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Fourier Analysis of DUST (Direxion Daily Gold Miners Index Bear 3x Shares ETF)


DUST (Direxion Daily Gold Miners Index Bear 3x Shares ETF) appears to have interesting cyclic behaviour every 22 weeks (135.4748*sine), 25 weeks (130.4261*sine), and 27 weeks (86.3467*cosine).

DUST (Direxion Daily Gold Miners Index Bear 3x Shares ETF) has an average price of 925.2 (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 7/17/2017 for DUST (Direxion Daily Gold Miners Index Bear 3x Shares ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0925.1953   0 
1-540.8648 377.6428 (1*2π)/346346 weeks
266.37826 73.69535 (2*2π)/346173 weeks
3119.4617 326.6322 (3*2π)/346115 weeks
4-42.41356 -80.43958 (4*2π)/34687 weeks
5130.6277 7.68645 (5*2π)/34669 weeks
6-114.9441 210.4451 (6*2π)/34658 weeks
7-16.42988 63.43656 (7*2π)/34649 weeks
857.05687 -105.1205 (8*2π)/34643 weeks
9-11.49157 152.3685 (9*2π)/34638 weeks
1011.31794 -20.00119 (10*2π)/34635 weeks
1113.92826 29.23826 (11*2π)/34631 weeks
12-47.96431 67.25441 (12*2π)/34629 weeks
1386.34671 -56.01363 (13*2π)/34627 weeks
145.74981 130.4261 (14*2π)/34625 weeks
15-31.7275 -67.38306 (15*2π)/34623 weeks
16-3.13705 135.4748 (16*2π)/34622 weeks
1732.01468 -7.86098 (17*2π)/34620 weeks
18-35.15707 -5.82369 (18*2π)/34619 weeks
19-20.61585 37.27336 (19*2π)/34618 weeks
2028.33208 26.64193 (20*2π)/34617 weeks
21-5.28888 12.98304 (21*2π)/34616 weeks
22-36.81805 21.93877 (22*2π)/34616 weeks
23.44648 -27.64749 (23*2π)/34615 weeks
2430.71827 17.33192 (24*2π)/34614 weeks
25-6.98947 11.68173 (25*2π)/34614 weeks
2620.56735 29.7644 (26*2π)/34613 weeks
27-35.87837 14.53541 (27*2π)/34613 weeks
2830.38615 -19.46793 (28*2π)/34612 weeks
29-17.62608 51.61402 (29*2π)/34612 weeks
30-16.64559 -21.51104 (30*2π)/34612 weeks
3145.81073 24.83615 (31*2π)/34611 weeks
32-39.4789 -8.4072 (32*2π)/34611 weeks
3338.08309 8.10069 (33*2π)/34610 weeks
34-12.78505 46.39926 (34*2π)/34610 weeks
35-30.20972 -6.61772 (35*2π)/34610 weeks
3639.79023 -6.72544 (36*2π)/34610 weeks
37-33.42669 -1.75784 (37*2π)/3469 weeks
381.674 10.90181 (38*2π)/3469 weeks
3920.1847 14.63984 (39*2π)/3469 weeks
405.08827 -5.28032 (40*2π)/3469 weeks
41-17.5205 -16.96267 (41*2π)/3468 weeks
4220.8481 31.9591 (42*2π)/3468 weeks
43-6.9097 19.65296 (43*2π)/3468 weeks
4414.2535 -27.58799 (44*2π)/3468 weeks
45-32.14766 13.62641 (45*2π)/3468 weeks
4622.89823 1.42562 (46*2π)/3468 weeks
4717.44715 -8.60303 (47*2π)/3467 weeks
48-9.11132 7.91082 (48*2π)/3467 weeks
4913.05941 -.84193 (49*2π)/3467 weeks
5015.74218 11.48282 (50*2π)/3467 weeks
5114.81414 -4.1463 (51*2π)/3467 weeks
52-1.26565 28.54099 (52*2π)/3467 weeks
532.16672 21.22924 (53*2π)/3467 weeks
545.35059 -18.5538 (54*2π)/3466 weeks
55-14.39526 21.21309 (55*2π)/3466 weeks
566.65857 1.88284 (56*2π)/3466 weeks
5717.27387 .63885 (57*2π)/3466 weeks
58-14.32635 18.01444 (58*2π)/3466 weeks
59-1.49679 -21.83508 (59*2π)/3466 weeks
6014.50239 18.90551 (60*2π)/3466 weeks
61-4.08136 -1.12289 (61*2π)/3466 weeks
6213.01333 -6.64994 (62*2π)/3466 weeks
6312.1143 26.08765 (63*2π)/3465 weeks
64-22.60815 -15.85006 (64*2π)/3465 weeks
6532.35635 9.91345 (65*2π)/3465 weeks
66-4.54166 30.25393 (66*2π)/3465 weeks
67-3.59712 -20.34722 (67*2π)/3465 weeks
6811.99714 7.74114 (68*2π)/3465 weeks
69-22.7063 11.2076 (69*2π)/3465 weeks
7037.11992 -3.79218 (70*2π)/3465 weeks
71-8.53728 9.07703 (71*2π)/3465 weeks
72-13.80667 -1.92178 (72*2π)/3465 weeks
7318.48375 6.51237 (73*2π)/3465 weeks
74-2.72789 5.5432 (74*2π)/3465 weeks
7513.54666 -2.9846 (75*2π)/3465 weeks
76-4.52673 6.56924 (76*2π)/3465 weeks
772.98243 8.7845 (77*2π)/3464 weeks
7814.1395 -7.27295 (78*2π)/3464 weeks
79-2.57174 13.76394 (79*2π)/3464 weeks
8016.12318 14.86145 (80*2π)/3464 weeks
81-17.87273 -11.93288 (81*2π)/3464 weeks
8213.06313 11.22549 (82*2π)/3464 weeks
83-4.11835 4.93256 (83*2π)/3464 weeks
8421.73459 -1.84733 (84*2π)/3464 weeks
853.62888 19.41298 (85*2π)/3464 weeks
86-24.32139 3.02492 (86*2π)/3464 weeks
8716.53056 10.46638 (87*2π)/3464 weeks
88-8.71538 -3.92158 (88*2π)/3464 weeks
89-5.06058 -7.0237 (89*2π)/3464 weeks
9014.13393 1.91057 (90*2π)/3464 weeks
91-3.99724 10.22816 (91*2π)/3464 weeks
9212.71604 -8.35131 (92*2π)/3464 weeks
93-.15391 7.36793 (93*2π)/3464 weeks
94-5.564 9.68504 (94*2π)/3464 weeks
9517.32914 -8.10164 (95*2π)/3464 weeks
96-8.45785 10.93369 (96*2π)/3464 weeks
977.46598 5.92212 (97*2π)/3464 weeks
98.74216 -4.4141 (98*2π)/3464 weeks
99-.67863 12.34615 (99*2π)/3463 weeks
1003.22571 -11.55496 (100*2π)/3463 weeks
1016.24511 20.34964 (101*2π)/3463 weeks
102-5.81107 -13.49428 (102*2π)/3463 weeks
10313.40001 8.40209 (103*2π)/3463 weeks
104-9.77113 6.75009 (104*2π)/3463 weeks
1059.50699 -4.0497 (105*2π)/3463 weeks
106-1.95166 5.42778 (106*2π)/3463 weeks
1074.70569 -5.1941 (107*2π)/3463 weeks
1082.83674 13.80057 (108*2π)/3463 weeks
1093.44202 -6.49063 (109*2π)/3463 weeks
110-2.9461 3.79027 (110*2π)/3463 weeks
1113.90033 4.90088 (111*2π)/3463 weeks
1128.95992 -9.78011 (112*2π)/3463 weeks
113-3.67074 14.58589 (113*2π)/3463 weeks
1143.61735 -3.58855 (114*2π)/3463 weeks
1156.5551 3.4093 (115*2π)/3463 weeks
116.26239 2.65453 (116*2π)/3463 weeks
1173.54941 -1.73435 (117*2π)/3463 weeks
118-2.98872 11.60169 (118*2π)/3463 weeks
1194.27028 -4.66675 (119*2π)/3463 weeks
1206.22294 -.62929 (120*2π)/3463 weeks
121-3.02107 6.36625 (121*2π)/3463 weeks
122-.82027 1.25743 (122*2π)/3463 weeks
1233.5161 .70049 (123*2π)/3463 weeks
1243.37739 -7.42006 (124*2π)/3463 weeks
1254.52081 2.03937 (125*2π)/3463 weeks
1264.66812 7.70117 (126*2π)/3463 weeks
127-.08874 3.54559 (127*2π)/3463 weeks
1282.07586 -3.11685 (128*2π)/3463 weeks
129-5.8653 -3.04035 (129*2π)/3463 weeks
1307.7747 2.67309 (130*2π)/3463 weeks
13114.86089 5.52256 (131*2π)/3463 weeks
132-9.16234 -7.42514 (132*2π)/3463 weeks
1338.20873 8.47078 (133*2π)/3463 weeks
134-1.06499 7.19576 (134*2π)/3463 weeks
1352.91087 -2.86354 (135*2π)/3463 weeks
136-2.17775 -3.68544 (136*2π)/3463 weeks
1374.00393 2.41395 (137*2π)/3463 weeks
1385.53261 6.67564 (138*2π)/3463 weeks
139-3.11583 -3.4131 (139*2π)/3462 weeks
1402.34172 4.82104 (140*2π)/3462 weeks
141-3.12898 -5.97281 (141*2π)/3462 weeks
1427.30912 5.85914 (142*2π)/3462 weeks
143-7.70309 -6.8267 (143*2π)/3462 weeks
14411.32092 -2.88045 (144*2π)/3462 weeks
145.63761 5.63128 (145*2π)/3462 weeks
146-1.92689 -13.83263 (146*2π)/3462 weeks
14712.25635 15.56914 (147*2π)/3462 weeks
148-4.56361 -6.01406 (148*2π)/3462 weeks
1494.05417 -5.9414 (149*2π)/3462 weeks
1504.91115 1.45546 (150*2π)/3462 weeks
1511.11398 -.86064 (151*2π)/3462 weeks
15211.81932 1.10555 (152*2π)/3462 weeks
1534.02443 -1.26881 (153*2π)/3462 weeks
154-9.71943 1.11469 (154*2π)/3462 weeks
15520.62465 -.94897 (155*2π)/3462 weeks
156-3.84231 4.52624 (156*2π)/3462 weeks
1575.37969 -2.96604 (157*2π)/3462 weeks
1585.97773 10.15624 (158*2π)/3462 weeks
159-11.75755 -.66799 (159*2π)/3462 weeks
16013.8964 -11.55244 (160*2π)/3462 weeks
1612.00065 7.82068 (161*2π)/3462 weeks
1626.70513 -.14488 (162*2π)/3462 weeks
163-1.55485 .0596 (163*2π)/3462 weeks
1642.0345 11.52328 (164*2π)/3462 weeks
1652.73139 -15.05383 (165*2π)/3462 weeks
1662.88785 9.41841 (166*2π)/3462 weeks
167-1.79492 -1.22582 (167*2π)/3462 weeks
1684.5698 -8.67763 (168*2π)/3462 weeks
1697.86956 12.78087 (169*2π)/3462 weeks
1702.79888 -15.0616 (170*2π)/3462 weeks
171.72809 13.45565 (171*2π)/3462 weeks
1724.23262 -2.86063 (172*2π)/3462 weeks
173-.87686   (173*2π)/3462 weeks
1744.23262 2.86063 (174*2π)/3462 weeks
175.72809 -13.45565 (175*2π)/3462 weeks
1762.79888 15.0616 (176*2π)/3462 weeks
1777.86956 -12.78087 (177*2π)/3462 weeks
1784.5698 8.67763 (178*2π)/3462 weeks
179-1.79492 1.22582 (179*2π)/3462 weeks
1802.88785 -9.41841 (180*2π)/3462 weeks
1812.73139 15.05383 (181*2π)/3462 weeks
1822.0345 -11.52328 (182*2π)/3462 weeks
183-1.55485 -.0596 (183*2π)/3462 weeks
1846.70513 .14488 (184*2π)/3462 weeks
1852.00065 -7.82068 (185*2π)/3462 weeks
18613.8964 11.55244 (186*2π)/3462 weeks
187-11.75755 .66799 (187*2π)/3462 weeks
1885.97773 -10.15624 (188*2π)/3462 weeks
1895.37969 2.96604 (189*2π)/3462 weeks
190-3.84231 -4.52624 (190*2π)/3462 weeks
19120.62465 .94897 (191*2π)/3462 weeks
192-9.71943 -1.11469 (192*2π)/3462 weeks
1934.02443 1.26881 (193*2π)/3462 weeks
19411.81932 -1.10555 (194*2π)/3462 weeks
1951.11398 .86064 (195*2π)/3462 weeks
1964.91115 -1.45546 (196*2π)/3462 weeks
1974.05417 5.9414 (197*2π)/3462 weeks
198-4.56361 6.01406 (198*2π)/3462 weeks
19912.25635 -15.56914 (199*2π)/3462 weeks
200-1.92689 13.83263 (200*2π)/3462 weeks
201.63761 -5.63128 (201*2π)/3462 weeks
20211.32092 2.88045 (202*2π)/3462 weeks
203-7.70309 6.8267 (203*2π)/3462 weeks
2047.30912 -5.85914 (204*2π)/3462 weeks
205-3.12898 5.97281 (205*2π)/3462 weeks
2062.34172 -4.82104 (206*2π)/3462 weeks
207-3.11583 3.4131 (207*2π)/3462 weeks
2085.53261 -6.67564 (208*2π)/3462 weeks
2094.00393 -2.41395 (209*2π)/3462 weeks
210-2.17775 3.68544 (210*2π)/3462 weeks
2112.91087 2.86354 (211*2π)/3462 weeks
212-1.06499 -7.19576 (212*2π)/3462 weeks
2138.20873 -8.47078 (213*2π)/3462 weeks
214-9.16234 7.42514 (214*2π)/3462 weeks
21514.86089 -5.52256 (215*2π)/3462 weeks
2167.7747 -2.67309 (216*2π)/3462 weeks
217-5.8653 3.04035 (217*2π)/3462 weeks
2182.07586 3.11685 (218*2π)/3462 weeks
219-.08874 -3.54559 (219*2π)/3462 weeks
2204.66812 -7.70117 (220*2π)/3462 weeks
2214.52081 -2.03937 (221*2π)/3462 weeks
2223.37739 7.42006 (222*2π)/3462 weeks
2233.5161 -.70049 (223*2π)/3462 weeks
224-.82027 -1.25743 (224*2π)/3462 weeks
225-3.02107 -6.36625 (225*2π)/3462 weeks
2266.22294 .62929 (226*2π)/3462 weeks
2274.27028 4.66675 (227*2π)/3462 weeks
228-2.98872 -11.60169 (228*2π)/3462 weeks
2293.54941 1.73435 (229*2π)/3462 weeks
230.26239 -2.65453 (230*2π)/3462 weeks
2316.5551 -3.4093 (231*2π)/3461 weeks
2323.61735 3.58855 (232*2π)/3461 weeks
233-3.67074 -14.58589 (233*2π)/3461 weeks
2348.95992 9.78011 (234*2π)/3461 weeks
2353.90033 -4.90088 (235*2π)/3461 weeks
236-2.9461 -3.79027 (236*2π)/3461 weeks
2373.44202 6.49063 (237*2π)/3461 weeks
2382.83674 -13.80057 (238*2π)/3461 weeks
2394.70569 5.1941 (239*2π)/3461 weeks
240-1.95166 -5.42778 (240*2π)/3461 weeks
2419.50699 4.0497 (241*2π)/3461 weeks
242-9.77113 -6.75009 (242*2π)/3461 weeks
24313.40001 -8.40209 (243*2π)/3461 weeks
244-5.81107 13.49428 (244*2π)/3461 weeks
2456.24511 -20.34964 (245*2π)/3461 weeks
2463.22571 11.55496 (246*2π)/3461 weeks
247-.67863 -12.34615 (247*2π)/3461 weeks
248.74216 4.4141 (248*2π)/3461 weeks
2497.46598 -5.92212 (249*2π)/3461 weeks
250-8.45785 -10.93369 (250*2π)/3461 weeks
25117.32914 8.10164 (251*2π)/3461 weeks
252-5.564 -9.68504 (252*2π)/3461 weeks
253-.15391 -7.36793 (253*2π)/3461 weeks
25412.71604 8.35131 (254*2π)/3461 weeks
255-3.99724 -10.22816 (255*2π)/3461 weeks
25614.13393 -1.91057 (256*2π)/3461 weeks
257-5.06058 7.0237 (257*2π)/3461 weeks
258-8.71538 3.92158 (258*2π)/3461 weeks
25916.53056 -10.46638 (259*2π)/3461 weeks
260-24.32139 -3.02492 (260*2π)/3461 weeks
2613.62888 -19.41298 (261*2π)/3461 weeks
26221.73459 1.84733 (262*2π)/3461 weeks
263-4.11835 -4.93256 (263*2π)/3461 weeks
26413.06313 -11.22549 (264*2π)/3461 weeks
265-17.87273 11.93288 (265*2π)/3461 weeks
26616.12318 -14.86145 (266*2π)/3461 weeks
267-2.57174 -13.76394 (267*2π)/3461 weeks
26814.1395 7.27295 (268*2π)/3461 weeks
2692.98243 -8.7845 (269*2π)/3461 weeks
270-4.52673 -6.56924 (270*2π)/3461 weeks
27113.54666 2.9846 (271*2π)/3461 weeks
272-2.72789 -5.5432 (272*2π)/3461 weeks
27318.48375 -6.51237 (273*2π)/3461 weeks
274-13.80667 1.92178 (274*2π)/3461 weeks
275-8.53728 -9.07703 (275*2π)/3461 weeks
27637.11992 3.79218 (276*2π)/3461 weeks
277-22.7063 -11.2076 (277*2π)/3461 weeks
27811.99714 -7.74114 (278*2π)/3461 weeks
279-3.59712 20.34722 (279*2π)/3461 weeks
280-4.54166 -30.25393 (280*2π)/3461 weeks
28132.35635 -9.91345 (281*2π)/3461 weeks
282-22.60815 15.85006 (282*2π)/3461 weeks
28312.1143 -26.08765 (283*2π)/3461 weeks
28413.01333 6.64994 (284*2π)/3461 weeks
285-4.08136 1.12289 (285*2π)/3461 weeks
28614.50239 -18.90551 (286*2π)/3461 weeks
287-1.49679 21.83508 (287*2π)/3461 weeks
288-14.32635 -18.01444 (288*2π)/3461 weeks
28917.27387 -.63885 (289*2π)/3461 weeks
2906.65857 -1.88284 (290*2π)/3461 weeks
291-14.39526 -21.21309 (291*2π)/3461 weeks
2925.35059 18.5538 (292*2π)/3461 weeks
2932.16672 -21.22924 (293*2π)/3461 weeks
294-1.26565 -28.54099 (294*2π)/3461 weeks
29514.81414 4.1463 (295*2π)/3461 weeks
29615.74218 -11.48282 (296*2π)/3461 weeks
29713.05941 .84193 (297*2π)/3461 weeks
298-9.11132 -7.91082 (298*2π)/3461 weeks
29917.44715 8.60303 (299*2π)/3461 weeks
30022.89823 -1.42562 (300*2π)/3461 weeks
301-32.14766 -13.62641 (301*2π)/3461 weeks
30214.2535 27.58799 (302*2π)/3461 weeks
303-6.9097 -19.65296 (303*2π)/3461 weeks
30420.8481 -31.9591 (304*2π)/3461 weeks
305-17.5205 16.96267 (305*2π)/3461 weeks
3065.08827 5.28032 (306*2π)/3461 weeks
30720.1847 -14.63984 (307*2π)/3461 weeks
3081.674 -10.90181 (308*2π)/3461 weeks
309-33.42669 1.75784 (309*2π)/3461 weeks
31039.79023 6.72544 (310*2π)/3461 weeks
311-30.20972 6.61772 (311*2π)/3461 weeks
312-12.78505 -46.39926 (312*2π)/3461 weeks
31338.08309 -8.10069 (313*2π)/3461 weeks
314-39.4789 8.4072 (314*2π)/3461 weeks
31545.81073 -24.83615 (315*2π)/3461 weeks
316-16.64559 21.51104 (316*2π)/3461 weeks
317-17.62608 -51.61402 (317*2π)/3461 weeks
31830.38615 19.46793 (318*2π)/3461 weeks
319-35.87837 -14.53541 (319*2π)/3461 weeks
32020.56735 -29.7644 (320*2π)/3461 weeks
321-6.98947 -11.68173 (321*2π)/3461 weeks
32230.71827 -17.33192 (322*2π)/3461 weeks
323.44648 27.64749 (323*2π)/3461 weeks
324-36.81805 -21.93877 (324*2π)/3461 weeks
325-5.28888 -12.98304 (325*2π)/3461 weeks
32628.33208 -26.64193 (326*2π)/3461 weeks
327-20.61585 -37.27336 (327*2π)/3461 weeks
328-35.15707 5.82369 (328*2π)/3461 weeks
32932.01468 7.86098 (329*2π)/3461 weeks
330-3.13705 -135.4748 (330*2π)/3461 weeks
331-31.7275 67.38306 (331*2π)/3461 weeks
3325.74981 -130.4261 (332*2π)/3461 weeks
33386.34671 56.01363 (333*2π)/3461 weeks
334-47.96431 -67.25441 (334*2π)/3461 weeks
33513.92826 -29.23826 (335*2π)/3461 weeks
33611.31794 20.00119 (336*2π)/3461 weeks
337-11.49157 -152.3685 (337*2π)/3461 weeks
33857.05687 105.1205 (338*2π)/3461 weeks
339-16.42988 -63.43656 (339*2π)/3461 weeks
340-114.9441 -210.4451 (340*2π)/3461 weeks
341130.6277 -7.68645 (341*2π)/3461 weeks
342-42.41356 80.43958 (342*2π)/3461 weeks
343119.4617 -326.6322 (343*2π)/3461 weeks
34466.37826 -73.69535 (344*2π)/3461 weeks



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