 weeks
17317.21143 5.08067 (173*2π)/2581 weeks
1742.85964 -27.77854 (174*2π)/2581 weeks
17528.28819 10.83281 (175*2π)/2581 weeks
176-15.98975 -14.61757 (176*2π)/2581 weeks
1779.30404 -26.18932 (177*2π)/2581 weeks
1789.14686 -19.45341 (178*2π)/2581 weeks
179-1.14287 -34.33193 (179*2π)/2581 weeks
18034.49263 -32.60391 (180*2π)/2581 weeks
1815.3507 -15.25414 (181*2π)/2581 weeks
18230.25684 -30.52097 (182*2π)/2581 weeks
1834.60613 -5.75791 (183*2π)/2581 weeks
18411.90799 -41.97112 (184*2π)/2581 weeks
18528.4772 -14.87369 (185*2π)/2581 weeks
186-10.06005 -15.15302 (186*2π)/2581 weeks
18715.76734 -54.15113 (187*2π)/2581 weeks
18823.87364 -17.3287 (188*2π)/2581 weeks
1892.92128 -40.64838 (189*2π)/2581 weeks
19033.76311 -22.89871 (190*2π)/2581 weeks
191-17.93059 -19.83313 (191*2π)/2581 weeks
19224.97977 -62.68101 (192*2π)/2581 weeks
19314.8605 -15.44045 (193*2π)/2581 weeks
1949.17952 -50.6362 (194*2π)/2581 weeks
19519.44676 -31.2989 (195*2π)/2581 weeks
19618.0034 -27.46507 (196*2π)/2581 weeks
197-5.20834 -17.21567 (197*2π)/2581 weeks
198-51.67122 -54.41013 (198*2π)/2581 weeks
199.98012 -129.6908 (199*2π)/2581 weeks
20087.08012 -80.8867 (200*2π)/2581 weeks
20121.34571 -28.0595 (201*2π)/2581 weeks
20255.07007 -75.31696 (202*2π)/2581 weeks
20334.41747 -16.51683 (203*2π)/2581 weeks
20422.6873 -62.05485 (204*2π)/2581 weeks
20543.0506 -40.23148 (205*2π)/2581 weeks
20615.59644 -47.28448 (206*2π)/2581 weeks
20765.88256 -73.55892 (207*2π)/2581 weeks
20848.93046 16.3456 (208*2π)/2581 weeks
209-5.34039 -20.49165 (209*2π)/2581 weeks
210-30.02679 -35.04433 (210*2π)/2581 weeks
211-11.90684 -88.5165 (211*2π)/2581 weeks
21217.23816 -109.4728 (212*2π)/2581 weeks
21359.85838 -69.27086 (213*2π)/2581 weeks
21415.02649 -67.78508 (214*2π)/2581 weeks
21557.46338 -85.04929 (215*2π)/2581 weeks
21635.39132 -59.37231 (216*2π)/2581 weeks
21754.22281 -62.57525 (217*2π)/2581 weeks
2188.55061 -58.9555 (218*2π)/2581 weeks
21924.35227 -122.2495 (219*2π)/2581 weeks
220121.592 -108.8262 (220*2π)/2581 weeks
22180.08498 -12.85931 (221*2π)/2581 weeks
22257.24877 -53.42455 (222*2π)/2581 weeks
22347.71975 -27.26606 (223*2π)/2581 weeks
22453.71522 -34.54232 (224*2π)/2581 weeks
225-19.09524 -48.10455 (225*2π)/2581 weeks
22678.52289 -90.3642 (226*2π)/2581 weeks
22720.63872 -23.69984 (227*2π)/2581 weeks
22839.4539 -57.2587 (228*2π)/2581 weeks
229-2.61989 -2.76177 (229*2π)/2581 weeks
230-79.93781 -112.028 (230*2π)/2581 weeks
23137.56268 -125.1412 (231*2π)/2581 weeks
232-41.31765 -127.479 (232*2π)/2581 weeks
23372.74759 -178.6316 (233*2π)/2581 weeks
23421.46861 -132.0291 (234*2π)/2581 weeks
23582.98851 -181.4975 (235*2π)/2581 weeks
236116.4857 -185.3198 (236*2π)/2581 weeks
237176.3818 -59.25664 (237*2π)/2581 weeks
23877.87031 -66.63803 (238*2π)/2581 weeks
23942.08673 -54.50732 (239*2π)/2581 weeks
24041.36878 -147.4563 (240*2π)/2581 weeks
24159.16621 -134.9062 (241*2π)/2581 weeks
24277.16296 -168.3747 (242*2π)/2581 weeks
243123.4397 -174.3846 (243*2π)/2581 weeks
24491.02149 -164.2484 (244*2π)/2581 weeks
245269.1583 -230.2329 (245*2π)/2581 weeks
246186.8449 56.59564 (246*2π)/2581 weeks
24766.606 -44.47425 (247*2π)/2581 weeks
248-52.89589 -153.8155 (248*2π)/2581 weeks
249171.6025 -287.8056 (249*2π)/2581 weeks
250233.1658 -216.3801 (250*2π)/2581 weeks
251283.9667 45.49599 (251*2π)/2581 weeks
252-60.2533 -104.5244 (252*2π)/2581 weeks
253129.2221 -303.3987 (253*2π)/2581 weeks
254169.2317 13.20971 (254*2π)/2581 weeks
255-243.386 -539.0774 (255*2π)/2581 weeks
256336.3358 -418.3743 (256*2π)/2581 weeks

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