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Fourier Analysis of DUST (DIREXION DAILY GOLD MINERS INDEX BEAR 3X SHARES DIREXION DAILY GOLD MINERS INDEX BEAR 3X SHARES)


DUST (DIREXION DAILY GOLD MINERS INDEX BEAR 3X SHARES DIREXION DAILY GOLD MINERS INDEX BEAR 3X SHARES) appears to have interesting cyclic behaviour every 25 weeks (120.2948*sine), 22 weeks (99.772*sine), and 37 weeks (84.0051*sine).

DUST (DIREXION DAILY GOLD MINERS INDEX BEAR 3X SHARES DIREXION DAILY GOLD MINERS INDEX BEAR 3X SHARES) has an average price of 860.03 (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 1/22/2018 for DUST (DIREXION DAILY GOLD MINERS INDEX BEAR 3X SHARES DIREXION DAILY GOLD MINERS INDEX BEAR 3X SHARES), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0860.0347   0 
1-499.739 517.2367 (1*2π)/373373 weeks
283.26856 60.36365 (2*2π)/373187 weeks
3207.2056 188.425 (3*2π)/373124 weeks
4-174.022 10.38464 (4*2π)/37393 weeks
562.53278 3.33063 (5*2π)/37375 weeks
6112.8744 220.1218 (6*2π)/37362 weeks
7-79.88172 3.49495 (7*2π)/37353 weeks
8-92.1293 15.57266 (8*2π)/37347 weeks
9142.4595 6.49866 (9*2π)/37341 weeks
10-71.55027 84.00511 (10*2π)/37337 weeks
1131.27662 2.37137 (11*2π)/37334 weeks
1218.3879 26.66569 (12*2π)/37331 weeks
13-53.61373 53.8457 (13*2π)/37329 weeks
1477.04888 -54.52759 (14*2π)/37327 weeks
1523.42669 120.2948 (15*2π)/37325 weeks
16-69.0079 -33.26765 (16*2π)/37323 weeks
1772.47216 99.77195 (17*2π)/37322 weeks
18-34.79045 -28.76982 (18*2π)/37321 weeks
19-30.27121 51.07164 (19*2π)/37320 weeks
2022.8075 18.72353 (20*2π)/37319 weeks
21-8.2201 -11.22281 (21*2π)/37318 weeks
22-6.91758 39.75452 (22*2π)/37317 weeks
231.46112 25.49388 (23*2π)/37316 weeks
24-36.41053 1.52627 (24*2π)/37316 weeks
2511.69146 -22.57311 (25*2π)/37315 weeks
2624.9809 21.92009 (26*2π)/37314 weeks
27-5.68057 8.98997 (27*2π)/37314 weeks
2819.80703 26.21825 (28*2π)/37313 weeks
29-31.33478 21.04751 (29*2π)/37313 weeks
3012.80157 -25.92635 (30*2π)/37312 weeks
3111.45224 51.18283 (31*2π)/37312 weeks
32-29.93707 -6.32494 (32*2π)/37312 weeks
3330.2082 -18.76147 (33*2π)/37311 weeks
34-18.62397 47.49296 (34*2π)/37311 weeks
3510.23283 -28.35234 (35*2π)/37311 weeks
3626.04406 31.68446 (36*2π)/37310 weeks
37-28.9565 28.43308 (37*2π)/37310 weeks
38-22.009 -17.98543 (38*2π)/37310 weeks
3936.751 16.6066 (39*2π)/37310 weeks
40-24.7759 -12.03207 (40*2π)/3739 weeks
41-.0273 9.71689 (41*2π)/3739 weeks
4219.95751 10.93741 (42*2π)/3739 weeks
43-1.75237 -5.82039 (43*2π)/3739 weeks
44-19.76042 1.86606 (44*2π)/3738 weeks
4536.52796 11.36381 (45*2π)/3738 weeks
46-3.67039 14.01575 (46*2π)/3738 weeks
47-24.08988 -11.74446 (47*2π)/3738 weeks
4819.62315 27.38584 (48*2π)/3738 weeks
49-6.6894 -28.74053 (49*2π)/3738 weeks
502.16909 7.00465 (50*2π)/3737 weeks
5121.80613 8.02368 (51*2π)/3737 weeks
52-5.79763 -4.08111 (52*2π)/3737 weeks
5311.69826 .38889 (53*2π)/3737 weeks
5412.58669 12.35528 (54*2π)/3737 weeks
5514.69035 -3.59892 (55*2π)/3737 weeks
561.58265 28.04277 (56*2π)/3737 weeks
575.2273 15.50881 (57*2π)/3737 weeks
58-11.18728 -13.63956 (58*2π)/3736 weeks
595.909 26.84336 (59*2π)/3736 weeks
60.74766 -7.59431 (60*2π)/3736 weeks
612.17592 -3.10896 (61*2π)/3736 weeks
628.26767 22.27753 (62*2π)/3736 weeks
63-18.26799 -.55732 (63*2π)/3736 weeks
6419.12507 -14.11038 (64*2π)/3736 weeks
65-.09996 16.75736 (65*2π)/3736 weeks
66-1.16045 -3.33534 (66*2π)/3736 weeks
6715.67974 -4.05282 (67*2π)/3736 weeks
687.61081 25.92097 (68*2π)/3735 weeks
69-20.78705 -15.11003 (69*2π)/3735 weeks
7031.28777 5.11098 (70*2π)/3735 weeks
712.21126 27.59764 (71*2π)/3735 weeks
72-17.49004 -13.09627 (72*2π)/3735 weeks
7313.54368 4.09693 (73*2π)/3735 weeks
74-.73016 21.48833 (74*2π)/3735 weeks
752.25068 -28.51402 (75*2π)/3735 weeks
768.83109 28.13317 (76*2π)/3735 weeks
77-1.19956 7.13406 (77*2π)/3735 weeks
78-.81071 -15.35972 (78*2π)/3735 weeks
798.7448 12.44157 (79*2π)/3735 weeks
80-3.17827 1.92996 (80*2π)/3735 weeks
8114.69293 1.61805 (81*2π)/3735 weeks
82-4.07682 4.09361 (82*2π)/3735 weeks
833.01114 8.14033 (83*2π)/3734 weeks
8410.11886 -8.25537 (84*2π)/3734 weeks
852.55506 16.29435 (85*2π)/3734 weeks
8613.68706 2.59421 (86*2π)/3734 weeks
87-21.07116 10.29635 (87*2π)/3734 weeks
8817.82573 -4.70075 (88*2π)/3734 weeks
89.4041 8.7728 (89*2π)/3734 weeks
90.07817 -8.23888 (90*2π)/3734 weeks
9116.75755 15.81935 (91*2π)/3734 weeks
92-1.46912 20.76411 (92*2π)/3734 weeks
93-14.21317 -12.91135 (93*2π)/3734 weeks
946.43049 17.80928 (94*2π)/3734 weeks
95-4.75766 -4.23489 (95*2π)/3734 weeks
96-3.96937 -7.60618 (96*2π)/3734 weeks
9713.26003 1.32023 (97*2π)/3734 weeks
98-1.33384 10.65042 (98*2π)/3734 weeks
995.53554 -10.70931 (99*2π)/3734 weeks
1003.52109 11.0543 (100*2π)/3734 weeks
1013.03836 8.59187 (101*2π)/3734 weeks
102-1.78217 -12.11019 (102*2π)/3734 weeks
10310.52867 16.79969 (103*2π)/3734 weeks
104-.96459 -4.13076 (104*2π)/3734 weeks
105-1.81827 7.68696 (105*2π)/3734 weeks
1068.23133 -.99908 (106*2π)/3734 weeks
107-7.14729 7.32982 (107*2π)/3733 weeks
1089.63008 -9.20083 (108*2π)/3733 weeks
109.34066 19.49727 (109*2π)/3733 weeks
110-3.7399 -13.06216 (110*2π)/3733 weeks
11112.95142 7.02694 (111*2π)/3733 weeks
112-7.47127 9.03282 (112*2π)/3733 weeks
1135.25776 -7.31781 (113*2π)/3733 weeks
1141.51176 7.30833 (114*2π)/3733 weeks
115-.47122 -3.29453 (115*2π)/3733 weeks
11611.40619 5.33105 (116*2π)/3733 weeks
117-8.10681 1.17063 (117*2π)/3733 weeks
1187.28472 4.18748 (118*2π)/3733 weeks
119.33297 -2.71102 (119*2π)/3733 weeks
120-2.76479 3.45686 (120*2π)/3733 weeks
12115.50194 -2.49539 (121*2π)/3733 weeks
122-7.58797 8.52911 (122*2π)/3733 weeks
1234.11903 -2.38911 (123*2π)/3733 weeks
1246.01322 3.43984 (124*2π)/3733 weeks
125.16947 2.7463 (125*2π)/3733 weeks
1261.85519 -1.11302 (126*2π)/3733 weeks
1273.09744 11.033 (127*2π)/3733 weeks
128-1.64551 -6.14535 (128*2π)/3733 weeks
1293.02698 -.05527 (129*2π)/3733 weeks
1304.4363 8.07531 (130*2π)/3733 weeks
131-1.04053 .21172 (131*2π)/3733 weeks
132-.61998 -2.03467 (132*2π)/3733 weeks
133-1.00318 1.62565 (133*2π)/3733 weeks
1348.3647 -3.57486 (134*2π)/3733 weeks
1354.76092 .65057 (135*2π)/3733 weeks
1362.11192 7.23676 (136*2π)/3733 weeks
137-.40052 3.44734 (137*2π)/3733 weeks
1382.09012 -2.79137 (138*2π)/3733 weeks
139-5.46333 -1.03189 (139*2π)/3733 weeks
1409.38847 .46013 (140*2π)/3733 weeks
14111.35489 -1.65705 (141*2π)/3733 weeks
142-11.0365 6.56683 (142*2π)/3733 weeks
14313.08015 -.56056 (143*2π)/3733 weeks
1441.58813 5.67284 (144*2π)/3733 weeks
145-5.08486 -.02827 (145*2π)/3733 weeks
1461.69933 3.22298 (146*2π)/3733 weeks
1474.29576 -4.56307 (147*2π)/3733 weeks
1482.79586 .70941 (148*2π)/3733 weeks
1491.50136 8.06669 (149*2π)/3733 weeks
150-.44873 -4.05971 (150*2π)/3732 weeks
1511.26257 4.77219 (151*2π)/3732 weeks
152-2.9258 -5.49638 (152*2π)/3732 weeks
1537.88236 3.92346 (153*2π)/3732 weeks
154-8.47329 -2.55487 (154*2π)/3732 weeks
1559.0995 -6.92714 (155*2π)/3732 weeks
1564.06283 5.28487 (156*2π)/3732 weeks
157-6.92085 -2.61725 (157*2π)/3732 weeks
15819.10381 -4.82393 (158*2π)/3732 weeks
159-8.37621 8.42232 (159*2π)/3732 weeks
1601.25966 -4.96739 (160*2π)/3732 weeks
1617.06555 -3.66553 (161*2π)/3732 weeks
1623.40424 .74438 (162*2π)/3732 weeks
1631.0293 -3.04099 (163*2π)/3732 weeks
1649.8625 3.79087 (164*2π)/3732 weeks
1654.70932 -1.01307 (165*2π)/3732 weeks
166-8.80076 1.69174 (166*2π)/3732 weeks
16718.53487 -4.94631 (167*2π)/3732 weeks
168-2.38019 7.88846 (168*2π)/3732 weeks
1692.84665 -2.95324 (169*2π)/3732 weeks
1709.09294 4.94306 (170*2π)/3732 weeks
171-6.73783 7.75275 (171*2π)/3732 weeks
172-2.09496 -14.386 (172*2π)/3732 weeks
17314.05772 4.39653 (173*2π)/3732 weeks
174-.49242 .68971 (174*2π)/3732 weeks
1755.65171 4.40753 (175*2π)/3732 weeks
1762.38014 -2.97339 (176*2π)/3732 weeks
177-4.91686 10.00295 (177*2π)/3732 weeks
1787.37095 -12.64258 (178*2π)/3732 weeks
1791.64759 8.43637 (179*2π)/3732 weeks
180-1.67368 -1.00877 (180*2π)/3732 weeks
1812.61606 -7.65425 (181*2π)/3732 weeks
18212.3328 7.64703 (182*2π)/3732 weeks
183-7.87708 -8.32317 (183*2π)/3732 weeks
18413.35449 9.56051 (184*2π)/3732 weeks
185-3.16415 -3.07599 (185*2π)/3732 weeks
1862.31645 2.73883 (186*2π)/3732 weeks
1872.31645 -2.73883 (187*2π)/3732 weeks
188-3.16415 3.07599 (188*2π)/3732 weeks
18913.35449 -9.56051 (189*2π)/3732 weeks
190-7.87708 8.32317 (190*2π)/3732 weeks
19112.3328 -7.64703 (191*2π)/3732 weeks
1922.61606 7.65425 (192*2π)/3732 weeks
193-1.67368 1.00877 (193*2π)/3732 weeks
1941.64759 -8.43637 (194*2π)/3732 weeks
1957.37095 12.64258 (195*2π)/3732 weeks
196-4.91686 -10.00295 (196*2π)/3732 weeks
1972.38014 2.97339 (197*2π)/3732 weeks
1985.65171 -4.40753 (198*2π)/3732 weeks
199-.49242 -.68971 (199*2π)/3732 weeks
20014.05772 -4.39653 (200*2π)/3732 weeks
201-2.09496 14.386 (201*2π)/3732 weeks
202-6.73783 -7.75275 (202*2π)/3732 weeks
2039.09294 -4.94306 (203*2π)/3732 weeks
2042.84665 2.95324 (204*2π)/3732 weeks
205-2.38019 -7.88846 (205*2π)/3732 weeks
20618.53487 4.94631 (206*2π)/3732 weeks
207-8.80076 -1.69174 (207*2π)/3732 weeks
2084.70932 1.01307 (208*2π)/3732 weeks
2099.8625 -3.79087 (209*2π)/3732 weeks
2101.0293 3.04099 (210*2π)/3732 weeks
2113.40424 -.74438 (211*2π)/3732 weeks
2127.06555 3.66553 (212*2π)/3732 weeks
2131.25966 4.96739 (213*2π)/3732 weeks
214-8.37621 -8.42232 (214*2π)/3732 weeks
21519.10381 4.82393 (215*2π)/3732 weeks
216-6.92085 2.61725 (216*2π)/3732 weeks
2174.06283 -5.28487 (217*2π)/3732 weeks
2189.0995 6.92714 (218*2π)/3732 weeks
219-8.47329 2.55487 (219*2π)/3732 weeks
2207.88236 -3.92346 (220*2π)/3732 weeks
221-2.9258 5.49638 (221*2π)/3732 weeks
2221.26257 -4.77219 (222*2π)/3732 weeks
223-.44873 4.05971 (223*2π)/3732 weeks
2241.50136 -8.06669 (224*2π)/3732 weeks
2252.79586 -.70941 (225*2π)/3732 weeks
2264.29576 4.56307 (226*2π)/3732 weeks
2271.69933 -3.22298 (227*2π)/3732 weeks
228-5.08486 .02827 (228*2π)/3732 weeks
2291.58813 -5.67284 (229*2π)/3732 weeks
23013.08015 .56056 (230*2π)/3732 weeks
231-11.0365 -6.56683 (231*2π)/3732 weeks
23211.35489 1.65705 (232*2π)/3732 weeks
2339.38847 -.46013 (233*2π)/3732 weeks
234-5.46333 1.03189 (234*2π)/3732 weeks
2352.09012 2.79137 (235*2π)/3732 weeks
236-.40052 -3.44734 (236*2π)/3732 weeks
2372.11192 -7.23676 (237*2π)/3732 weeks
2384.76092 -.65057 (238*2π)/3732 weeks
2398.3647 3.57486 (239*2π)/3732 weeks
240-1.00318 -1.62565 (240*2π)/3732 weeks
241-.61998 2.03467 (241*2π)/3732 weeks
242-1.04053 -.21172 (242*2π)/3732 weeks
2434.4363 -8.07531 (243*2π)/3732 weeks
2443.02698 .05527 (244*2π)/3732 weeks
245-1.64551 6.14535 (245*2π)/3732 weeks
2463.09744 -11.033 (246*2π)/3732 weeks
2471.85519 1.11302 (247*2π)/3732 weeks
248.16947 -2.7463 (248*2π)/3732 weeks
2496.01322 -3.43984 (249*2π)/3731 weeks
2504.11903 2.38911 (250*2π)/3731 weeks
251-7.58797 -8.52911 (251*2π)/3731 weeks
25215.50194 2.49539 (252*2π)/3731 weeks
253-2.76479 -3.45686 (253*2π)/3731 weeks
254.33297 2.71102 (254*2π)/3731 weeks
2557.28472 -4.18748 (255*2π)/3731 weeks
256-8.10681 -1.17063 (256*2π)/3731 weeks
25711.40619 -5.33105 (257*2π)/3731 weeks
258-.47122 3.29453 (258*2π)/3731 weeks
2591.51176 -7.30833 (259*2π)/3731 weeks
2605.25776 7.31781 (260*2π)/3731 weeks
261-7.47127 -9.03282 (261*2π)/3731 weeks
26212.95142 -7.02694 (262*2π)/3731 weeks
263-3.7399 13.06216 (263*2π)/3731 weeks
264.34066 -19.49727 (264*2π)/3731 weeks
2659.63008 9.20083 (265*2π)/3731 weeks
266-7.14729 -7.32982 (266*2π)/3731 weeks
2678.23133 .99908 (267*2π)/3731 weeks
268-1.81827 -7.68696 (268*2π)/3731 weeks
269-.96459 4.13076 (269*2π)/3731 weeks
27010.52867 -16.79969 (270*2π)/3731 weeks
271-1.78217 12.11019 (271*2π)/3731 weeks
2723.03836 -8.59187 (272*2π)/3731 weeks
2733.52109 -11.0543 (273*2π)/3731 weeks
2745.53554 10.70931 (274*2π)/3731 weeks
275-1.33384 -10.65042 (275*2π)/3731 weeks
27613.26003 -1.32023 (276*2π)/3731 weeks
277-3.96937 7.60618 (277*2π)/3731 weeks
278-4.75766 4.23489 (278*2π)/3731 weeks
2796.43049 -17.80928 (279*2π)/3731 weeks
280-14.21317 12.91135 (280*2π)/3731 weeks
281-1.46912 -20.76411 (281*2π)/3731 weeks
28216.75755 -15.81935 (282*2π)/3731 weeks
283.07817 8.23888 (283*2π)/3731 weeks
284.4041 -8.7728 (284*2π)/3731 weeks
28517.82573 4.70075 (285*2π)/3731 weeks
286-21.07116 -10.29635 (286*2π)/3731 weeks
28713.68706 -2.59421 (287*2π)/3731 weeks
2882.55506 -16.29435 (288*2π)/3731 weeks
28910.11886 8.25537 (289*2π)/3731 weeks
2903.01114 -8.14033 (290*2π)/3731 weeks
291-4.07682 -4.09361 (291*2π)/3731 weeks
29214.69293 -1.61805 (292*2π)/3731 weeks
293-3.17827 -1.92996 (293*2π)/3731 weeks
2948.7448 -12.44157 (294*2π)/3731 weeks
295-.81071 15.35972 (295*2π)/3731 weeks
296-1.19956 -7.13406 (296*2π)/3731 weeks
2978.83109 -28.13317 (297*2π)/3731 weeks
2982.25068 28.51402 (298*2π)/3731 weeks
299-.73016 -21.48833 (299*2π)/3731 weeks
30013.54368 -4.09693 (300*2π)/3731 weeks
301-17.49004 13.09627 (301*2π)/3731 weeks
3022.21126 -27.59764 (302*2π)/3731 weeks
30331.28777 -5.11098 (303*2π)/3731 weeks
304-20.78705 15.11003 (304*2π)/3731 weeks
3057.61081 -25.92097 (305*2π)/3731 weeks
30615.67974 4.05282 (306*2π)/3731 weeks
307-1.16045 3.33534 (307*2π)/3731 weeks
308-.09996 -16.75736 (308*2π)/3731 weeks
30919.12507 14.11038 (309*2π)/3731 weeks
310-18.26799 .55732 (310*2π)/3731 weeks
3118.26767 -22.27753 (311*2π)/3731 weeks
3122.17592 3.10896 (312*2π)/3731 weeks
313.74766 7.59431 (313*2π)/3731 weeks
3145.909 -26.84336 (314*2π)/3731 weeks
315-11.18728 13.63956 (315*2π)/3731 weeks
3165.2273 -15.50881 (316*2π)/3731 weeks
3171.58265 -28.04277 (317*2π)/3731 weeks
31814.69035 3.59892 (318*2π)/3731 weeks
31912.58669 -12.35528 (319*2π)/3731 weeks
32011.69826 -.38889 (320*2π)/3731 weeks
321-5.79763 4.08111 (321*2π)/3731 weeks
32221.80613 -8.02368 (322*2π)/3731 weeks
3232.16909 -7.00465 (323*2π)/3731 weeks
324-6.6894 28.74053 (324*2π)/3731 weeks
32519.62315 -27.38584 (325*2π)/3731 weeks
326-24.08988 11.74446 (326*2π)/3731 weeks
327-3.67039 -14.01575 (327*2π)/3731 weeks
32836.52796 -11.36381 (328*2π)/3731 weeks
329-19.76042 -1.86606 (329*2π)/3731 weeks
330-1.75237 5.82039 (330*2π)/3731 weeks
33119.95751 -10.93741 (331*2π)/3731 weeks
332-.0273 -9.71689 (332*2π)/3731 weeks
333-24.7759 12.03207 (333*2π)/3731 weeks
33436.751 -16.6066 (334*2π)/3731 weeks
335-22.009 17.98543 (335*2π)/3731 weeks
336-28.9565 -28.43308 (336*2π)/3731 weeks
33726.04406 -31.68446 (337*2π)/3731 weeks
33810.23283 28.35234 (338*2π)/3731 weeks
339-18.62397 -47.49296 (339*2π)/3731 weeks
34030.2082 18.76147 (340*2π)/3731 weeks
341-29.93707 6.32494 (341*2π)/3731 weeks
34211.45224 -51.18283 (342*2π)/3731 weeks
34312.80157 25.92635 (343*2π)/3731 weeks
344-31.33478 -21.04751 (344*2π)/3731 weeks
34519.80703 -26.21825 (345*2π)/3731 weeks
346-5.68057 -8.98997 (346*2π)/3731 weeks
34724.9809 -21.92009 (347*2π)/3731 weeks
34811.69146 22.57311 (348*2π)/3731 weeks
349-36.41053 -1.52627 (349*2π)/3731 weeks
3501.46112 -25.49388 (350*2π)/3731 weeks
351-6.91758 -39.75452 (351*2π)/3731 weeks
352-8.2201 11.22281 (352*2π)/3731 weeks
35322.8075 -18.72353 (353*2π)/3731 weeks
354-30.27121 -51.07164 (354*2π)/3731 weeks
355-34.79045 28.76982 (355*2π)/3731 weeks
35672.47216 -99.77195 (356*2π)/3731 weeks
357-69.0079 33.26765 (357*2π)/3731 weeks
35823.42669 -120.2948 (358*2π)/3731 weeks
35977.04888 54.52759 (359*2π)/3731 weeks
360-53.61373 -53.8457 (360*2π)/3731 weeks
36118.3879 -26.66569 (361*2π)/3731 weeks
36231.27662 -2.37137 (362*2π)/3731 weeks
363-71.55027 -84.00511 (363*2π)/3731 weeks
364142.4595 -6.49866 (364*2π)/3731 weeks
365-92.1293 -15.57266 (365*2π)/3731 weeks
366-79.88172 -3.49495 (366*2π)/3731 weeks
367112.8744 -220.1218 (367*2π)/3731 weeks
36862.53278 -3.33063 (368*2π)/3731 weeks
369-174.022 -10.38464 (369*2π)/3731 weeks
370207.2056 -188.425 (370*2π)/3731 weeks
37183.26856 -60.36365 (371*2π)/3731 weeks



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