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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 29 weeks (507.4892*sine), 32 weeks (462.1569*sine), and 35 weeks (369.6324*sine).

NUGT (Direxion Daily Gold Miners Index Bull 3x Shares ETF) has an average price of 3,110.56 (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 9/5/2017 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
03,110.562   0 
13,463.76 3,635.327 (1*2π)/353353 weeks
2547.908 2,982.699 (2*2π)/353177 weeks
346.88618 1,679.908 (3*2π)/353118 weeks
4-72.46162 1,463.968 (4*2π)/35388 weeks
5-458.9659 811.2804 (5*2π)/35371 weeks
623.3036 222.7625 (6*2π)/35359 weeks
7434.9959 496.6959 (7*2π)/35350 weeks
8149.1925 797.8837 (8*2π)/35344 weeks
9-90.60055 525.6045 (9*2π)/35339 weeks
1052.40409 369.6324 (10*2π)/35335 weeks
11124.7185 462.1569 (11*2π)/35332 weeks
12-32.96381 507.4892 (12*2π)/35329 weeks
13-189.3859 358.7392 (13*2π)/35327 weeks
14-135.5216 88.74256 (14*2π)/35325 weeks
1577.45879 85.54153 (15*2π)/35324 weeks
1683.64497 131.7696 (16*2π)/35322 weeks
17123.6182 110.3722 (17*2π)/35321 weeks
18213.5892 132.0497 (18*2π)/35320 weeks
19196.333 253.888 (19*2π)/35319 weeks
2085.66726 234.7139 (20*2π)/35318 weeks
21123.5583 132.7535 (21*2π)/35317 weeks
22251.899 189.7506 (22*2π)/35316 weeks
23202.1057 382.2522 (23*2π)/35315 weeks
24-28.14392 376.1377 (24*2π)/35315 weeks
25-98.946 179.0504 (25*2π)/35314 weeks
2613.89487 69.71672 (26*2π)/35314 weeks
27104.1217 102.1017 (27*2π)/35313 weeks
28109.8674 149.1176 (28*2π)/35313 weeks
29126.4905 153.4948 (29*2π)/35312 weeks
30126.148 229.5926 (30*2π)/35312 weeks
3118.60892 247.7551 (31*2π)/35311 weeks
32-36.44302 158.8312 (32*2π)/35311 weeks
33-21.28915 84.87495 (33*2π)/35311 weeks
3449.39505 11.64996 (34*2π)/35310 weeks
35167.4788 46.83603 (35*2π)/35310 weeks
36171.9701 153.22 (36*2π)/35310 weeks
37123.7602 173.9193 (37*2π)/35310 weeks
38117.1843 205.8391 (38*2π)/3539 weeks
3949.07504 225.2853 (39*2π)/3539 weeks
403.53323 175.5021 (40*2π)/3539 weeks
4112.39187 133.4123 (41*2π)/3539 weeks
4216.81165 126.8963 (42*2π)/3538 weeks
4321.01913 79.77473 (43*2π)/3538 weeks
4496.60548 72.67254 (44*2π)/3538 weeks
45125.8109 143.651 (45*2π)/3538 weeks
4685.33165 206.2483 (46*2π)/3538 weeks
4714.9429 210.6209 (47*2π)/3538 weeks
48-30.74662 180.5683 (48*2π)/3537 weeks
49-41.11626 140.7671 (49*2π)/3537 weeks
50-60.23904 127.6031 (50*2π)/3537 weeks
51-95.36459 69.39628 (51*2π)/3537 weeks
52-60.74631 -18.65263 (52*2π)/3537 weeks
5333.69179 -39.37363 (53*2π)/3537 weeks
5488.75302 6.37398 (54*2π)/3537 weeks
5596.7933 51.1813 (55*2π)/3536 weeks
5689.78371 80.21242 (56*2π)/3536 weeks
5760.23634 100.2701 (57*2π)/3536 weeks
5840.79512 82.4404 (58*2π)/3536 weeks
5955.10078 72.7478 (59*2π)/3536 weeks
6058.34737 92.60318 (60*2π)/3536 weeks
6144.17513 99.24088 (61*2π)/3536 weeks
6226.1398 107.2627 (62*2π)/3536 weeks
63-8.79925 85.90707 (63*2π)/3536 weeks
646.65879 39.33071 (64*2π)/3536 weeks
6536.3741 54.85316 (65*2π)/3535 weeks
668.46429 58.46727 (66*2π)/3535 weeks
6729.46879 15.97541 (67*2π)/3535 weeks
6877.03703 45.81848 (68*2π)/3535 weeks
6947.67887 83.49244 (69*2π)/3535 weeks
7020.12089 61.34111 (70*2π)/3535 weeks
7127.52122 43.78139 (71*2π)/3535 weeks
7244.65644 38.77206 (72*2π)/3535 weeks
7353.60698 58.16106 (73*2π)/3535 weeks
7439.29613 68.69588 (74*2π)/3535 weeks
7530.04471 63.24946 (75*2π)/3535 weeks
7623.67076 60.4218 (76*2π)/3535 weeks
7718.55571 54.16455 (77*2π)/3535 weeks
7813.31624 49.66943 (78*2π)/3535 weeks
794.57146 39.05943 (79*2π)/3534 weeks
806.49375 9.38466 (80*2π)/3534 weeks
8138.14217 -3.64176 (81*2π)/3534 weeks
8267.82435 13.57336 (82*2π)/3534 weeks
8363.35722 55.79069 (83*2π)/3534 weeks
8424.83646 67.67203 (84*2π)/3534 weeks
85-16.38383 41.15249 (85*2π)/3534 weeks
86-20.46451 -31.74568 (86*2π)/3534 weeks
8757.42442 -73.70152 (87*2π)/3534 weeks
88125.297 -29.83793 (88*2π)/3534 weeks
89140.7484 30.58592 (89*2π)/3534 weeks
90119.4668 88.17839 (90*2π)/3534 weeks
9161.03952 114.511 (91*2π)/3534 weeks
928.39645 85.43059 (92*2π)/3534 weeks
934.23558 44.17992 (93*2π)/3534 weeks
9414.52472 23.12606 (94*2π)/3534 weeks
9533.06444 11.55468 (95*2π)/3534 weeks
9648.7307 22.43809 (96*2π)/3534 weeks
9736.03935 28.57302 (97*2π)/3534 weeks
9835.75446 13.07573 (98*2π)/3534 weeks
9954.60178 3.28411 (99*2π)/3534 weeks
10069.19778 28.52931 (100*2π)/3534 weeks
10147.16627 37.9978 (101*2π)/3533 weeks
10240.00036 22.82889 (102*2π)/3533 weeks
10355.17467 17.23511 (103*2π)/3533 weeks
10449.94372 34.20492 (104*2π)/3533 weeks
10537.68555 13.77822 (105*2π)/3533 weeks
10666.29027 10.16207 (106*2π)/3533 weeks
10766.39547 34.17913 (107*2π)/3533 weeks
10850.21619 37.77534 (108*2π)/3533 weeks
10943.60938 27.14393 (109*2π)/3533 weeks
11051.70248 21.11909 (110*2π)/3533 weeks
11155.95931 28.65005 (111*2π)/3533 weeks
11255.4543 31.68398 (112*2π)/3533 weeks
11348.4351 40.90041 (113*2π)/3533 weeks
11430.95628 35.3681 (114*2π)/3533 weeks
11530.39084 14.29548 (115*2π)/3533 weeks
11643.98166 13.97259 (116*2π)/3533 weeks
11742.67295 14.35785 (117*2π)/3533 weeks
11849.8372 9.51336 (118*2π)/3533 weeks
11953.26263 13.86239 (119*2π)/3533 weeks
12054.63099 13.82864 (120*2π)/3533 weeks
12152.93029 18.81726 (121*2π)/3533 weeks
12249.5348 10.5176 (122*2π)/3533 weeks
12365.22743 3.21495 (123*2π)/3533 weeks
12481.92814 21.63008 (124*2π)/3533 weeks
12572.71817 47.44189 (125*2π)/3533 weeks
12645.39361 53.27173 (126*2π)/3533 weeks
12725.82582 37.06987 (127*2π)/3533 weeks
12824.057 10.80807 (128*2π)/3533 weeks
12946.19356 -6.0138 (129*2π)/3533 weeks
13076.87303 7.22494 (130*2π)/3533 weeks
13176.34244 48.62626 (131*2π)/3533 weeks
13231.42453 60.63115 (132*2π)/3533 weeks
1338.49088 22.61389 (133*2π)/3533 weeks
13429.94887 -.97827 (134*2π)/3533 weeks
13536.51637 7.72796 (135*2π)/3533 weeks
13636.17897 -8.04378 (136*2π)/3533 weeks
13765.24238 -12.22189 (137*2π)/3533 weeks
13876.62936 20.55995 (138*2π)/3533 weeks
13941.58958 33.93297 (139*2π)/3533 weeks
14030.50415 -2.87307 (140*2π)/3533 weeks
14166.17086 -14.26232 (141*2π)/3533 weeks
14278.51545 12.41633 (142*2π)/3532 weeks
14367.98117 16.7839 (143*2π)/3532 weeks
14477.68989 18.17451 (144*2π)/3532 weeks
14580.93042 39.87922 (145*2π)/3532 weeks
14655.3819 57.60322 (146*2π)/3532 weeks
14737.21635 39.22956 (147*2π)/3532 weeks
14844.04621 34.60116 (148*2π)/3532 weeks
14932.96133 36.37838 (149*2π)/3532 weeks
15031.70204 15.17444 (150*2π)/3532 weeks
15155.64055 19.84654 (151*2π)/3532 weeks
15248.16393 45.45546 (152*2π)/3532 weeks
15320.50739 46.17951 (153*2π)/3532 weeks
1547.97232 22.50553 (154*2π)/3532 weeks
15521.10994 6.28793 (155*2π)/3532 weeks
15629.98729 13.64929 (156*2π)/3532 weeks
15721.03033 15.49217 (157*2π)/3532 weeks
15812.47095 1.19465 (158*2π)/3532 weeks
15921.77493 -13.54028 (159*2π)/3532 weeks
16034.56546 -20.35284 (160*2π)/3532 weeks
16155.76048 -21.25997 (161*2π)/3532 weeks
16277.71352 7.60846 (162*2π)/3532 weeks
16348.59833 43.12932 (163*2π)/3532 weeks
1646.26144 24.49808 (164*2π)/3532 weeks
1657.46776 -17.75631 (165*2π)/3532 weeks
16640.46413 -32.89191 (166*2π)/3532 weeks
16763.26998 -18.15304 (167*2π)/3532 weeks
16867.53745 .86419 (168*2π)/3532 weeks
16962.57967 11.15618 (169*2π)/3532 weeks
17058.25389 27.88368 (170*2π)/3532 weeks
17129.97117 35.39315 (171*2π)/3532 weeks
1729.86469 10.05354 (172*2π)/3532 weeks
17321.13754 -11.83947 (173*2π)/3532 weeks
17432.5645 -19.76404 (174*2π)/3532 weeks
17548.2752 -20.74407 (175*2π)/3532 weeks
17663.80845 -11.64964 (176*2π)/3532 weeks
17763.80845 11.64964 (177*2π)/3532 weeks
17848.2752 20.74407 (178*2π)/3532 weeks
17932.5645 19.76404 (179*2π)/3532 weeks
18021.13754 11.83947 (180*2π)/3532 weeks
1819.86469 -10.05354 (181*2π)/3532 weeks
18229.97117 -35.39315 (182*2π)/3532 weeks
18358.25389 -27.88368 (183*2π)/3532 weeks
18462.57967 -11.15618 (184*2π)/3532 weeks
18567.53745 -.86419 (185*2π)/3532 weeks
18663.26998 18.15304 (186*2π)/3532 weeks
18740.46413 32.89191 (187*2π)/3532 weeks
1887.46776 17.75631 (188*2π)/3532 weeks
1896.26144 -24.49808 (189*2π)/3532 weeks
19048.59833 -43.12932 (190*2π)/3532 weeks
19177.71352 -7.60846 (191*2π)/3532 weeks
19255.76048 21.25997 (192*2π)/3532 weeks
19334.56546 20.35284 (193*2π)/3532 weeks
19421.77493 13.54028 (194*2π)/3532 weeks
19512.47095 -1.19465 (195*2π)/3532 weeks
19621.03033 -15.49217 (196*2π)/3532 weeks
19729.98729 -13.64929 (197*2π)/3532 weeks
19821.10994 -6.28793 (198*2π)/3532 weeks
1997.97232 -22.50553 (199*2π)/3532 weeks
20020.50739 -46.17951 (200*2π)/3532 weeks
20148.16393 -45.45546 (201*2π)/3532 weeks
20255.64055 -19.84654 (202*2π)/3532 weeks
20331.70204 -15.17444 (203*2π)/3532 weeks
20432.96133 -36.37838 (204*2π)/3532 weeks
20544.04621 -34.60116 (205*2π)/3532 weeks
20637.21635 -39.22956 (206*2π)/3532 weeks
20755.3819 -57.60322 (207*2π)/3532 weeks
20880.93042 -39.87922 (208*2π)/3532 weeks
20977.68989 -18.17451 (209*2π)/3532 weeks
21067.98117 -16.7839 (210*2π)/3532 weeks
21178.51545 -12.41633 (211*2π)/3532 weeks
21266.17086 14.26232 (212*2π)/3532 weeks
21330.50415 2.87307 (213*2π)/3532 weeks
21441.58958 -33.93297 (214*2π)/3532 weeks
21576.62936 -20.55995 (215*2π)/3532 weeks
21665.24238 12.22189 (216*2π)/3532 weeks
21736.17897 8.04378 (217*2π)/3532 weeks
21836.51637 -7.72796 (218*2π)/3532 weeks
21929.94887 .97827 (219*2π)/3532 weeks
2208.49088 -22.61389 (220*2π)/3532 weeks
22131.42453 -60.63115 (221*2π)/3532 weeks
22276.34244 -48.62626 (222*2π)/3532 weeks
22376.87303 -7.22494 (223*2π)/3532 weeks
22446.19356 6.0138 (224*2π)/3532 weeks
22524.057 -10.80807 (225*2π)/3532 weeks
22625.82582 -37.06987 (226*2π)/3532 weeks
22745.39361 -53.27173 (227*2π)/3532 weeks
22872.71817 -47.44189 (228*2π)/3532 weeks
22981.92814 -21.63008 (229*2π)/3532 weeks
23065.22743 -3.21495 (230*2π)/3532 weeks
23149.5348 -10.5176 (231*2π)/3532 weeks
23252.93029 -18.81726 (232*2π)/3532 weeks
23354.63099 -13.82864 (233*2π)/3532 weeks
23453.26263 -13.86239 (234*2π)/3532 weeks
23549.8372 -9.51336 (235*2π)/3532 weeks
23642.67295 -14.35785 (236*2π)/3531 weeks
23743.98166 -13.97259 (237*2π)/3531 weeks
23830.39084 -14.29548 (238*2π)/3531 weeks
23930.95628 -35.3681 (239*2π)/3531 weeks
24048.4351 -40.90041 (240*2π)/3531 weeks
24155.4543 -31.68398 (241*2π)/3531 weeks
24255.95931 -28.65005 (242*2π)/3531 weeks
24351.70248 -21.11909 (243*2π)/3531 weeks
24443.60938 -27.14393 (244*2π)/3531 weeks
24550.21619 -37.77534 (245*2π)/3531 weeks
24666.39547 -34.17913 (246*2π)/3531 weeks
24766.29027 -10.16207 (247*2π)/3531 weeks
24837.68555 -13.77822 (248*2π)/3531 weeks
24949.94372 -34.20492 (249*2π)/3531 weeks
25055.17467 -17.23511 (250*2π)/3531 weeks
25140.00036 -22.82889 (251*2π)/3531 weeks
25247.16627 -37.9978 (252*2π)/3531 weeks
25369.19778 -28.52931 (253*2π)/3531 weeks
25454.60178 -3.28411 (254*2π)/3531 weeks
25535.75446 -13.07573 (255*2π)/3531 weeks
25636.03935 -28.57302 (256*2π)/3531 weeks
25748.7307 -22.43809 (257*2π)/3531 weeks
25833.06444 -11.55468 (258*2π)/3531 weeks
25914.52472 -23.12606 (259*2π)/3531 weeks
2604.23558 -44.17992 (260*2π)/3531 weeks
2618.39645 -85.43059 (261*2π)/3531 weeks
26261.03952 -114.511 (262*2π)/3531 weeks
263119.4668 -88.17839 (263*2π)/3531 weeks
264140.7484 -30.58592 (264*2π)/3531 weeks
265125.297 29.83793 (265*2π)/3531 weeks
26657.42442 73.70152 (266*2π)/3531 weeks
267-20.46451 31.74568 (267*2π)/3531 weeks
268-16.38383 -41.15249 (268*2π)/3531 weeks
26924.83646 -67.67203 (269*2π)/3531 weeks
27063.35722 -55.79069 (270*2π)/3531 weeks
27167.82435 -13.57336 (271*2π)/3531 weeks
27238.14217 3.64176 (272*2π)/3531 weeks
2736.49375 -9.38466 (273*2π)/3531 weeks
2744.57146 -39.05943 (274*2π)/3531 weeks
27513.31624 -49.66943 (275*2π)/3531 weeks
27618.55571 -54.16455 (276*2π)/3531 weeks
27723.67076 -60.4218 (277*2π)/3531 weeks
27830.04471 -63.24946 (278*2π)/3531 weeks
27939.29613 -68.69588 (279*2π)/3531 weeks
28053.60698 -58.16106 (280*2π)/3531 weeks
28144.65644 -38.77206 (281*2π)/3531 weeks
28227.52122 -43.78139 (282*2π)/3531 weeks
28320.12089 -61.34111 (283*2π)/3531 weeks
28447.67887 -83.49244 (284*2π)/3531 weeks
28577.03703 -45.81848 (285*2π)/3531 weeks
28629.46879 -15.97541 (286*2π)/3531 weeks
2878.46429 -58.46727 (287*2π)/3531 weeks
28836.3741 -54.85316 (288*2π)/3531 weeks
2896.65879 -39.33071 (289*2π)/3531 weeks
290-8.79925 -85.90707 (290*2π)/3531 weeks
29126.1398 -107.2627 (291*2π)/3531 weeks
29244.17513 -99.24088 (292*2π)/3531 weeks
29358.34737 -92.60318 (293*2π)/3531 weeks
29455.10078 -72.7478 (294*2π)/3531 weeks
29540.79512 -82.4404 (295*2π)/3531 weeks
29660.23634 -100.2701 (296*2π)/3531 weeks
29789.78371 -80.21242 (297*2π)/3531 weeks
29896.7933 -51.1813 (298*2π)/3531 weeks
29988.75302 -6.37398 (299*2π)/3531 weeks
30033.69179 39.37363 (300*2π)/3531 weeks
301-60.74631 18.65263 (301*2π)/3531 weeks
302-95.36459 -69.39628 (302*2π)/3531 weeks
303-60.23904 -127.6031 (303*2π)/3531 weeks
304-41.11626 -140.7671 (304*2π)/3531 weeks
305-30.74662 -180.5683 (305*2π)/3531 weeks
30614.9429 -210.6209 (306*2π)/3531 weeks
30785.33165 -206.2483 (307*2π)/3531 weeks
308125.8109 -143.651 (308*2π)/3531 weeks
30996.60548 -72.67254 (309*2π)/3531 weeks
31021.01913 -79.77473 (310*2π)/3531 weeks
31116.81165 -126.8963 (311*2π)/3531 weeks
31212.39187 -133.4123 (312*2π)/3531 weeks
3133.53323 -175.5021 (313*2π)/3531 weeks
31449.07504 -225.2853 (314*2π)/3531 weeks
315117.1843 -205.8391 (315*2π)/3531 weeks
316123.7602 -173.9193 (316*2π)/3531 weeks
317171.9701 -153.22 (317*2π)/3531 weeks
318167.4788 -46.83603 (318*2π)/3531 weeks
31949.39505 -11.64996 (319*2π)/3531 weeks
320-21.28915 -84.87495 (320*2π)/3531 weeks
321-36.44302 -158.8312 (321*2π)/3531 weeks
32218.60892 -247.7551 (322*2π)/3531 weeks
323126.148 -229.5926 (323*2π)/3531 weeks
324126.4905 -153.4948 (324*2π)/3531 weeks
325109.8674 -149.1176 (325*2π)/3531 weeks
326104.1217 -102.1017 (326*2π)/3531 weeks
32713.89487 -69.71672 (327*2π)/3531 weeks
328-98.946 -179.0504 (328*2π)/3531 weeks
329-28.14392 -376.1377 (329*2π)/3531 weeks
330202.1057 -382.2522 (330*2π)/3531 weeks
331251.899 -189.7506 (331*2π)/3531 weeks
332123.5583 -132.7535 (332*2π)/3531 weeks
33385.66726 -234.7139 (333*2π)/3531 weeks
334196.333 -253.888 (334*2π)/3531 weeks
335213.5892 -132.0497 (335*2π)/3531 weeks
336123.6182 -110.3722 (336*2π)/3531 weeks
33783.64497 -131.7696 (337*2π)/3531 weeks
33877.45879 -85.54153 (338*2π)/3531 weeks
339-135.5216 -88.74256 (339*2π)/3531 weeks
340-189.3859 -358.7392 (340*2π)/3531 weeks
341-32.96381 -507.4892 (341*2π)/3531 weeks
342124.7185 -462.1569 (342*2π)/3531 weeks
34352.40409 -369.6324 (343*2π)/3531 weeks
344-90.60055 -525.6045 (344*2π)/3531 weeks
345149.1925 -797.8837 (345*2π)/3531 weeks
346434.9959 -496.6959 (346*2π)/3531 weeks
34723.3036 -222.7625 (347*2π)/3531 weeks
348-458.9659 -811.2804 (348*2π)/3531 weeks
349-72.46162 -1,463.968 (349*2π)/3531 weeks
35046.88618 -1,679.908 (350*2π)/3531 weeks
351547.908 -2,982.699 (351*2π)/3531 weeks



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