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Fourier Analysis of NUGT (DIREXION DAILY GOLD MINERS INDEX BULL 3X SHARES DIREXION DAILY GOLD MINERS INDEX BULL 3X SHARES)


NUGT (DIREXION DAILY GOLD MINERS INDEX BULL 3X SHARES DIREXION DAILY GOLD MINERS INDEX BULL 3X SHARES) appears to have interesting cyclic behaviour every 30 weeks (501.7137*sine), 28 weeks (414.7826*sine), and 33 weeks (408.5679*sine).

NUGT (DIREXION DAILY GOLD MINERS INDEX BULL 3X SHARES DIREXION DAILY GOLD MINERS INDEX BULL 3X SHARES) has an average price of 3,034.03 (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 11/6/2017 for NUGT (DIREXION DAILY GOLD MINERS INDEX BULL 3X SHARES DIREXION DAILY GOLD MINERS INDEX BULL 3X SHARES), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
03,034.033   0 
13,472.171 3,516.123 (1*2π)/362362 weeks
2611.9384 2,985.872 (2*2π)/362181 weeks
335.49923 1,694.87 (3*2π)/362121 weeks
4-18.09246 1,446.31 (4*2π)/36291 weeks
5-440.8662 896.9598 (5*2π)/36272 weeks
6-79.75126 238.053 (6*2π)/36260 weeks
7397.8046 407.0724 (7*2π)/36252 weeks
8234.9485 773.2679 (8*2π)/36245 weeks
9-80.93533 589.6054 (9*2π)/36240 weeks
1015.11218 368.3061 (10*2π)/36236 weeks
11127.4723 408.5679 (11*2π)/36233 weeks
1220.85749 501.7137 (12*2π)/36230 weeks
13-147.4506 414.7826 (13*2π)/36228 weeks
14-193.2484 173.0136 (14*2π)/36226 weeks
1519.85895 50.40376 (15*2π)/36224 weeks
1687.59115 131.8977 (16*2π)/36223 weeks
17101.5829 112.6053 (17*2π)/36221 weeks
18162.2176 101.1923 (18*2π)/36220 weeks
19223.2942 196.2968 (19*2π)/36219 weeks
20131.232 262.4693 (20*2π)/36218 weeks
2177.76682 174.5535 (21*2π)/36217 weeks
22181.2897 127.8881 (22*2π)/36216 weeks
23259.0247 264.034 (23*2π)/36216 weeks
24104.9111 407.4399 (24*2π)/36215 weeks
25-82.95831 302.6904 (25*2π)/36214 weeks
26-67.21535 118.9524 (26*2π)/36214 weeks
2753.78402 69.78893 (27*2π)/36213 weeks
28112.0369 116.2708 (28*2π)/36213 weeks
29103.8657 145.1839 (29*2π)/36212 weeks
30132.0917 161.8588 (30*2π)/36212 weeks
31103.5072 240.727 (31*2π)/36212 weeks
32-1.41046 229.2277 (32*2π)/36211 weeks
33-34.05827 139.725 (33*2π)/36211 weeks
34-16.54028 70.73112 (34*2π)/36211 weeks
3563.55965 7.95426 (35*2π)/36210 weeks
36170.8391 57.08555 (36*2π)/36210 weeks
37163.4796 154.8847 (37*2π)/36210 weeks
38120.365 169.3662 (38*2π)/36210 weeks
39113.0354 202.2971 (39*2π)/3629 weeks
4047.44994 219.6253 (40*2π)/3629 weeks
413.6464 172.2742 (41*2π)/3629 weeks
4211.11996 131.2282 (42*2π)/3629 weeks
4317.7608 124.8681 (43*2π)/3628 weeks
4416.70817 82.91479 (44*2π)/3628 weeks
4585.54949 65.70623 (45*2π)/3628 weeks
46123.2691 129.2817 (46*2π)/3628 weeks
4793.6328 193.5062 (47*2π)/3628 weeks
4825.79645 209.1427 (48*2π)/3628 weeks
49-21.65687 184.4527 (49*2π)/3627 weeks
50-41.07112 143.0432 (50*2π)/3627 weeks
51-50.32177 129.3005 (51*2π)/3627 weeks
52-87.51422 91.79396 (52*2π)/3627 weeks
53-79.37971 7.44009 (53*2π)/3627 weeks
542.17926 -42.2216 (54*2π)/3627 weeks
5574.15584 -12.64795 (55*2π)/3627 weeks
5694.81033 34.37286 (56*2π)/3626 weeks
5790.08543 66.50639 (57*2π)/3626 weeks
5874.52222 94.63483 (58*2π)/3626 weeks
5944.30933 91.23936 (59*2π)/3626 weeks
6044.79208 71.56267 (60*2π)/3626 weeks
6160.06629 78.9151 (61*2π)/3626 weeks
6249.32642 94.77126 (62*2π)/3626 weeks
6337.73566 99.8995 (63*2π)/3626 weeks
6410.24803 103.0312 (64*2π)/3626 weeks
65-11.79656 64.83907 (65*2π)/3626 weeks
6623.19834 37.89746 (66*2π)/3625 weeks
6731.55652 62.55812 (67*2π)/3625 weeks
685.29109 41.95056 (68*2π)/3625 weeks
6945.37824 14.20548 (69*2π)/3625 weeks
7073.1137 59.92976 (70*2π)/3625 weeks
7136.17874 81.10578 (71*2π)/3625 weeks
7220.76057 55.03615 (72*2π)/3625 weeks
7329.5842 40.77793 (73*2π)/3625 weeks
7447.26228 39.21634 (74*2π)/3625 weeks
7551.23965 58.9784 (75*2π)/3625 weeks
7636.56 66.67796 (76*2π)/3625 weeks
7729.00579 61.4323 (77*2π)/3625 weeks
7822.73274 58.59071 (78*2π)/3625 weeks
7918.05221 52.59983 (79*2π)/3625 weeks
8012.95 48.35246 (80*2π)/3625 weeks
814.68707 38.30944 (81*2π)/3624 weeks
825.55153 10.23291 (82*2π)/3624 weeks
8335.06961 -3.7314 (83*2π)/3624 weeks
8464.02492 10.5452 (84*2π)/3624 weeks
8565.30013 50.69205 (85*2π)/3624 weeks
8630.13647 66.14433 (86*2π)/3624 weeks
87-10.29654 46.98481 (87*2π)/3624 weeks
88-26.33102 -15.92822 (88*2π)/3624 weeks
8936.30051 -70.52248 (89*2π)/3624 weeks
90112.4432 -42.7552 (90*2π)/3624 weeks
91136.8312 14.5423 (91*2π)/3624 weeks
92127.0324 70.94396 (92*2π)/3624 weeks
9379.42711 108.9423 (93*2π)/3624 weeks
9420.58957 97.96241 (94*2π)/3624 weeks
951.57544 55.02134 (95*2π)/3624 weeks
9610.1696 29.73878 (96*2π)/3624 weeks
9723.80081 13.78142 (97*2π)/3624 weeks
9843.48088 14.24338 (98*2π)/3624 weeks
9942.39254 29.45326 (99*2π)/3624 weeks
10032.0432 20.00232 (100*2π)/3624 weeks
10140.5509 6.52685 (101*2π)/3624 weeks
10265.5262 11.27608 (102*2π)/3624 weeks
10359.0619 37.3353 (103*2π)/3624 weeks
10440.49109 31.94615 (104*2π)/3623 weeks
10543.00227 16.89705 (105*2π)/3623 weeks
10657.50741 23.40419 (106*2π)/3623 weeks
10740.6337 31.14902 (107*2π)/3623 weeks
10844.09788 6.18445 (108*2π)/3623 weeks
10968.86802 17.3432 (109*2π)/3623 weeks
11060.68279 36.43414 (110*2π)/3623 weeks
11146.28873 35.09733 (111*2π)/3623 weeks
11243.54427 23.96734 (112*2π)/3623 weeks
11352.35417 21.04749 (113*2π)/3623 weeks
11453.777 28.59117 (114*2π)/3623 weeks
11554.07838 32.15167 (115*2π)/3623 weeks
11645.41475 40.5099 (116*2π)/3623 weeks
11729.15855 33.00467 (117*2π)/3623 weeks
11830.79831 12.90238 (118*2π)/3623 weeks
11943.00768 13.83805 (119*2π)/3623 weeks
12041.60803 13.90337 (120*2π)/3623 weeks
12148.55955 9.26808 (121*2π)/3623 weeks
12251.97975 13.42404 (122*2π)/3623 weeks
12352.97903 13.39737 (123*2π)/3623 weeks
12452.28541 18.36894 (124*2π)/3623 weeks
12547.95505 11.66276 (125*2π)/3623 weeks
12660.74956 2.91685 (126*2π)/3623 weeks
12778.99306 16.95162 (127*2π)/3623 weeks
12874.57426 42.28151 (128*2π)/3623 weeks
12949.75057 52.85675 (129*2π)/3623 weeks
13028.07159 40.87309 (130*2π)/3623 weeks
13121.18749 17.7099 (131*2π)/3623 weeks
13237.39585 -2.80533 (132*2π)/3623 weeks
13367.53017 -.72337 (133*2π)/3623 weeks
13481.1332 33.11751 (134*2π)/3623 weeks
13547.74581 61.27696 (135*2π)/3623 weeks
1369.76319 38.31915 (136*2π)/3623 weeks
13718.03098 3.69495 (137*2π)/3623 weeks
13838.37605 4.82292 (138*2π)/3623 weeks
13932.10546 1.33431 (139*2π)/3623 weeks
14048.20467 -15.15142 (140*2π)/3623 weeks
14174.7805 1.21961 (141*2π)/3623 weeks
14261.98154 33.5269 (142*2π)/3623 weeks
14328.39938 19.67224 (143*2π)/3623 weeks
14442.5949 -14.44262 (144*2π)/3623 weeks
14574.75887 -4.96175 (145*2π)/3622 weeks
14671.47589 17.47878 (146*2π)/3622 weeks
14767.79322 14.73729 (147*2π)/3622 weeks
14879.00762 23.13562 (148*2π)/3622 weeks
14975.12219 46.52695 (149*2π)/3622 weeks
15045.47274 53.37993 (150*2π)/3622 weeks
15137.45173 34.18172 (151*2π)/3622 weeks
15242.08175 35.50208 (152*2π)/3622 weeks
15329.22062 33.02119 (153*2π)/3622 weeks
15434.86481 12.39426 (154*2π)/3622 weeks
15555.89482 23.22477 (155*2π)/3622 weeks
15644.08275 45.98751 (156*2π)/3622 weeks
15717.70829 43.44473 (157*2π)/3622 weeks
1588.01817 20.11865 (158*2π)/3622 weeks
15921.38626 6.0265 (159*2π)/3622 weeks
16029.15022 13.53652 (160*2π)/3622 weeks
16120.56212 15.11966 (161*2π)/3622 weeks
16212.10816 1.70968 (162*2π)/3622 weeks
16320.56555 -12.70486 (163*2π)/3622 weeks
16432.5721 -19.29964 (164*2π)/3622 weeks
16551.77673 -21.29638 (165*2π)/3622 weeks
16675.21374 1.68021 (166*2π)/3622 weeks
16754.50299 39.68557 (167*2π)/3622 weeks
16810.9503 30.51327 (168*2π)/3622 weeks
1693.32379 -9.8548 (169*2π)/3622 weeks
17031.85215 -32.04253 (170*2π)/3622 weeks
17158.25689 -22.3283 (171*2π)/3622 weeks
17266.26051 -4.05829 (172*2π)/3622 weeks
17361.76078 9.0283 (173*2π)/3622 weeks
17460.78462 20.5465 (174*2π)/3622 weeks
17540.71033 35.48055 (175*2π)/3622 weeks
17613.18394 21.35322 (176*2π)/3622 weeks
17714.40948 -6.36227 (177*2π)/3622 weeks
17826.68088 -15.70716 (178*2π)/3622 weeks
17940.37303 -21.06542 (179*2π)/3622 weeks
18054.99033 -17.34181 (180*2π)/3622 weeks
18166.18572   (181*2π)/3622 weeks
18254.99033 17.34181 (182*2π)/3622 weeks
18340.37303 21.06542 (183*2π)/3622 weeks
18426.68088 15.70716 (184*2π)/3622 weeks
18514.40948 6.36227 (185*2π)/3622 weeks
18613.18394 -21.35322 (186*2π)/3622 weeks
18740.71033 -35.48055 (187*2π)/3622 weeks
18860.78462 -20.5465 (188*2π)/3622 weeks
18961.76078 -9.0283 (189*2π)/3622 weeks
19066.26051 4.05829 (190*2π)/3622 weeks
19158.25689 22.3283 (191*2π)/3622 weeks
19231.85215 32.04253 (192*2π)/3622 weeks
1933.32379 9.8548 (193*2π)/3622 weeks
19410.9503 -30.51327 (194*2π)/3622 weeks
19554.50299 -39.68557 (195*2π)/3622 weeks
19675.21374 -1.68021 (196*2π)/3622 weeks
19751.77673 21.29638 (197*2π)/3622 weeks
19832.5721 19.29964 (198*2π)/3622 weeks
19920.56555 12.70486 (199*2π)/3622 weeks
20012.10816 -1.70968 (200*2π)/3622 weeks
20120.56212 -15.11966 (201*2π)/3622 weeks
20229.15022 -13.53652 (202*2π)/3622 weeks
20321.38626 -6.0265 (203*2π)/3622 weeks
2048.01817 -20.11865 (204*2π)/3622 weeks
20517.70829 -43.44473 (205*2π)/3622 weeks
20644.08275 -45.98751 (206*2π)/3622 weeks
20755.89482 -23.22477 (207*2π)/3622 weeks
20834.86481 -12.39426 (208*2π)/3622 weeks
20929.22062 -33.02119 (209*2π)/3622 weeks
21042.08175 -35.50208 (210*2π)/3622 weeks
21137.45173 -34.18172 (211*2π)/3622 weeks
21245.47274 -53.37993 (212*2π)/3622 weeks
21375.12219 -46.52695 (213*2π)/3622 weeks
21479.00762 -23.13562 (214*2π)/3622 weeks
21567.79322 -14.73729 (215*2π)/3622 weeks
21671.47589 -17.47878 (216*2π)/3622 weeks
21774.75887 4.96175 (217*2π)/3622 weeks
21842.5949 14.44262 (218*2π)/3622 weeks
21928.39938 -19.67224 (219*2π)/3622 weeks
22061.98154 -33.5269 (220*2π)/3622 weeks
22174.7805 -1.21961 (221*2π)/3622 weeks
22248.20467 15.15142 (222*2π)/3622 weeks
22332.10546 -1.33431 (223*2π)/3622 weeks
22438.37605 -4.82292 (224*2π)/3622 weeks
22518.03098 -3.69495 (225*2π)/3622 weeks
2269.76319 -38.31915 (226*2π)/3622 weeks
22747.74581 -61.27696 (227*2π)/3622 weeks
22881.1332 -33.11751 (228*2π)/3622 weeks
22967.53017 .72337 (229*2π)/3622 weeks
23037.39585 2.80533 (230*2π)/3622 weeks
23121.18749 -17.7099 (231*2π)/3622 weeks
23228.07159 -40.87309 (232*2π)/3622 weeks
23349.75057 -52.85675 (233*2π)/3622 weeks
23474.57426 -42.28151 (234*2π)/3622 weeks
23578.99306 -16.95162 (235*2π)/3622 weeks
23660.74956 -2.91685 (236*2π)/3622 weeks
23747.95505 -11.66276 (237*2π)/3622 weeks
23852.28541 -18.36894 (238*2π)/3622 weeks
23952.97903 -13.39737 (239*2π)/3622 weeks
24051.97975 -13.42404 (240*2π)/3622 weeks
24148.55955 -9.26808 (241*2π)/3622 weeks
24241.60803 -13.90337 (242*2π)/3621 weeks
24343.00768 -13.83805 (243*2π)/3621 weeks
24430.79831 -12.90238 (244*2π)/3621 weeks
24529.15855 -33.00467 (245*2π)/3621 weeks
24645.41475 -40.5099 (246*2π)/3621 weeks
24754.07838 -32.15167 (247*2π)/3621 weeks
24853.777 -28.59117 (248*2π)/3621 weeks
24952.35417 -21.04749 (249*2π)/3621 weeks
25043.54427 -23.96734 (250*2π)/3621 weeks
25146.28873 -35.09733 (251*2π)/3621 weeks
25260.68279 -36.43414 (252*2π)/3621 weeks
25368.86802 -17.3432 (253*2π)/3621 weeks
25444.09788 -6.18445 (254*2π)/3621 weeks
25540.6337 -31.14902 (255*2π)/3621 weeks
25657.50741 -23.40419 (256*2π)/3621 weeks
25743.00227 -16.89705 (257*2π)/3621 weeks
25840.49109 -31.94615 (258*2π)/3621 weeks
25959.0619 -37.3353 (259*2π)/3621 weeks
26065.5262 -11.27608 (260*2π)/3621 weeks
26140.5509 -6.52685 (261*2π)/3621 weeks
26232.0432 -20.00232 (262*2π)/3621 weeks
26342.39254 -29.45326 (263*2π)/3621 weeks
26443.48088 -14.24338 (264*2π)/3621 weeks
26523.80081 -13.78142 (265*2π)/3621 weeks
26610.1696 -29.73878 (266*2π)/3621 weeks
2671.57544 -55.02134 (267*2π)/3621 weeks
26820.58957 -97.96241 (268*2π)/3621 weeks
26979.42711 -108.9423 (269*2π)/3621 weeks
270127.0324 -70.94396 (270*2π)/3621 weeks
271136.8312 -14.5423 (271*2π)/3621 weeks
272112.4432 42.7552 (272*2π)/3621 weeks
27336.30051 70.52248 (273*2π)/3621 weeks
274-26.33102 15.92822 (274*2π)/3621 weeks
275-10.29654 -46.98481 (275*2π)/3621 weeks
27630.13647 -66.14433 (276*2π)/3621 weeks
27765.30013 -50.69205 (277*2π)/3621 weeks
27864.02492 -10.5452 (278*2π)/3621 weeks
27935.06961 3.7314 (279*2π)/3621 weeks
2805.55153 -10.23291 (280*2π)/3621 weeks
2814.68707 -38.30944 (281*2π)/3621 weeks
28212.95 -48.35246 (282*2π)/3621 weeks
28318.05221 -52.59983 (283*2π)/3621 weeks
28422.73274 -58.59071 (284*2π)/3621 weeks
28529.00579 -61.4323 (285*2π)/3621 weeks
28636.56 -66.67796 (286*2π)/3621 weeks
28751.23965 -58.9784 (287*2π)/3621 weeks
28847.26228 -39.21634 (288*2π)/3621 weeks
28929.5842 -40.77793 (289*2π)/3621 weeks
29020.76057 -55.03615 (290*2π)/3621 weeks
29136.17874 -81.10578 (291*2π)/3621 weeks
29273.1137 -59.92976 (292*2π)/3621 weeks
29345.37824 -14.20548 (293*2π)/3621 weeks
2945.29109 -41.95056 (294*2π)/3621 weeks
29531.55652 -62.55812 (295*2π)/3621 weeks
29623.19834 -37.89746 (296*2π)/3621 weeks
297-11.79656 -64.83907 (297*2π)/3621 weeks
29810.24803 -103.0312 (298*2π)/3621 weeks
29937.73566 -99.8995 (299*2π)/3621 weeks
30049.32642 -94.77126 (300*2π)/3621 weeks
30160.06629 -78.9151 (301*2π)/3621 weeks
30244.79208 -71.56267 (302*2π)/3621 weeks
30344.30933 -91.23936 (303*2π)/3621 weeks
30474.52222 -94.63483 (304*2π)/3621 weeks
30590.08543 -66.50639 (305*2π)/3621 weeks
30694.81033 -34.37286 (306*2π)/3621 weeks
30774.15584 12.64795 (307*2π)/3621 weeks
3082.17926 42.2216 (308*2π)/3621 weeks
309-79.37971 -7.44009 (309*2π)/3621 weeks
310-87.51422 -91.79396 (310*2π)/3621 weeks
311-50.32177 -129.3005 (311*2π)/3621 weeks
312-41.07112 -143.0432 (312*2π)/3621 weeks
313-21.65687 -184.4527 (313*2π)/3621 weeks
31425.79645 -209.1427 (314*2π)/3621 weeks
31593.6328 -193.5062 (315*2π)/3621 weeks
316123.2691 -129.2817 (316*2π)/3621 weeks
31785.54949 -65.70623 (317*2π)/3621 weeks
31816.70817 -82.91479 (318*2π)/3621 weeks
31917.7608 -124.8681 (319*2π)/3621 weeks
32011.11996 -131.2282 (320*2π)/3621 weeks
3213.6464 -172.2742 (321*2π)/3621 weeks
32247.44994 -219.6253 (322*2π)/3621 weeks
323113.0354 -202.2971 (323*2π)/3621 weeks
324120.365 -169.3662 (324*2π)/3621 weeks
325163.4796 -154.8847 (325*2π)/3621 weeks
326170.8391 -57.08555 (326*2π)/3621 weeks
32763.55965 -7.95426 (327*2π)/3621 weeks
328-16.54028 -70.73112 (328*2π)/3621 weeks
329-34.05827 -139.725 (329*2π)/3621 weeks
330-1.41046 -229.2277 (330*2π)/3621 weeks
331103.5072 -240.727 (331*2π)/3621 weeks
332132.0917 -161.8588 (332*2π)/3621 weeks
333103.8657 -145.1839 (333*2π)/3621 weeks
334112.0369 -116.2708 (334*2π)/3621 weeks
33553.78402 -69.78893 (335*2π)/3621 weeks
336-67.21535 -118.9524 (336*2π)/3621 weeks
337-82.95831 -302.6904 (337*2π)/3621 weeks
338104.9111 -407.4399 (338*2π)/3621 weeks
339259.0247 -264.034 (339*2π)/3621 weeks
340181.2897 -127.8881 (340*2π)/3621 weeks
34177.76682 -174.5535 (341*2π)/3621 weeks
342131.232 -262.4693 (342*2π)/3621 weeks
343223.2942 -196.2968 (343*2π)/3621 weeks
344162.2176 -101.1923 (344*2π)/3621 weeks
345101.5829 -112.6053 (345*2π)/3621 weeks
34687.59115 -131.8977 (346*2π)/3621 weeks
34719.85895 -50.40376 (347*2π)/3621 weeks
348-193.2484 -173.0136 (348*2π)/3621 weeks
349-147.4506 -414.7826 (349*2π)/3621 weeks
35020.85749 -501.7137 (350*2π)/3621 weeks
351127.4723 -408.5679 (351*2π)/3621 weeks
35215.11218 -368.3061 (352*2π)/3621 weeks
353-80.93533 -589.6054 (353*2π)/3621 weeks
354234.9485 -773.2679 (354*2π)/3621 weeks
355397.8046 -407.0724 (355*2π)/3621 weeks
356-79.75126 -238.053 (356*2π)/3621 weeks
357-440.8662 -896.9598 (357*2π)/3621 weeks
358-18.09246 -1,446.31 (358*2π)/3621 weeks
35935.49923 -1,694.87 (359*2π)/3621 weeks
360611.9384 -2,985.872 (360*2π)/3621 weeks



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