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Fourier Analysis of NUGT (Direxion Daily Gold Miners Inde)


NUGT (Direxion Daily Gold Miners Inde) appears to have interesting cyclic behaviour every 30 weeks (138.2887*sine), 33 weeks (113.3779*sine), and 16 weeks (70.4796*cosine).

NUGT (Direxion Daily Gold Miners Inde) has an average price of 835.9 (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 3/20/2017 for NUGT (Direxion Daily Gold Miners Inde), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0835.9005   0 
1856.9395 995.6013 (1*2π)/329329 weeks
296.76732 740.2272 (2*2π)/329165 weeks
323.40764 421.4343 (3*2π)/329110 weeks
4-65.61681 363.6219 (4*2π)/32982 weeks
5-102.8964 134.897 (5*2π)/32966 weeks
673.87583 75.09351 (6*2π)/32955 weeks
797.85215 195.0604 (7*2π)/32947 weeks
8-13.61546 180.8076 (8*2π)/32941 weeks
9.20188 104.0624 (9*2π)/32937 weeks
1034.86537 113.3779 (10*2π)/32933 weeks
11.46973 138.2887 (11*2π)/32930 weeks
12-47.60723 103.6624 (12*2π)/32927 weeks
13-39.59188 26.61182 (13*2π)/32925 weeks
1421.48499 23.65596 (14*2π)/32924 weeks
1522.91593 34.68408 (15*2π)/32922 weeks
1635.66386 28.98758 (16*2π)/32921 weeks
1761.13778 43.54111 (17*2π)/32919 weeks
1842.70087 72.31554 (18*2π)/32918 weeks
1920.98539 50.91798 (19*2π)/32917 weeks
2050.47483 35.42859 (20*2π)/32916 weeks
2170.47961 78.82993 (21*2π)/32916 weeks
2215.46612 111.6625 (22*2π)/32915 weeks
23-28.29758 66.31172 (23*2π)/32914 weeks
24-5.55887 21.92029 (24*2π)/32914 weeks
2525.55181 24.99363 (25*2π)/32913 weeks
2630.29204 39.63443 (26*2π)/32913 weeks
2733.82887 41.13651 (27*2π)/32912 weeks
2833.08435 62.91365 (28*2π)/32912 weeks
291.77264 64.97793 (29*2π)/32911 weeks
30-9.48882 38.35513 (30*2π)/32911 weeks
31-3.517 16.99446 (31*2π)/32911 weeks
3224.55071 1.84822 (32*2π)/32910 weeks
3350.29532 25.43512 (33*2π)/32910 weeks
3438.57886 47.23909 (34*2π)/32910 weeks
3533.90418 49.4017 (35*2π)/3299 weeks
3620.98087 61.23259 (36*2π)/3299 weeks
372.53254 51.98763 (37*2π)/3299 weeks
382.08409 37.6637 (38*2π)/3299 weeks
395.37555 34.64632 (39*2π)/3298 weeks
404.80181 22.74465 (40*2π)/3298 weeks
4125.80013 19.5294 (41*2π)/3298 weeks
4233.57011 39.99767 (42*2π)/3298 weeks
4320.30158 56.8146 (43*2π)/3298 weeks
441.06204 55.31351 (44*2π)/3297 weeks
45-10.45614 45.0458 (45*2π)/3297 weeks
46-11.65479 36.86083 (46*2π)/3297 weeks
47-21.19182 30.2265 (47*2π)/3297 weeks
48-23.89738 6.42138 (48*2π)/3297 weeks
49-1.62781 -11.56304 (49*2π)/3297 weeks
5020.65681 -3.38273 (50*2π)/3297 weeks
5126.3394 10.7156 (51*2π)/3296 weeks
5224.68124 19.86693 (52*2π)/3296 weeks
5317.55489 27.06835 (53*2π)/3296 weeks
5410.98828 22.65726 (54*2π)/3296 weeks
5514.84001 19.62751 (55*2π)/3296 weeks
5615.30151 25.24385 (56*2π)/3296 weeks
5711.43365 26.94598 (57*2π)/3296 weeks
584.82694 28.91475 (58*2π)/3296 weeks
59-3.25573 19.07861 (59*2π)/3296 weeks
606.53829 10.55279 (60*2π)/3295 weeks
617.73237 17.78209 (61*2π)/3295 weeks
622.45896 8.56762 (62*2π)/3295 weeks
6317.47699 6.04829 (63*2π)/3295 weeks
6416.70145 20.89576 (64*2π)/3295 weeks
655.80381 18.76517 (65*2π)/3295 weeks
666.85366 12.56344 (66*2π)/3295 weeks
6711.327 10.38945 (67*2π)/3295 weeks
6814.50409 15.42811 (68*2π)/3295 weeks
6910.47758 18.42644 (69*2π)/3295 weeks
708.05641 16.94586 (70*2π)/3295 weeks
716.11674 16.04225 (71*2π)/3295 weeks
724.81418 14.26924 (72*2π)/3295 weeks
732.83119 12.5812 (73*2π)/3295 weeks
74.12829 7.84045 (74*2π)/3294 weeks
755.3643 -.22534 (75*2π)/3294 weeks
7614.97822 .67509 (76*2π)/3294 weeks
7719.65244 10.94839 (77*2π)/3294 weeks
7810.22233 18.10792 (78*2π)/3294 weeks
79-2.11361 13.74872 (79*2π)/3294 weeks
80-7.0919 -4.92915 (80*2π)/3294 weeks
8113.11752 -19.84176 (81*2π)/3294 weeks
8233.57673 -8.34964 (82*2π)/3294 weeks
8337.90814 9.10522 (83*2π)/3294 weeks
8430.60118 25.38125 (84*2π)/3294 weeks
8512.88993 30.50263 (85*2π)/3294 weeks
86.80784 19.5105 (86*2π)/3294 weeks
872.08221 9.633 (87*2π)/3294 weeks
885.69073 4.31163 (88*2π)/3294 weeks
8911.71073 3.66313 (89*2π)/3294 weeks
9011.64803 8.16631 (90*2π)/3294 weeks
918.9864 4.99254 (91*2π)/3294 weeks
9212.45594 1.15195 (92*2π)/3294 weeks
9318.90403 5.83253 (93*2π)/3294 weeks
9413.5017 10.50906 (94*2π)/3294 weeks
9510.76054 6.47125 (95*2π)/3293 weeks
9614.929 4.69885 (96*2π)/3293 weeks
9712.96974 9.28176 (97*2π)/3293 weeks
9810.92836 2.68117 (98*2π)/3293 weeks
9918.78528 4.30146 (99*2π)/3293 weeks
10016.59483 10.09781 (100*2π)/3293 weeks
10112.47953 9.36078 (101*2π)/3293 weeks
10212.54556 6.12588 (102*2π)/3293 weeks
10315.18688 6.51661 (103*2π)/3293 weeks
10414.65626 8.02205 (104*2π)/3293 weeks
10514.11493 10.26033 (105*2π)/3293 weeks
1069.38793 10.50342 (106*2π)/3293 weeks
1077.53034 4.89895 (107*2π)/3293 weeks
10811.77261 3.57958 (108*2π)/3293 weeks
10911.55807 3.98264 (109*2π)/3293 weeks
11013.46945 2.62789 (110*2π)/3293 weeks
11114.28896 3.82072 (111*2π)/3293 weeks
11214.93423 3.87855 (112*2π)/3293 weeks
11313.7937 4.82604 (113*2π)/3293 weeks
11414.15893 1.74415 (114*2π)/3293 weeks
11519.96302 1.96852 (115*2π)/3293 weeks
11621.77175 9.23978 (116*2π)/3293 weeks
11715.64501 14.54461 (117*2π)/3293 weeks
1188.42358 12.11346 (118*2π)/3293 weeks
1195.81199 5.35289 (119*2π)/3293 weeks
12010.60231 -.90721 (120*2π)/3293 weeks
12119.63353 .68257 (121*2π)/3293 weeks
12221.31328 12.00747 (122*2π)/3293 weeks
1238.81575 16.44612 (123*2π)/3293 weeks
1242.38512 5.61145 (124*2π)/3293 weeks
1258.90962 -.17729 (125*2π)/3293 weeks
1269.35213 1.73411 (126*2π)/3293 weeks
12711.30109 -3.46107 (127*2π)/3293 weeks
12819.91921 -1.00678 (128*2π)/3293 weeks
12917.68341 8.95923 (129*2π)/3293 weeks
1307.68386 5.01879 (130*2π)/3293 weeks
13113.21379 -4.42581 (131*2π)/3293 weeks
13221.4097 .5215 (132*2π)/3292 weeks
13318.67074 4.91209 (133*2π)/3292 weeks
13420.11315 4.29254 (134*2π)/3292 weeks
13522.02218 9.70999 (135*2π)/3292 weeks
13615.6554 15.53612 (136*2π)/3292 weeks
13710.01001 10.58485 (137*2π)/3292 weeks
13811.82266 9.4471 (138*2π)/3292 weeks
1398.3111 9.32844 (139*2π)/3292 weeks
1409.93646 3.33485 (140*2π)/3292 weeks
14115.58523 7.5357 (141*2π)/3292 weeks
14210.4383 13.26955 (142*2π)/3292 weeks
1433.15878 10.03491 (143*2π)/3292 weeks
1443.43385 2.97537 (144*2π)/3292 weeks
1457.89252 2.32285 (145*2π)/3292 weeks
1466.58285 4.31849 (146*2π)/3292 weeks
1473.43037 1.87539 (147*2π)/3292 weeks
1485.15179 -3.03699 (148*2π)/3292 weeks
1498.77977 -5.21717 (149*2π)/3292 weeks
15014.60465 -5.82104 (150*2π)/3292 weeks
15120.93032 2.23845 (151*2π)/3292 weeks
15211.92872 11.80497 (152*2π)/3292 weeks
153.87918 4.79794 (153*2π)/3292 weeks
1543.78454 -6.65047 (154*2π)/3292 weeks
15513.41118 -8.11335 (155*2π)/3292 weeks
15617.93099 -2.93852 (156*2π)/3292 weeks
15717.47802 1.91294 (157*2π)/3292 weeks
15816.99342 4.8613 (158*2π)/3292 weeks
15911.68061 9.74536 (159*2π)/3292 weeks
1603.43077 5.54236 (160*2π)/3292 weeks
1614.58138 -2.40587 (161*2π)/3292 weeks
1628.05921 -4.94667 (162*2π)/3292 weeks
16312.55888 -5.71722 (163*2π)/3292 weeks
16417.07683 -3.32902 (164*2π)/3292 weeks
16517.07683 3.32902 (165*2π)/3292 weeks
16612.55888 5.71722 (166*2π)/3292 weeks
1678.05921 4.94667 (167*2π)/3292 weeks
1684.58138 2.40587 (168*2π)/3292 weeks
1693.43077 -5.54236 (169*2π)/3292 weeks
17011.68061 -9.74536 (170*2π)/3292 weeks
17116.99342 -4.8613 (171*2π)/3292 weeks
17217.47802 -1.91294 (172*2π)/3292 weeks
17317.93099 2.93852 (173*2π)/3292 weeks
17413.41118 8.11335 (174*2π)/3292 weeks
1753.78454 6.65047 (175*2π)/3292 weeks
176.87918 -4.79794 (176*2π)/3292 weeks
17711.92872 -11.80497 (177*2π)/3292 weeks
17820.93032 -2.23845 (178*2π)/3292 weeks
17914.60465 5.82104 (179*2π)/3292 weeks
1808.77977 5.21717 (180*2π)/3292 weeks
1815.15179 3.03699 (181*2π)/3292 weeks
1823.43037 -1.87539 (182*2π)/3292 weeks
1836.58285 -4.31849 (183*2π)/3292 weeks
1847.89252 -2.32285 (184*2π)/3292 weeks
1853.43385 -2.97537 (185*2π)/3292 weeks
1863.15878 -10.03491 (186*2π)/3292 weeks
18710.4383 -13.26955 (187*2π)/3292 weeks
18815.58523 -7.5357 (188*2π)/3292 weeks
1899.93646 -3.33485 (189*2π)/3292 weeks
1908.3111 -9.32844 (190*2π)/3292 weeks
19111.82266 -9.4471 (191*2π)/3292 weeks
19210.01001 -10.58485 (192*2π)/3292 weeks
19315.6554 -15.53612 (193*2π)/3292 weeks
19422.02218 -9.70999 (194*2π)/3292 weeks
19520.11315 -4.29254 (195*2π)/3292 weeks
19618.67074 -4.91209 (196*2π)/3292 weeks
19721.4097 -.5215 (197*2π)/3292 weeks
19813.21379 4.42581 (198*2π)/3292 weeks
1997.68386 -5.01879 (199*2π)/3292 weeks
20017.68341 -8.95923 (200*2π)/3292 weeks
20119.91921 1.00678 (201*2π)/3292 weeks
20211.30109 3.46107 (202*2π)/3292 weeks
2039.35213 -1.73411 (203*2π)/3292 weeks
2048.90962 .17729 (204*2π)/3292 weeks
2052.38512 -5.61145 (205*2π)/3292 weeks
2068.81575 -16.44612 (206*2π)/3292 weeks
20721.31328 -12.00747 (207*2π)/3292 weeks
20819.63353 -.68257 (208*2π)/3292 weeks
20910.60231 .90721 (209*2π)/3292 weeks
2105.81199 -5.35289 (210*2π)/3292 weeks
2118.42358 -12.11346 (211*2π)/3292 weeks
21215.64501 -14.54461 (212*2π)/3292 weeks
21321.77175 -9.23978 (213*2π)/3292 weeks
21419.96302 -1.96852 (214*2π)/3292 weeks
21514.15893 -1.74415 (215*2π)/3292 weeks
21613.7937 -4.82604 (216*2π)/3292 weeks
21714.93423 -3.87855 (217*2π)/3292 weeks
21814.28896 -3.82072 (218*2π)/3292 weeks
21913.46945 -2.62789 (219*2π)/3292 weeks
22011.55807 -3.98264 (220*2π)/3291 weeks
22111.77261 -3.57958 (221*2π)/3291 weeks
2227.53034 -4.89895 (222*2π)/3291 weeks
2239.38793 -10.50342 (223*2π)/3291 weeks
22414.11493 -10.26033 (224*2π)/3291 weeks
22514.65626 -8.02205 (225*2π)/3291 weeks
22615.18688 -6.51661 (226*2π)/3291 weeks
22712.54556 -6.12588 (227*2π)/3291 weeks
22812.47953 -9.36078 (228*2π)/3291 weeks
22916.59483 -10.09781 (229*2π)/3291 weeks
23018.78528 -4.30146 (230*2π)/3291 weeks
23110.92836 -2.68117 (231*2π)/3291 weeks
23212.96974 -9.28176 (232*2π)/3291 weeks
23314.929 -4.69885 (233*2π)/3291 weeks
23410.76054 -6.47125 (234*2π)/3291 weeks
23513.5017 -10.50906 (235*2π)/3291 weeks
23618.90403 -5.83253 (236*2π)/3291 weeks
23712.45594 -1.15195 (237*2π)/3291 weeks
2388.9864 -4.99254 (238*2π)/3291 weeks
23911.64803 -8.16631 (239*2π)/3291 weeks
24011.71073 -3.66313 (240*2π)/3291 weeks
2415.69073 -4.31163 (241*2π)/3291 weeks
2422.08221 -9.633 (242*2π)/3291 weeks
243.80784 -19.5105 (243*2π)/3291 weeks
24412.88993 -30.50263 (244*2π)/3291 weeks
24530.60118 -25.38125 (245*2π)/3291 weeks
24637.90814 -9.10522 (246*2π)/3291 weeks
24733.57673 8.34964 (247*2π)/3291 weeks
24813.11752 19.84176 (248*2π)/3291 weeks
249-7.0919 4.92915 (249*2π)/3291 weeks
250-2.11361 -13.74872 (250*2π)/3291 weeks
25110.22233 -18.10792 (251*2π)/3291 weeks
25219.65244 -10.94839 (252*2π)/3291 weeks
25314.97822 -.67509 (253*2π)/3291 weeks
2545.3643 .22534 (254*2π)/3291 weeks
255.12829 -7.84045 (255*2π)/3291 weeks
2562.83119 -12.5812 (256*2π)/3291 weeks
2574.81418 -14.26924 (257*2π)/3291 weeks
2586.11674 -16.04225 (258*2π)/3291 weeks
2598.05641 -16.94586 (259*2π)/3291 weeks
26010.47758 -18.42644 (260*2π)/3291 weeks
26114.50409 -15.42811 (261*2π)/3291 weeks
26211.327 -10.38945 (262*2π)/3291 weeks
2636.85366 -12.56344 (263*2π)/3291 weeks
2645.80381 -18.76517 (264*2π)/3291 weeks
26516.70145 -20.89576 (265*2π)/3291 weeks
26617.47699 -6.04829 (266*2π)/3291 weeks
2672.45896 -8.56762 (267*2π)/3291 weeks
2687.73237 -17.78209 (268*2π)/3291 weeks
2696.53829 -10.55279 (269*2π)/3291 weeks
270-3.25573 -19.07861 (270*2π)/3291 weeks
2714.82694 -28.91475 (271*2π)/3291 weeks
27211.43365 -26.94598 (272*2π)/3291 weeks
27315.30151 -25.24385 (273*2π)/3291 weeks
27414.84001 -19.62751 (274*2π)/3291 weeks
27510.98828 -22.65726 (275*2π)/3291 weeks
27617.55489 -27.06835 (276*2π)/3291 weeks
27724.68124 -19.86693 (277*2π)/3291 weeks
27826.3394 -10.7156 (278*2π)/3291 weeks
27920.65681 3.38273 (279*2π)/3291 weeks
280-1.62781 11.56304 (280*2π)/3291 weeks
281-23.89738 -6.42138 (281*2π)/3291 weeks
282-21.19182 -30.2265 (282*2π)/3291 weeks
283-11.65479 -36.86083 (283*2π)/3291 weeks
284-10.45614 -45.0458 (284*2π)/3291 weeks
2851.06204 -55.31351 (285*2π)/3291 weeks
28620.30158 -56.8146 (286*2π)/3291 weeks
28733.57011 -39.99767 (287*2π)/3291 weeks
28825.80013 -19.5294 (288*2π)/3291 weeks
2894.80181 -22.74465 (289*2π)/3291 weeks
2905.37555 -34.64632 (290*2π)/3291 weeks
2912.08409 -37.6637 (291*2π)/3291 weeks
2922.53254 -51.98763 (292*2π)/3291 weeks
29320.98087 -61.23259 (293*2π)/3291 weeks
29433.90418 -49.4017 (294*2π)/3291 weeks
29538.57886 -47.23909 (295*2π)/3291 weeks
29650.29532 -25.43512 (296*2π)/3291 weeks
29724.55071 -1.84822 (297*2π)/3291 weeks
298-3.517 -16.99446 (298*2π)/3291 weeks
299-9.48882 -38.35513 (299*2π)/3291 weeks
3001.77264 -64.97793 (300*2π)/3291 weeks
30133.08435 -62.91365 (301*2π)/3291 weeks
30233.82887 -41.13651 (302*2π)/3291 weeks
30330.29204 -39.63443 (303*2π)/3291 weeks
30425.55181 -24.99363 (304*2π)/3291 weeks
305-5.55887 -21.92029 (305*2π)/3291 weeks
306-28.29758 -66.31172 (306*2π)/3291 weeks
30715.46612 -111.6625 (307*2π)/3291 weeks
30870.47961 -78.82993 (308*2π)/3291 weeks
30950.47483 -35.42859 (309*2π)/3291 weeks
31020.98539 -50.91798 (310*2π)/3291 weeks
31142.70087 -72.31554 (311*2π)/3291 weeks
31261.13778 -43.54111 (312*2π)/3291 weeks
31335.66386 -28.98758 (313*2π)/3291 weeks
31422.91593 -34.68408 (314*2π)/3291 weeks
31521.48499 -23.65596 (315*2π)/3291 weeks
316-39.59188 -26.61182 (316*2π)/3291 weeks
317-47.60723 -103.6624 (317*2π)/3291 weeks
318.46973 -138.2887 (318*2π)/3291 weeks
31934.86537 -113.3779 (319*2π)/3291 weeks
320.20188 -104.0624 (320*2π)/3291 weeks
321-13.61546 -180.8076 (321*2π)/3291 weeks
32297.85215 -195.0604 (322*2π)/3291 weeks
32373.87583 -75.09351 (323*2π)/3291 weeks
324-102.8964 -134.897 (324*2π)/3291 weeks
325-65.61681 -363.6219 (325*2π)/3291 weeks
32623.40764 -421.4343 (326*2π)/3291 weeks
32796.76732 -740.2272 (327*2π)/3291 weeks

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