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Fourier Analysis of NUGT (Direxion Daily Gold Miners Index Bull 3x Shares ETF)


NUGT (Direxion Daily Gold Miners Index Bull 3x Shares ETF) appears to have interesting cyclic behaviour every 31 weeks (508.3858*sine), 29 weeks (497.5228*sine), and 35 weeks (383.9555*sine).

NUGT (Direxion Daily Gold Miners Index Bull 3x Shares ETF) has an average price of 3,190.11 (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 12/8/2010 to 7/10/2017 for NUGT (Direxion Daily Gold Miners Index Bull 3x Shares ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
03,190.112   0 
13,465.876 3,752.067 (1*2π)/345345 weeks
2499.3333 2,986.875 (2*2π)/345173 weeks
362.22612 1,682.633 (3*2π)/345115 weeks
4-131.5717 1,477.991 (4*2π)/34586 weeks
5-464.1536 728.8547 (5*2π)/34569 weeks
6116.1315 230.3295 (6*2π)/34558 weeks
7448.7199 588.9774 (7*2π)/34549 weeks
874.09435 796.0172 (8*2π)/34543 weeks
9-73.76489 475.3764 (9*2π)/34538 weeks
1085.47399 383.9555 (10*2π)/34535 weeks
1196.57436 508.3858 (11*2π)/34531 weeks
12-88.84944 497.5228 (12*2π)/34529 weeks
13-215.3604 288.181 (13*2π)/34527 weeks
14-52.20127 50.32213 (14*2π)/34525 weeks
1596.92678 124.4201 (15*2π)/34523 weeks
1697.34544 123.1855 (16*2π)/34522 weeks
17154.2113 106.7895 (17*2π)/34520 weeks
18236.2171 191.1467 (18*2π)/34519 weeks
19146.3243 276.5615 (19*2π)/34518 weeks
2082.28513 185.055 (20*2π)/34517 weeks
21196.6882 136.7916 (21*2π)/34516 weeks
22270.0076 296.1198 (22*2π)/34516 weeks
2377.03364 428.6891 (23*2π)/34515 weeks
24-102.678 280.2798 (24*2π)/34514 weeks
25-43.96924 98.45338 (25*2π)/34514 weeks
2682.55588 84.37528 (26*2π)/34513 weeks
27120.6355 140.8504 (27*2π)/34513 weeks
28116.855 150.7747 (28*2π)/34512 weeks
29143.9987 204.8697 (29*2π)/34512 weeks
3054.02079 264.9749 (30*2π)/34512 weeks
31-34.22985 192.1266 (31*2π)/34511 weeks
32-26.92633 106.3207 (32*2π)/34511 weeks
3324.31202 23.9593 (33*2π)/34510 weeks
34151.2261 27.87166 (34*2π)/34510 weeks
35185.6524 141.5953 (35*2π)/34510 weeks
36130.4379 180.6779 (36*2π)/34510 weeks
37125.1732 204.2014 (37*2π)/3459 weeks
3859.56497 233.6404 (38*2π)/3459 weeks
394.7909 185.9055 (39*2π)/3459 weeks
4011.15209 138.8665 (40*2π)/3459 weeks
4118.5726 131.1886 (41*2π)/3458 weeks
4220.6935 83.75558 (42*2π)/3458 weeks
4398.92197 74.99242 (43*2π)/3458 weeks
44128.6848 149.3687 (44*2π)/3458 weeks
4584.34988 213.5718 (45*2π)/3458 weeks
4611.64414 214.7054 (46*2π)/3458 weeks
47-34.54833 181.4719 (47*2π)/3457 weeks
48-42.23114 143.2239 (48*2π)/3457 weeks
49-67.48324 127.6753 (49*2π)/3457 weeks
50-98.04499 56.70185 (50*2π)/3457 weeks
51-46.1636 -30.97214 (51*2π)/3457 weeks
5251.25597 -33.91803 (52*2π)/3457 weeks
5395.83326 18.04118 (53*2π)/3457 weeks
5497.53249 60.97826 (54*2π)/3456 weeks
5587.50073 92.01142 (55*2π)/3456 weeks
5652.3728 100.4418 (56*2π)/3456 weeks
5744.09842 78.03209 (57*2π)/3456 weeks
5861.80788 79.83936 (58*2π)/3456 weeks
5953.32085 99.0806 (59*2π)/3456 weeks
6040.46327 104.6396 (60*2π)/3456 weeks
6110.71223 108.33 (61*2π)/3456 weeks
62-11.96487 65.42773 (62*2π)/3456 weeks
6328.03748 41.87012 (63*2π)/3455 weeks
6428.26282 68.40318 (64*2π)/3455 weeks
658.88912 33.56359 (65*2π)/3455 weeks
6662.98141 20.51753 (66*2π)/3455 weeks
6768.05292 76.19939 (67*2π)/3455 weeks
6825.30426 77.40782 (68*2π)/3455 weeks
6924.28773 51.48483 (69*2π)/3455 weeks
7037.92729 40.38363 (70*2π)/3455 weeks
7156.24649 51.86001 (71*2π)/3455 weeks
7246.7113 69.1172 (72*2π)/3455 weeks
7332.62449 66.25932 (73*2π)/3455 weeks
7426.8384 63.44139 (74*2π)/3455 weeks
7520.20447 57.62445 (75*2π)/3455 weeks
7615.72277 52.56378 (76*2π)/3455 weeks
777.13697 43.09627 (77*2π)/3454 weeks
782.89472 15.54652 (78*2π)/3454 weeks
7933.23756 -3.97752 (79*2π)/3454 weeks
8066.05374 9.55091 (80*2π)/3454 weeks
8169.097 53.21769 (81*2π)/3454 weeks
8229.96023 69.83084 (82*2π)/3454 weeks
83-14.13203 45.78674 (83*2π)/3454 weeks
84-23.23044 -28.30648 (84*2π)/3454 weeks
8556.11902 -75.78493 (85*2π)/3454 weeks
86128.5275 -31.09507 (86*2π)/3454 weeks
87144.7116 32.45734 (87*2π)/3454 weeks
88120.9877 92.70904 (88*2π)/3454 weeks
8958.41601 117.6173 (89*2π)/3454 weeks
906.38372 83.6227 (90*2π)/3454 weeks
915.39997 42.40565 (91*2π)/3454 weeks
9216.72847 21.17298 (92*2π)/3454 weeks
9337.5322 11.76568 (93*2π)/3454 weeks
9449.57567 26.58536 (94*2π)/3454 weeks
9534.96236 26.65754 (95*2π)/3454 weeks
9639.00923 10.67151 (96*2π)/3454 weeks
9763.65526 6.6174 (97*2π)/3454 weeks
9866.20485 36.36762 (98*2π)/3454 weeks
9944.01439 35.2151 (99*2π)/3453 weeks
10044.43657 18.58526 (100*2π)/3453 weeks
10160.61268 24.22097 (101*2π)/3453 weeks
10242.27401 32.49453 (102*2π)/3453 weeks
10348.74667 5.68705 (103*2π)/3453 weeks
10472.9078 21.71003 (104*2π)/3453 weeks
10560.874 39.36653 (105*2π)/3453 weeks
10646.8776 34.72712 (106*2π)/3453 weeks
10748.27372 23.06601 (107*2π)/3453 weeks
10857.93097 24.72261 (108*2π)/3453 weeks
10955.87273 30.51105 (109*2π)/3453 weeks
11054.84076 38.0772 (110*2π)/3453 weeks
11138.75687 41.71127 (111*2π)/3453 weeks
11227.65839 23.74938 (112*2π)/3453 weeks
11342.80499 11.89758 (113*2π)/3453 weeks
11445.19733 16.10086 (114*2π)/3453 weeks
11547.65712 9.55734 (115*2π)/3453 weeks
11654.33012 13.01321 (116*2π)/3453 weeks
11754.51312 14.10175 (117*2π)/3453 weeks
11856.40589 18.63351 (118*2π)/3453 weeks
11950.5451 13.8354 (119*2π)/3453 weeks
12062.30615 3.21788 (120*2π)/3453 weeks
12182.88554 17.00121 (121*2π)/3453 weeks
12278.22723 44.88667 (122*2π)/3453 weeks
12350.61096 55.43758 (123*2π)/3453 weeks
12428.03898 40.62931 (124*2π)/3453 weeks
12523.58508 13.86155 (125*2π)/3453 weeks
12645.18225 -5.46616 (126*2π)/3453 weeks
12777.79903 5.88122 (127*2π)/3453 weeks
12879.37182 48.70807 (128*2π)/3453 weeks
12932.70157 62.39927 (129*2π)/3453 weeks
1308.8486 22.63438 (130*2π)/3453 weeks
13131.80629 -1.01578 (131*2π)/3453 weeks
13236.93653 7.56722 (132*2π)/3453 weeks
13338.88329 -10.01516 (133*2π)/3453 weeks
13470.29432 -10.18502 (134*2π)/3453 weeks
13576.11337 25.99709 (135*2π)/3453 weeks
13637.15333 31.01833 (136*2π)/3453 weeks
13736.05374 -9.23882 (137*2π)/3453 weeks
13874.17829 -10.56707 (138*2π)/3453 weeks
13977.67124 16.80368 (139*2π)/3452 weeks
14070.81116 15.93075 (140*2π)/3452 weeks
14182.83801 23.45553 (141*2π)/3452 weeks
14279.09354 48.97857 (142*2π)/3452 weeks
14346.59888 55.38224 (143*2π)/3452 weeks
14440.27649 34.80759 (144*2π)/3452 weeks
14543.05735 38.19616 (145*2π)/3452 weeks
14628.62678 30.89986 (146*2π)/3452 weeks
14743.33858 12.00282 (147*2π)/3452 weeks
14859.05352 33.22158 (148*2π)/3452 weeks
14937.00163 51.04169 (149*2π)/3452 weeks
15011.38134 37.11546 (150*2π)/3452 weeks
15113.0453 11.40441 (151*2π)/3452 weeks
15229.58534 8.30335 (152*2π)/3452 weeks
15326.0243 16.52787 (153*2π)/3452 weeks
15414.23438 10.17279 (154*2π)/3452 weeks
15517.30289 -8.8766 (155*2π)/3452 weeks
15630.25064 -18.08291 (156*2π)/3452 weeks
15748.28912 -23.09841 (157*2π)/3452 weeks
15876.00726 -7.27265 (158*2π)/3452 weeks
15964.65145 37.4896 (159*2π)/3452 weeks
16015.75091 36.01065 (160*2π)/3452 weeks
1612.64873 -7.52681 (161*2π)/3452 weeks
16232.88197 -33.5671 (162*2π)/3452 weeks
16361.76761 -22.96852 (163*2π)/3452 weeks
16469.79502 -2.90549 (164*2π)/3452 weeks
16564.67467 10.20825 (165*2π)/3452 weeks
16662.37252 25.48294 (166*2π)/3452 weeks
16735.34535 37.41393 (167*2π)/3452 weeks
16810.66511 13.90226 (168*2π)/3452 weeks
16920.41584 -11.35996 (169*2π)/3452 weeks
17032.53778 -19.94912 (170*2π)/3452 weeks
17149.13329 -21.57695 (171*2π)/3452 weeks
17265.56844 -12.2432 (172*2π)/3452 weeks
17365.56844 12.2432 (173*2π)/3452 weeks
17449.13329 21.57695 (174*2π)/3452 weeks
17532.53778 19.94912 (175*2π)/3452 weeks
17620.41584 11.35996 (176*2π)/3452 weeks
17710.66511 -13.90226 (177*2π)/3452 weeks
17835.34535 -37.41393 (178*2π)/3452 weeks
17962.37252 -25.48294 (179*2π)/3452 weeks
18064.67467 -10.20825 (180*2π)/3452 weeks
18169.79502 2.90549 (181*2π)/3452 weeks
18261.76761 22.96852 (182*2π)/3452 weeks
18332.88197 33.5671 (183*2π)/3452 weeks
1842.64873 7.52681 (184*2π)/3452 weeks
18515.75091 -36.01065 (185*2π)/3452 weeks
18664.65145 -37.4896 (186*2π)/3452 weeks
18776.00726 7.27265 (187*2π)/3452 weeks
18848.28912 23.09841 (188*2π)/3452 weeks
18930.25064 18.08291 (189*2π)/3452 weeks
19017.30289 8.8766 (190*2π)/3452 weeks
19114.23438 -10.17279 (191*2π)/3452 weeks
19226.0243 -16.52787 (192*2π)/3452 weeks
19329.58534 -8.30335 (193*2π)/3452 weeks
19413.0453 -11.40441 (194*2π)/3452 weeks
19511.38134 -37.11546 (195*2π)/3452 weeks
19637.00163 -51.04169 (196*2π)/3452 weeks
19759.05352 -33.22158 (197*2π)/3452 weeks
19843.33858 -12.00282 (198*2π)/3452 weeks
19928.62678 -30.89986 (199*2π)/3452 weeks
20043.05735 -38.19616 (200*2π)/3452 weeks
20140.27649 -34.80759 (201*2π)/3452 weeks
20246.59888 -55.38224 (202*2π)/3452 weeks
20379.09354 -48.97857 (203*2π)/3452 weeks
20482.83801 -23.45553 (204*2π)/3452 weeks
20570.81116 -15.93075 (205*2π)/3452 weeks
20677.67124 -16.80368 (206*2π)/3452 weeks
20774.17829 10.56707 (207*2π)/3452 weeks
20836.05374 9.23882 (208*2π)/3452 weeks
20937.15333 -31.01833 (209*2π)/3452 weeks
21076.11337 -25.99709 (210*2π)/3452 weeks
21170.29432 10.18502 (211*2π)/3452 weeks
21238.88329 10.01516 (212*2π)/3452 weeks
21336.93653 -7.56722 (213*2π)/3452 weeks
21431.80629 1.01578 (214*2π)/3452 weeks
2158.8486 -22.63438 (215*2π)/3452 weeks
21632.70157 -62.39927 (216*2π)/3452 weeks
21779.37182 -48.70807 (217*2π)/3452 weeks
21877.79903 -5.88122 (218*2π)/3452 weeks
21945.18225 5.46616 (219*2π)/3452 weeks
22023.58508 -13.86155 (220*2π)/3452 weeks
22128.03898 -40.62931 (221*2π)/3452 weeks
22250.61096 -55.43758 (222*2π)/3452 weeks
22378.22723 -44.88667 (223*2π)/3452 weeks
22482.88554 -17.00121 (224*2π)/3452 weeks
22562.30615 -3.21788 (225*2π)/3452 weeks
22650.5451 -13.8354 (226*2π)/3452 weeks
22756.40589 -18.63351 (227*2π)/3452 weeks
22854.51312 -14.10175 (228*2π)/3452 weeks
22954.33012 -13.01321 (229*2π)/3452 weeks
23047.65712 -9.55734 (230*2π)/3452 weeks
23145.19733 -16.10086 (231*2π)/3451 weeks
23242.80499 -11.89758 (232*2π)/3451 weeks
23327.65839 -23.74938 (233*2π)/3451 weeks
23438.75687 -41.71127 (234*2π)/3451 weeks
23554.84076 -38.0772 (235*2π)/3451 weeks
23655.87273 -30.51105 (236*2π)/3451 weeks
23757.93097 -24.72261 (237*2π)/3451 weeks
23848.27372 -23.06601 (238*2π)/3451 weeks
23946.8776 -34.72712 (239*2π)/3451 weeks
24060.874 -39.36653 (240*2π)/3451 weeks
24172.9078 -21.71003 (241*2π)/3451 weeks
24248.74667 -5.68705 (242*2π)/3451 weeks
24342.27401 -32.49453 (243*2π)/3451 weeks
24460.61268 -24.22097 (244*2π)/3451 weeks
24544.43657 -18.58526 (245*2π)/3451 weeks
24644.01439 -35.2151 (246*2π)/3451 weeks
24766.20485 -36.36762 (247*2π)/3451 weeks
24863.65526 -6.6174 (248*2π)/3451 weeks
24939.00923 -10.67151 (249*2π)/3451 weeks
25034.96236 -26.65754 (250*2π)/3451 weeks
25149.57567 -26.58536 (251*2π)/3451 weeks
25237.5322 -11.76568 (252*2π)/3451 weeks
25316.72847 -21.17298 (253*2π)/3451 weeks
2545.39997 -42.40565 (254*2π)/3451 weeks
2556.38372 -83.6227 (255*2π)/3451 weeks
25658.41601 -117.6173 (256*2π)/3451 weeks
257120.9877 -92.70904 (257*2π)/3451 weeks
258144.7116 -32.45734 (258*2π)/3451 weeks
259128.5275 31.09507 (259*2π)/3451 weeks
26056.11902 75.78493 (260*2π)/3451 weeks
261-23.23044 28.30648 (261*2π)/3451 weeks
262-14.13203 -45.78674 (262*2π)/3451 weeks
26329.96023 -69.83084 (263*2π)/3451 weeks
26469.097 -53.21769 (264*2π)/3451 weeks
26566.05374 -9.55091 (265*2π)/3451 weeks
26633.23756 3.97752 (266*2π)/3451 weeks
2672.89472 -15.54652 (267*2π)/3451 weeks
2687.13697 -43.09627 (268*2π)/3451 weeks
26915.72277 -52.56378 (269*2π)/3451 weeks
27020.20447 -57.62445 (270*2π)/3451 weeks
27126.8384 -63.44139 (271*2π)/3451 weeks
27232.62449 -66.25932 (272*2π)/3451 weeks
27346.7113 -69.1172 (273*2π)/3451 weeks
27456.24649 -51.86001 (274*2π)/3451 weeks
27537.92729 -40.38363 (275*2π)/3451 weeks
27624.28773 -51.48483 (276*2π)/3451 weeks
27725.30426 -77.40782 (277*2π)/3451 weeks
27868.05292 -76.19939 (278*2π)/3451 weeks
27962.98141 -20.51753 (279*2π)/3451 weeks
2808.88912 -33.56359 (280*2π)/3451 weeks
28128.26282 -68.40318 (281*2π)/3451 weeks
28228.03748 -41.87012 (282*2π)/3451 weeks
283-11.96487 -65.42773 (283*2π)/3451 weeks
28410.71223 -108.33 (284*2π)/3451 weeks
28540.46327 -104.6396 (285*2π)/3451 weeks
28653.32085 -99.0806 (286*2π)/3451 weeks
28761.80788 -79.83936 (287*2π)/3451 weeks
28844.09842 -78.03209 (288*2π)/3451 weeks
28952.3728 -100.4418 (289*2π)/3451 weeks
29087.50073 -92.01142 (290*2π)/3451 weeks
29197.53249 -60.97826 (291*2π)/3451 weeks
29295.83326 -18.04118 (292*2π)/3451 weeks
29351.25597 33.91803 (293*2π)/3451 weeks
294-46.1636 30.97214 (294*2π)/3451 weeks
295-98.04499 -56.70185 (295*2π)/3451 weeks
296-67.48324 -127.6753 (296*2π)/3451 weeks
297-42.23114 -143.2239 (297*2π)/3451 weeks
298-34.54833 -181.4719 (298*2π)/3451 weeks
29911.64414 -214.7054 (299*2π)/3451 weeks
30084.34988 -213.5718 (300*2π)/3451 weeks
301128.6848 -149.3687 (301*2π)/3451 weeks
30298.92197 -74.99242 (302*2π)/3451 weeks
30320.6935 -83.75558 (303*2π)/3451 weeks
30418.5726 -131.1886 (304*2π)/3451 weeks
30511.15209 -138.8665 (305*2π)/3451 weeks
3064.7909 -185.9055 (306*2π)/3451 weeks
30759.56497 -233.6404 (307*2π)/3451 weeks
308125.1732 -204.2014 (308*2π)/3451 weeks
309130.4379 -180.6779 (309*2π)/3451 weeks
310185.6524 -141.5953 (310*2π)/3451 weeks
311151.2261 -27.87166 (311*2π)/3451 weeks
31224.31202 -23.9593 (312*2π)/3451 weeks
313-26.92633 -106.3207 (313*2π)/3451 weeks
314-34.22985 -192.1266 (314*2π)/3451 weeks
31554.02079 -264.9749 (315*2π)/3451 weeks
316143.9987 -204.8697 (316*2π)/3451 weeks
317116.855 -150.7747 (317*2π)/3451 weeks
318120.6355 -140.8504 (318*2π)/3451 weeks
31982.55588 -84.37528 (319*2π)/3451 weeks
320-43.96924 -98.45338 (320*2π)/3451 weeks
321-102.678 -280.2798 (321*2π)/3451 weeks
32277.03364 -428.6891 (322*2π)/3451 weeks
323270.0076 -296.1198 (323*2π)/3451 weeks
324196.6882 -136.7916 (324*2π)/3451 weeks
32582.28513 -185.055 (325*2π)/3451 weeks
326146.3243 -276.5615 (326*2π)/3451 weeks
327236.2171 -191.1467 (327*2π)/3451 weeks
328154.2113 -106.7895 (328*2π)/3451 weeks
32997.34544 -123.1855 (329*2π)/3451 weeks
33096.92678 -124.4201 (330*2π)/3451 weeks
331-52.20127 -50.32213 (331*2π)/3451 weeks
332-215.3604 -288.181 (332*2π)/3451 weeks
333-88.84944 -497.5228 (333*2π)/3451 weeks
33496.57436 -508.3858 (334*2π)/3451 weeks
33585.47399 -383.9555 (335*2π)/3451 weeks
336-73.76489 -475.3764 (336*2π)/3451 weeks
33774.09435 -796.0172 (337*2π)/3451 weeks
338448.7199 -588.9774 (338*2π)/3451 weeks
339116.1315 -230.3295 (339*2π)/3451 weeks
340-464.1536 -728.8547 (340*2π)/3451 weeks
341-131.5717 -1,477.991 (341*2π)/3451 weeks
34262.22612 -1,682.633 (342*2π)/3451 weeks
343499.3333 -2,986.875 (343*2π)/3451 weeks



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