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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 29 weeks (137.3378*sine), 32 weeks (131.1549*sine), and 16 weeks (72.3851*cosine).

NUGT (Direxion Daily Gold Miners Inde) has an average price of 861.78 (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 1/9/2017 for NUGT (Direxion Daily Gold Miners Inde), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0861.7802   0 
1848.0098 1,033.294 (1*2π)/319319 weeks
279.77897 733.9253 (2*2π)/319160 weeks
327.84215 426.1084 (3*2π)/319106 weeks
4-87.22122 352.5328 (4*2π)/31980 weeks
5-82.5464 106.1376 (5*2π)/31964 weeks
698.28722 95.05972 (6*2π)/31953 weeks
774.06888 217.5907 (7*2π)/31946 weeks
8-24.14292 160.3546 (8*2π)/31940 weeks
912.94698 103.2979 (9*2π)/31935 weeks
1032.53899 131.1549 (10*2π)/31932 weeks
11-18.60186 137.3378 (11*2π)/31929 weeks
12-58.04676 79.55706 (12*2π)/31927 weeks
13-9.7543 12.9231 (13*2π)/31925 weeks
1425.85835 36.32087 (14*2π)/31923 weeks
1529.2995 32.17692 (15*2π)/31921 weeks
1650.75685 30.30583 (16*2π)/31920 weeks
1759.10841 65.42255 (17*2π)/31919 weeks
1825.35604 67.23305 (18*2π)/31918 weeks
1935.30084 36.51931 (19*2π)/31917 weeks
2072.38506 59.05745 (20*2π)/31916 weeks
2141.23952 113.793 (21*2π)/31915 weeks
22-22.59986 88.00439 (22*2π)/31915 weeks
23-16.20455 30.388 (23*2π)/31914 weeks
2421.30751 22.15406 (24*2π)/31913 weeks
2532.4797 38.52672 (25*2π)/31913 weeks
2632.76064 41.02654 (26*2π)/31912 weeks
2737.05765 60.74332 (27*2π)/31912 weeks
285.54676 69.0446 (28*2π)/31911 weeks
29-10.08745 41.79195 (29*2π)/31911 weeks
30-4.34869 18.9824 (30*2π)/31911 weeks
3124.24721 1.78216 (31*2π)/31910 weeks
3251.8984 26.27888 (32*2π)/31910 weeks
3339.20605 48.81004 (33*2π)/31910 weeks
3434.93823 51.76497 (34*2π)/3199 weeks
3519.42496 63.27782 (35*2π)/3199 weeks
361.67211 51.26844 (36*2π)/3199 weeks
373.15374 37.32648 (37*2π)/3199 weeks
384.50105 34.86357 (38*2π)/3198 weeks
398.29654 19.99039 (39*2π)/3198 weeks
4031.16432 24.596 (40*2π)/3198 weeks
4132.62804 47.34221 (41*2π)/3198 weeks
4213.86834 60.20808 (42*2π)/3198 weeks
43-3.64192 54.27846 (43*2π)/3197 weeks
44-11.62343 41.41174 (44*2π)/3197 weeks
45-14.77646 36.59934 (45*2π)/3197 weeks
46-26.15418 21.71599 (46*2π)/3197 weeks
47-16.65858 -5.29849 (47*2π)/3197 weeks
4811.96958 -10.00897 (48*2π)/3197 weeks
4925.90503 4.80637 (49*2π)/3197 weeks
5026.2123 17.09798 (50*2π)/3196 weeks
5122.42777 26.19044 (51*2π)/3196 weeks
5212.58767 25.97822 (52*2π)/3196 weeks
5313.41148 20.10856 (53*2π)/3196 weeks
5416.99384 24.27517 (54*2π)/3196 weeks
5512.70584 27.33882 (55*2π)/3196 weeks
567.58728 29.74833 (56*2π)/3196 weeks
57-2.76796 22.94762 (57*2π)/3196 weeks
584.33981 10.50795 (58*2π)/3196 weeks
599.17804 17.48508 (59*2π)/3195 weeks
601.74495 10.62117 (60*2π)/3195 weeks
6116.58361 5.25323 (61*2π)/3195 weeks
6217.8622 21.08017 (62*2π)/3195 weeks
636.08717 19.63035 (63*2π)/3195 weeks
647.0871 12.95301 (64*2π)/3195 weeks
6511.92576 10.75924 (65*2π)/3195 weeks
6614.79617 16.31705 (66*2π)/3195 weeks
6710.30258 18.93354 (67*2π)/3195 weeks
688.0992 17.43418 (68*2π)/3195 weeks
695.98976 16.28135 (69*2π)/3195 weeks
704.7388 14.51896 (70*2π)/3195 weeks
712.41855 12.31191 (71*2π)/3194 weeks
72.2758 5.49715 (72*2π)/3194 weeks
738.44364 -1.0148 (73*2π)/3194 weeks
7418.05699 2.84258 (74*2π)/3194 weeks
7517.63671 15.48593 (75*2π)/3194 weeks
765.58939 18.64251 (76*2π)/3194 weeks
77-6.45202 8.36733 (77*2π)/3194 weeks
78-.63581 -14.84455 (78*2π)/3194 weeks
7926.11732 -17.2881 (79*2π)/3194 weeks
8038.40141 .52715 (80*2π)/3194 weeks
8136.8315 18.91754 (81*2π)/3194 weeks
8221.7059 31.27548 (82*2π)/3194 weeks
833.69765 25.74058 (83*2π)/3194 weeks
841.00805 12.65144 (84*2π)/3194 weeks
854.22219 6.07189 (85*2π)/3194 weeks
8610.19669 3.16015 (86*2π)/3194 weeks
8713.1647 7.58509 (87*2π)/3194 weeks
889.18875 6.36053 (88*2π)/3194 weeks
8911.53071 1.88919 (89*2π)/3194 weeks
9019.16286 4.26309 (90*2π)/3194 weeks
9114.95767 10.96685 (91*2π)/3194 weeks
9211.05292 7.25738 (92*2π)/3193 weeks
9314.96227 4.5701 (93*2π)/3193 weeks
9413.78749 9.56558 (94*2π)/3193 weeks
9511.1279 2.92963 (95*2π)/3193 weeks
9619.40622 4.51461 (96*2π)/3193 weeks
9716.90768 10.5062 (97*2π)/3193 weeks
9812.6882 9.44042 (98*2π)/3193 weeks
9913.21471 6.14352 (99*2π)/3193 weeks
10015.79442 7.14849 (100*2π)/3193 weeks
10115.2379 8.41096 (101*2π)/3193 weeks
10213.91279 11.08452 (102*2π)/3193 weeks
1038.68304 9.87244 (103*2π)/3193 weeks
1048.90944 3.58045 (104*2π)/3193 weeks
10512.34516 4.11872 (105*2π)/3193 weeks
10611.97011 3.29204 (106*2π)/3193 weeks
10714.46275 3.20086 (107*2π)/3193 weeks
10814.61377 3.95598 (108*2π)/3193 weeks
10915.41712 4.87828 (109*2π)/3193 weeks
11013.6589 3.86826 (110*2π)/3193 weeks
11117.11496 .86407 (111*2π)/3193 weeks
11222.66941 5.58825 (112*2π)/3193 weeks
11319.86959 13.44684 (113*2π)/3193 weeks
11411.48387 14.43602 (114*2π)/3193 weeks
1156.46508 8.68739 (115*2π)/3193 weeks
1168.48819 .74287 (116*2π)/3193 weeks
11717.30675 -1.29193 (117*2π)/3193 weeks
11823.21956 8.2671 (118*2π)/3193 weeks
11913.02054 17.48176 (119*2π)/3193 weeks
1202.28369 8.76175 (120*2π)/3193 weeks
1217.46949 -.17786 (121*2π)/3193 weeks
12210.14042 2.10815 (122*2π)/3193 weeks
12310.64607 -2.8398 (123*2π)/3193 weeks
12419.78618 -2.00383 (124*2π)/3193 weeks
12519.07312 8.6641 (125*2π)/3193 weeks
1268.14007 5.77044 (126*2π)/3193 weeks
12713.39053 -4.51785 (127*2π)/3193 weeks
12822.0921 .65032 (128*2π)/3192 weeks
12919.1445 5.01471 (129*2π)/3192 weeks
13021.04246 4.61052 (130*2π)/3192 weeks
13122.52148 10.81984 (131*2π)/3192 weeks
13214.68006 15.87097 (132*2π)/3192 weeks
13310.50647 10.00221 (133*2π)/3192 weeks
13411.83953 10.19334 (134*2π)/3192 weeks
1357.72266 8.32934 (135*2π)/3192 weeks
13612.35907 3.31765 (136*2π)/3192 weeks
13715.48411 10.30177 (137*2π)/3192 weeks
1387.92852 13.69584 (138*2π)/3192 weeks
1392.25577 7.61133 (139*2π)/3192 weeks
1405.48454 1.82717 (140*2π)/3192 weeks
1418.28258 3.86323 (141*2π)/3192 weeks
1425.38247 4.15551 (142*2π)/3192 weeks
1433.81468 -.89788 (143*2π)/3192 weeks
1447.29445 -4.4524 (144*2π)/3192 weeks
14511.94032 -6.23497 (145*2π)/3192 weeks
14619.89577 -2.989 (146*2π)/3192 weeks
14717.68982 9.96053 (147*2π)/3192 weeks
1483.61668 9.14673 (148*2π)/3192 weeks
1491.37979 -3.68714 (149*2π)/3192 weeks
15011.10832 -9.12104 (150*2π)/3192 weeks
15117.84292 -4.55788 (151*2π)/3192 weeks
15218.50645 1.09592 (152*2π)/3192 weeks
15317.54905 3.98506 (153*2π)/3192 weeks
15413.57471 9.59972 (154*2π)/3192 weeks
1554.28573 6.94823 (155*2π)/3192 weeks
1564.18784 -1.931 (156*2π)/3192 weeks
1578.0263 -4.88755 (157*2π)/3192 weeks
15812.73783 -5.93146 (158*2π)/3192 weeks
15917.5426 -3.51375 (159*2π)/3192 weeks
16017.5426 3.51375 (160*2π)/3192 weeks
16112.73783 5.93146 (161*2π)/3192 weeks
1628.0263 4.88755 (162*2π)/3192 weeks
1634.18784 1.931 (163*2π)/3192 weeks
1644.28573 -6.94823 (164*2π)/3192 weeks
16513.57471 -9.59972 (165*2π)/3192 weeks
16617.54905 -3.98506 (166*2π)/3192 weeks
16718.50645 -1.09592 (167*2π)/3192 weeks
16817.84292 4.55788 (168*2π)/3192 weeks
16911.10832 9.12104 (169*2π)/3192 weeks
1701.37979 3.68714 (170*2π)/3192 weeks
1713.61668 -9.14673 (171*2π)/3192 weeks
17217.68982 -9.96053 (172*2π)/3192 weeks
17319.89577 2.989 (173*2π)/3192 weeks
17411.94032 6.23497 (174*2π)/3192 weeks
1757.29445 4.4524 (175*2π)/3192 weeks
1763.81468 .89788 (176*2π)/3192 weeks
1775.38247 -4.15551 (177*2π)/3192 weeks
1788.28258 -3.86323 (178*2π)/3192 weeks
1795.48454 -1.82717 (179*2π)/3192 weeks
1802.25577 -7.61133 (180*2π)/3192 weeks
1817.92852 -13.69584 (181*2π)/3192 weeks
18215.48411 -10.30177 (182*2π)/3192 weeks
18312.35907 -3.31765 (183*2π)/3192 weeks
1847.72266 -8.32934 (184*2π)/3192 weeks
18511.83953 -10.19334 (185*2π)/3192 weeks
18610.50647 -10.00221 (186*2π)/3192 weeks
18714.68006 -15.87097 (187*2π)/3192 weeks
18822.52148 -10.81984 (188*2π)/3192 weeks
18921.04246 -4.61052 (189*2π)/3192 weeks
19019.1445 -5.01471 (190*2π)/3192 weeks
19122.0921 -.65032 (191*2π)/3192 weeks
19213.39053 4.51785 (192*2π)/3192 weeks
1938.14007 -5.77044 (193*2π)/3192 weeks
19419.07312 -8.6641 (194*2π)/3192 weeks
19519.78618 2.00383 (195*2π)/3192 weeks
19610.64607 2.8398 (196*2π)/3192 weeks
19710.14042 -2.10815 (197*2π)/3192 weeks
1987.46949 .17786 (198*2π)/3192 weeks
1992.28369 -8.76175 (199*2π)/3192 weeks
20013.02054 -17.48176 (200*2π)/3192 weeks
20123.21956 -8.2671 (201*2π)/3192 weeks
20217.30675 1.29193 (202*2π)/3192 weeks
2038.48819 -.74287 (203*2π)/3192 weeks
2046.46508 -8.68739 (204*2π)/3192 weeks
20511.48387 -14.43602 (205*2π)/3192 weeks
20619.86959 -13.44684 (206*2π)/3192 weeks
20722.66941 -5.58825 (207*2π)/3192 weeks
20817.11496 -.86407 (208*2π)/3192 weeks
20913.6589 -3.86826 (209*2π)/3192 weeks
21015.41712 -4.87828 (210*2π)/3192 weeks
21114.61377 -3.95598 (211*2π)/3192 weeks
21214.46275 -3.20086 (212*2π)/3192 weeks
21311.97011 -3.29204 (213*2π)/3191 weeks
21412.34516 -4.11872 (214*2π)/3191 weeks
2158.90944 -3.58045 (215*2π)/3191 weeks
2168.68304 -9.87244 (216*2π)/3191 weeks
21713.91279 -11.08452 (217*2π)/3191 weeks
21815.2379 -8.41096 (218*2π)/3191 weeks
21915.79442 -7.14849 (219*2π)/3191 weeks
22013.21471 -6.14352 (220*2π)/3191 weeks
22112.6882 -9.44042 (221*2π)/3191 weeks
22216.90768 -10.5062 (222*2π)/3191 weeks
22319.40622 -4.51461 (223*2π)/3191 weeks
22411.1279 -2.92963 (224*2π)/3191 weeks
22513.78749 -9.56558 (225*2π)/3191 weeks
22614.96227 -4.5701 (226*2π)/3191 weeks
22711.05292 -7.25738 (227*2π)/3191 weeks
22814.95767 -10.96685 (228*2π)/3191 weeks
22919.16286 -4.26309 (229*2π)/3191 weeks
23011.53071 -1.88919 (230*2π)/3191 weeks
2319.18875 -6.36053 (231*2π)/3191 weeks
23213.1647 -7.58509 (232*2π)/3191 weeks
23310.19669 -3.16015 (233*2π)/3191 weeks
2344.22219 -6.07189 (234*2π)/3191 weeks
2351.00805 -12.65144 (235*2π)/3191 weeks
2363.69765 -25.74058 (236*2π)/3191 weeks
23721.7059 -31.27548 (237*2π)/3191 weeks
23836.8315 -18.91754 (238*2π)/3191 weeks
23938.40141 -.52715 (239*2π)/3191 weeks
24026.11732 17.2881 (240*2π)/3191 weeks
241-.63581 14.84455 (241*2π)/3191 weeks
242-6.45202 -8.36733 (242*2π)/3191 weeks
2435.58939 -18.64251 (243*2π)/3191 weeks
24417.63671 -15.48593 (244*2π)/3191 weeks
24518.05699 -2.84258 (245*2π)/3191 weeks
2468.44364 1.0148 (246*2π)/3191 weeks
247.2758 -5.49715 (247*2π)/3191 weeks
2482.41855 -12.31191 (248*2π)/3191 weeks
2494.7388 -14.51896 (249*2π)/3191 weeks
2505.98976 -16.28135 (250*2π)/3191 weeks
2518.0992 -17.43418 (251*2π)/3191 weeks
25210.30258 -18.93354 (252*2π)/3191 weeks
25314.79617 -16.31705 (253*2π)/3191 weeks
25411.92576 -10.75924 (254*2π)/3191 weeks
2557.0871 -12.95301 (255*2π)/3191 weeks
2566.08717 -19.63035 (256*2π)/3191 weeks
25717.8622 -21.08017 (257*2π)/3191 weeks
25816.58361 -5.25323 (258*2π)/3191 weeks
2591.74495 -10.62117 (259*2π)/3191 weeks
2609.17804 -17.48508 (260*2π)/3191 weeks
2614.33981 -10.50795 (261*2π)/3191 weeks
262-2.76796 -22.94762 (262*2π)/3191 weeks
2637.58728 -29.74833 (263*2π)/3191 weeks
26412.70584 -27.33882 (264*2π)/3191 weeks
26516.99384 -24.27517 (265*2π)/3191 weeks
26613.41148 -20.10856 (266*2π)/3191 weeks
26712.58767 -25.97822 (267*2π)/3191 weeks
26822.42777 -26.19044 (268*2π)/3191 weeks
26926.2123 -17.09798 (269*2π)/3191 weeks
27025.90503 -4.80637 (270*2π)/3191 weeks
27111.96958 10.00897 (271*2π)/3191 weeks
272-16.65858 5.29849 (272*2π)/3191 weeks
273-26.15418 -21.71599 (273*2π)/3191 weeks
274-14.77646 -36.59934 (274*2π)/3191 weeks
275-11.62343 -41.41174 (275*2π)/3191 weeks
276-3.64192 -54.27846 (276*2π)/3191 weeks
27713.86834 -60.20808 (277*2π)/3191 weeks
27832.62804 -47.34221 (278*2π)/3191 weeks
27931.16432 -24.596 (279*2π)/3191 weeks
2808.29654 -19.99039 (280*2π)/3191 weeks
2814.50105 -34.86357 (281*2π)/3191 weeks
2823.15374 -37.32648 (282*2π)/3191 weeks
2831.67211 -51.26844 (283*2π)/3191 weeks
28419.42496 -63.27782 (284*2π)/3191 weeks
28534.93823 -51.76497 (285*2π)/3191 weeks
28639.20605 -48.81004 (286*2π)/3191 weeks
28751.8984 -26.27888 (287*2π)/3191 weeks
28824.24721 -1.78216 (288*2π)/3191 weeks
289-4.34869 -18.9824 (289*2π)/3191 weeks
290-10.08745 -41.79195 (290*2π)/3191 weeks
2915.54676 -69.0446 (291*2π)/3191 weeks
29237.05765 -60.74332 (292*2π)/3191 weeks
29332.76064 -41.02654 (293*2π)/3191 weeks
29432.4797 -38.52672 (294*2π)/3191 weeks
29521.30751 -22.15406 (295*2π)/3191 weeks
296-16.20455 -30.388 (296*2π)/3191 weeks
297-22.59986 -88.00439 (297*2π)/3191 weeks
29841.23952 -113.793 (298*2π)/3191 weeks
29972.38506 -59.05745 (299*2π)/3191 weeks
30035.30084 -36.51931 (300*2π)/3191 weeks
30125.35604 -67.23305 (301*2π)/3191 weeks
30259.10841 -65.42255 (302*2π)/3191 weeks
30350.75685 -30.30583 (303*2π)/3191 weeks
30429.2995 -32.17692 (304*2π)/3191 weeks
30525.85835 -36.32087 (305*2π)/3191 weeks
306-9.7543 -12.9231 (306*2π)/3191 weeks
307-58.04676 -79.55706 (307*2π)/3191 weeks
308-18.60186 -137.3378 (308*2π)/3191 weeks
30932.53899 -131.1549 (309*2π)/3191 weeks
31012.94698 -103.2979 (310*2π)/3191 weeks
311-24.14292 -160.3546 (311*2π)/3191 weeks
31274.06888 -217.5907 (312*2π)/3191 weeks
31398.28722 -95.05972 (313*2π)/3191 weeks
314-82.5464 -106.1376 (314*2π)/3191 weeks
315-87.22122 -352.5328 (315*2π)/3191 weeks
31627.84215 -426.1084 (316*2π)/3191 weeks
31779.77897 -733.9253 (317*2π)/3191 weeks

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