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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 (102.61*cosine), 26 weeks (99.5798*cosine), and 21 weeks (84.9902*cosine).

DUST (Direxion Daily Gold Miners Index Bear 3x Shares ETF) has an average price of 895.01 (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 10/9/2017 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
0895.0098   0 
1-527.1486 443.5463 (1*2π)/358358 weeks
274.21818 72.43523 (2*2π)/358179 weeks
3176.0889 269.0553 (3*2π)/358119 weeks
4-110.9169 -58.65397 (4*2π)/35890 weeks
586.20903 -2.75073 (5*2π)/35872 weeks
6-11.75941 260.2646 (6*2π)/35860 weeks
7-11.75015 17.43629 (7*2π)/35851 weeks
8-53.00144 -84.27477 (8*2π)/35845 weeks
994.88518 131.849 (9*2π)/35840 weeks
10-53.34323 -8.54536 (10*2π)/35836 weeks
1120.16391 36.93701 (11*2π)/35833 weeks
1218.79155 65.17214 (12*2π)/35830 weeks
13-37.83136 -60.46368 (13*2π)/35828 weeks
1499.57979 81.01703 (14*2π)/35826 weeks
15-86.46764 61.10451 (15*2π)/35824 weeks
16102.61 -1.45654 (16*2π)/35822 weeks
17-84.9902 27.31518 (17*2π)/35821 weeks
189.04097 60.96127 (18*2π)/35820 weeks
1916.72545 -4.96323 (19*2π)/35819 weeks
20-23.71587 -1.17389 (20*2π)/35818 weeks
213.2173 43.67157 (21*2π)/35817 weeks
222.48654 22.51499 (22*2π)/35816 weeks
23-38.25783 4.01356 (23*2π)/35816 weeks
2412.54702 -23.49185 (24*2π)/35815 weeks
2524.2913 24.63621 (25*2π)/35814 weeks
26-3.64102 5.98197 (26*2π)/35814 weeks
2716.48551 33.99522 (27*2π)/35813 weeks
28-34.89964 9.0768 (28*2π)/35813 weeks
2931.73228 -16.69358 (29*2π)/35812 weeks
30-16.35808 50.2169 (30*2π)/35812 weeks
31-18.07429 -19.3861 (31*2π)/35812 weeks
3246.11849 14.41882 (32*2π)/35811 weeks
33-42.13242 6.0564 (33*2π)/35811 weeks
3435.73223 -3.1236 (34*2π)/35811 weeks
35.74224 46.70628 (35*2π)/35810 weeks
36-31.94522 2.69016 (36*2π)/35810 weeks
3719.55566 -28.72036 (37*2π)/35810 weeks
38-24.49552 31.91569 (38*2π)/3589 weeks
3915.59016 -.14008 (39*2π)/3589 weeks
4013.71243 -8.2032 (40*2π)/3589 weeks
41-13.11098 5.51753 (41*2π)/3589 weeks
42-8.74709 16.83672 (42*2π)/3589 weeks
4336.78988 -9.4604 (43*2π)/3588 weeks
44-5.60981 17.12455 (44*2π)/3588 weeks
45-27.55562 -2.10633 (45*2π)/3588 weeks
4626.57134 22.25978 (46*2π)/3588 weeks
47-10.23416 -29.24863 (47*2π)/3588 weeks
481.79844 6.88437 (48*2π)/3587 weeks
4921.52822 11.21342 (49*2π)/3587 weeks
50-2.95228 -7.16218 (50*2π)/3587 weeks
5112.28302 .43488 (51*2π)/3587 weeks
527.95103 13.62095 (52*2π)/3587 weeks
5324.17816 2.57112 (53*2π)/3587 weeks
54-7.09092 19.19948 (54*2π)/3587 weeks
55-5.81933 22.7757 (55*2π)/3587 weeks
5615.33779 -13.6218 (56*2π)/3586 weeks
57-17.32485 14.54999 (57*2π)/3586 weeks
585.62358 3.06606 (58*2π)/3586 weeks
5917.19492 1.6083 (59*2π)/3586 weeks
60-13.5547 17.84897 (60*2π)/3586 weeks
61-4.03519 -20.30714 (61*2π)/3586 weeks
6217.79247 16.19927 (62*2π)/3586 weeks
63-5.35775 .79215 (63*2π)/3586 weeks
648.86047 -7.16195 (64*2π)/3586 weeks
6518.05059 19.35226 (65*2π)/3586 weeks
66-26.79745 2.49716 (66*2π)/3585 weeks
6732.32494 -7.91286 (67*2π)/3585 weeks
687.63258 27.09045 (68*2π)/3585 weeks
69-23.17707 -7.39947 (69*2π)/3585 weeks
7015.04425 2.83853 (70*2π)/3585 weeks
71.61785 22.10575 (71*2π)/3585 weeks
724.05228 -29.83487 (72*2π)/3585 weeks
734.86006 28.67397 (73*2π)/3585 weeks
74-2.37234 8.80114 (74*2π)/3585 weeks
757.10855 -15.89468 (75*2π)/3585 weeks
763.98423 12.51778 (76*2π)/3585 weeks
77-2.19663 -2.2988 (77*2π)/3585 weeks
7813.06832 10.69133 (78*2π)/3585 weeks
791.37312 -1.5068 (79*2π)/3585 weeks
80-4.25314 3.46731 (80*2π)/3584 weeks
8119.56357 3.94405 (81*2π)/3584 weeks
82-4.00087 3.73112 (82*2π)/3584 weeks
836.77719 24.2866 (83*2π)/3584 weeks
84-5.10285 -18.65663 (84*2π)/3584 weeks
857.73748 12.36494 (85*2π)/3584 weeks
86-4.9275 2.19872 (86*2π)/3584 weeks
8722.33243 2.33262 (87*2π)/3584 weeks
883.09561 18.89675 (88*2π)/3584 weeks
89-23.40005 1.79718 (89*2π)/3584 weeks
9016.49718 9.10461 (90*2π)/3584 weeks
91-9.81807 -2.91662 (91*2π)/3584 weeks
92-5.46555 -4.77483 (92*2π)/3584 weeks
9313.98236 -1.0423 (93*2π)/3584 weeks
94.08597 11.46393 (94*2π)/3584 weeks
954.95702 -11.26227 (95*2π)/3584 weeks
963.10037 11.26707 (96*2π)/3584 weeks
971.96649 9.80155 (97*2π)/3584 weeks
983.11125 -13.82109 (98*2π)/3584 weeks
993.96413 18.82801 (99*2π)/3584 weeks
1004.61218 -3.22608 (100*2π)/3584 weeks
101-4.74431 3.33791 (101*2π)/3584 weeks
1029.50554 5.95407 (102*2π)/3584 weeks
103-9.02844 -1.84745 (103*2π)/3583 weeks
10417.94911 1.53736 (104*2π)/3583 weeks
105-14.91104 9.30032 (105*2π)/3583 weeks
10612.21761 -8.73436 (106*2π)/3583 weeks
1074.14826 13.80111 (107*2π)/3583 weeks
108-7.48772 -5.1212 (108*2π)/3583 weeks
1098.89909 4.713 (109*2π)/3583 weeks
110-2.94722 .91598 (110*2π)/3583 weeks
1119.77555 -2.48045 (111*2π)/3583 weeks
112-5.26549 10.55211 (112*2π)/3583 weeks
1137.9709 -2.12141 (113*2π)/3583 weeks
114-2.73962 -.0968 (114*2π)/3583 weeks
115.72821 5.45471 (115*2π)/3583 weeks
11612.77755 -7.1471 (116*2π)/3583 weeks
117-5.97152 11.95153 (117*2π)/3583 weeks
1183.9306 -3.00702 (118*2π)/3583 weeks
1196.31665 3.43503 (119*2π)/3583 weeks
120.22474 2.70285 (120*2π)/3583 weeks
1212.68215 -1.50193 (121*2π)/3583 weeks
122-.02277 11.87738 (122*2π)/3583 weeks
1231.90528 -6.02447 (123*2π)/3583 weeks
1244.22198 -.92201 (124*2π)/3583 weeks
125-.00294 8.56717 (125*2π)/3583 weeks
126.03762 .94622 (126*2π)/3583 weeks
1272.62543 -2.13239 (127*2π)/3583 weeks
128-2.07233 -4.06207 (128*2π)/3583 weeks
1297.41929 2.36934 (129*2π)/3583 weeks
1307.67845 3.49347 (130*2π)/3583 weeks
131-.55285 3.89931 (131*2π)/3583 weeks
132-3.0265 .04085 (132*2π)/3583 weeks
1331.27694 4.42623 (133*2π)/3583 weeks
1346.94456 -8.5791 (134*2π)/3583 weeks
1353.87345 -2.60616 (135*2π)/3583 weeks
136-.74866 16.16491 (136*2π)/3583 weeks
1379.18431 -9.2465 (137*2π)/3583 weeks
1382.01088 6.81943 (138*2π)/3583 weeks
139-5.32326 3.30804 (139*2π)/3583 weeks
1403.41969 2.13552 (140*2π)/3583 weeks
1412.87791 -5.36599 (141*2π)/3583 weeks
1422.77882 1.03844 (142*2π)/3583 weeks
1431.7096 8.37425 (143*2π)/3583 weeks
144.0857 -4.2726 (144*2π)/3582 weeks
145.28158 5.06347 (145*2π)/3582 weeks
146-1.23209 -6.93756 (146*2π)/3582 weeks
1475.62377 6.92972 (147*2π)/3582 weeks
148-6.82452 -7.50343 (148*2π)/3582 weeks
14910.94537 -2.66668 (149*2π)/3582 weeks
150.96412 5.49861 (150*2π)/3582 weeks
151-3.74842 -11.86079 (151*2π)/3582 weeks
15215.95125 12.05443 (152*2π)/3582 weeks
153-7.1291 -3.95099 (153*2π)/3582 weeks
1542.57525 -5.3611 (154*2π)/3582 weeks
1556.35044 1.02156 (155*2π)/3582 weeks
1562.30157 .43352 (156*2π)/3582 weeks
1579.42465 -4.53133 (157*2π)/3582 weeks
158.67598 2.25872 (158*2π)/3582 weeks
159-.00391 8.98395 (159*2π)/3582 weeks
16010.19939 -15.04336 (160*2π)/3582 weeks
1613.10043 12.59297 (161*2π)/3582 weeks
1621.01823 -2.78219 (162*2π)/3582 weeks
1639.69425 2.33784 (163*2π)/3582 weeks
164-4.75095 9.69918 (164*2π)/3582 weeks
165-4.81795 -13.70052 (165*2π)/3582 weeks
16615.35618 3.42207 (166*2π)/3582 weeks
167-.53966 .75221 (167*2π)/3582 weeks
1685.44344 4.9878 (168*2π)/3582 weeks
1694.14514 -3.01364 (169*2π)/3582 weeks
170-8.92277 7.60517 (170*2π)/3582 weeks
17112.72186 -8.82502 (171*2π)/3582 weeks
172-1.76338 6.16967 (172*2π)/3582 weeks
173-1.75229 -2.22967 (173*2π)/3582 weeks
1747.7095 -8.13116 (174*2π)/3582 weeks
1752.0033 13.43741 (175*2π)/3582 weeks
1767.892 -13.88832 (176*2π)/3582 weeks
177-1.73608 11.79341 (177*2π)/3582 weeks
1784.40552 -2.32028 (178*2π)/3582 weeks
179-.86004   (179*2π)/3582 weeks
1804.40552 2.32028 (180*2π)/3582 weeks
181-1.73608 -11.79341 (181*2π)/3582 weeks
1827.892 13.88832 (182*2π)/3582 weeks
1832.0033 -13.43741 (183*2π)/3582 weeks
1847.7095 8.13116 (184*2π)/3582 weeks
185-1.75229 2.22967 (185*2π)/3582 weeks
186-1.76338 -6.16967 (186*2π)/3582 weeks
18712.72186 8.82502 (187*2π)/3582 weeks
188-8.92277 -7.60517 (188*2π)/3582 weeks
1894.14514 3.01364 (189*2π)/3582 weeks
1905.44344 -4.9878 (190*2π)/3582 weeks
191-.53966 -.75221 (191*2π)/3582 weeks
19215.35618 -3.42207 (192*2π)/3582 weeks
193-4.81795 13.70052 (193*2π)/3582 weeks
194-4.75095 -9.69918 (194*2π)/3582 weeks
1959.69425 -2.33784 (195*2π)/3582 weeks
1961.01823 2.78219 (196*2π)/3582 weeks
1973.10043 -12.59297 (197*2π)/3582 weeks
19810.19939 15.04336 (198*2π)/3582 weeks
199-.00391 -8.98395 (199*2π)/3582 weeks
200.67598 -2.25872 (200*2π)/3582 weeks
2019.42465 4.53133 (201*2π)/3582 weeks
2022.30157 -.43352 (202*2π)/3582 weeks
2036.35044 -1.02156 (203*2π)/3582 weeks
2042.57525 5.3611 (204*2π)/3582 weeks
205-7.1291 3.95099 (205*2π)/3582 weeks
20615.95125 -12.05443 (206*2π)/3582 weeks
207-3.74842 11.86079 (207*2π)/3582 weeks
208.96412 -5.49861 (208*2π)/3582 weeks
20910.94537 2.66668 (209*2π)/3582 weeks
210-6.82452 7.50343 (210*2π)/3582 weeks
2115.62377 -6.92972 (211*2π)/3582 weeks
212-1.23209 6.93756 (212*2π)/3582 weeks
213.28158 -5.06347 (213*2π)/3582 weeks
214.0857 4.2726 (214*2π)/3582 weeks
2151.7096 -8.37425 (215*2π)/3582 weeks
2162.77882 -1.03844 (216*2π)/3582 weeks
2172.87791 5.36599 (217*2π)/3582 weeks
2183.41969 -2.13552 (218*2π)/3582 weeks
219-5.32326 -3.30804 (219*2π)/3582 weeks
2202.01088 -6.81943 (220*2π)/3582 weeks
2219.18431 9.2465 (221*2π)/3582 weeks
222-.74866 -16.16491 (222*2π)/3582 weeks
2233.87345 2.60616 (223*2π)/3582 weeks
2246.94456 8.5791 (224*2π)/3582 weeks
2251.27694 -4.42623 (225*2π)/3582 weeks
226-3.0265 -.04085 (226*2π)/3582 weeks
227-.55285 -3.89931 (227*2π)/3582 weeks
2287.67845 -3.49347 (228*2π)/3582 weeks
2297.41929 -2.36934 (229*2π)/3582 weeks
230-2.07233 4.06207 (230*2π)/3582 weeks
2312.62543 2.13239 (231*2π)/3582 weeks
232.03762 -.94622 (232*2π)/3582 weeks
233-.00294 -8.56717 (233*2π)/3582 weeks
2344.22198 .92201 (234*2π)/3582 weeks
2351.90528 6.02447 (235*2π)/3582 weeks
236-.02277 -11.87738 (236*2π)/3582 weeks
2372.68215 1.50193 (237*2π)/3582 weeks
238.22474 -2.70285 (238*2π)/3582 weeks
2396.31665 -3.43503 (239*2π)/3581 weeks
2403.9306 3.00702 (240*2π)/3581 weeks
241-5.97152 -11.95153 (241*2π)/3581 weeks
24212.77755 7.1471 (242*2π)/3581 weeks
243.72821 -5.45471 (243*2π)/3581 weeks
244-2.73962 .0968 (244*2π)/3581 weeks
2457.9709 2.12141 (245*2π)/3581 weeks
246-5.26549 -10.55211 (246*2π)/3581 weeks
2479.77555 2.48045 (247*2π)/3581 weeks
248-2.94722 -.91598 (248*2π)/3581 weeks
2498.89909 -4.713 (249*2π)/3581 weeks
250-7.48772 5.1212 (250*2π)/3581 weeks
2514.14826 -13.80111 (251*2π)/3581 weeks
25212.21761 8.73436 (252*2π)/3581 weeks
253-14.91104 -9.30032 (253*2π)/3581 weeks
25417.94911 -1.53736 (254*2π)/3581 weeks
255-9.02844 1.84745 (255*2π)/3581 weeks
2569.50554 -5.95407 (256*2π)/3581 weeks
257-4.74431 -3.33791 (257*2π)/3581 weeks
2584.61218 3.22608 (258*2π)/3581 weeks
2593.96413 -18.82801 (259*2π)/3581 weeks
2603.11125 13.82109 (260*2π)/3581 weeks
2611.96649 -9.80155 (261*2π)/3581 weeks
2623.10037 -11.26707 (262*2π)/3581 weeks
2634.95702 11.26227 (263*2π)/3581 weeks
264.08597 -11.46393 (264*2π)/3581 weeks
26513.98236 1.0423 (265*2π)/3581 weeks
266-5.46555 4.77483 (266*2π)/3581 weeks
267-9.81807 2.91662 (267*2π)/3581 weeks
26816.49718 -9.10461 (268*2π)/3581 weeks
269-23.40005 -1.79718 (269*2π)/3581 weeks
2703.09561 -18.89675 (270*2π)/3581 weeks
27122.33243 -2.33262 (271*2π)/3581 weeks
272-4.9275 -2.19872 (272*2π)/3581 weeks
2737.73748 -12.36494 (273*2π)/3581 weeks
274-5.10285 18.65663 (274*2π)/3581 weeks
2756.77719 -24.2866 (275*2π)/3581 weeks
276-4.00087 -3.73112 (276*2π)/3581 weeks
27719.56357 -3.94405 (277*2π)/3581 weeks
278-4.25314 -3.46731 (278*2π)/3581 weeks
2791.37312 1.5068 (279*2π)/3581 weeks
28013.06832 -10.69133 (280*2π)/3581 weeks
281-2.19663 2.2988 (281*2π)/3581 weeks
2823.98423 -12.51778 (282*2π)/3581 weeks
2837.10855 15.89468 (283*2π)/3581 weeks
284-2.37234 -8.80114 (284*2π)/3581 weeks
2854.86006 -28.67397 (285*2π)/3581 weeks
2864.05228 29.83487 (286*2π)/3581 weeks
287.61785 -22.10575 (287*2π)/3581 weeks
28815.04425 -2.83853 (288*2π)/3581 weeks
289-23.17707 7.39947 (289*2π)/3581 weeks
2907.63258 -27.09045 (290*2π)/3581 weeks
29132.32494 7.91286 (291*2π)/3581 weeks
292-26.79745 -2.49716 (292*2π)/3581 weeks
29318.05059 -19.35226 (293*2π)/3581 weeks
2948.86047 7.16195 (294*2π)/3581 weeks
295-5.35775 -.79215 (295*2π)/3581 weeks
29617.79247 -16.19927 (296*2π)/3581 weeks
297-4.03519 20.30714 (297*2π)/3581 weeks
298-13.5547 -17.84897 (298*2π)/3581 weeks
29917.19492 -1.6083 (299*2π)/3581 weeks
3005.62358 -3.06606 (300*2π)/3581 weeks
301-17.32485 -14.54999 (301*2π)/3581 weeks
30215.33779 13.6218 (302*2π)/3581 weeks
303-5.81933 -22.7757 (303*2π)/3581 weeks
304-7.09092 -19.19948 (304*2π)/3581 weeks
30524.17816 -2.57112 (305*2π)/3581 weeks
3067.95103 -13.62095 (306*2π)/3581 weeks
30712.28302 -.43488 (307*2π)/3581 weeks
308-2.95228 7.16218 (308*2π)/3581 weeks
30921.52822 -11.21342 (309*2π)/3581 weeks
3101.79844 -6.88437 (310*2π)/3581 weeks
311-10.23416 29.24863 (311*2π)/3581 weeks
31226.57134 -22.25978 (312*2π)/3581 weeks
313-27.55562 2.10633 (313*2π)/3581 weeks
314-5.60981 -17.12455 (314*2π)/3581 weeks
31536.78988 9.4604 (315*2π)/3581 weeks
316-8.74709 -16.83672 (316*2π)/3581 weeks
317-13.11098 -5.51753 (317*2π)/3581 weeks
31813.71243 8.2032 (318*2π)/3581 weeks
31915.59016 .14008 (319*2π)/3581 weeks
320-24.49552 -31.91569 (320*2π)/3581 weeks
32119.55566 28.72036 (321*2π)/3581 weeks
322-31.94522 -2.69016 (322*2π)/3581 weeks
323.74224 -46.70628 (323*2π)/3581 weeks
32435.73223 3.1236 (324*2π)/3581 weeks
325-42.13242 -6.0564 (325*2π)/3581 weeks
32646.11849 -14.41882 (326*2π)/3581 weeks
327-18.07429 19.3861 (327*2π)/3581 weeks
328-16.35808 -50.2169 (328*2π)/3581 weeks
32931.73228 16.69358 (329*2π)/3581 weeks
330-34.89964 -9.0768 (330*2π)/3581 weeks
33116.48551 -33.99522 (331*2π)/3581 weeks
332-3.64102 -5.98197 (332*2π)/3581 weeks
33324.2913 -24.63621 (333*2π)/3581 weeks
33412.54702 23.49185 (334*2π)/3581 weeks
335-38.25783 -4.01356 (335*2π)/3581 weeks
3362.48654 -22.51499 (336*2π)/3581 weeks
3373.2173 -43.67157 (337*2π)/3581 weeks
338-23.71587 1.17389 (338*2π)/3581 weeks
33916.72545 4.96323 (339*2π)/3581 weeks
3409.04097 -60.96127 (340*2π)/3581 weeks
341-84.9902 -27.31518 (341*2π)/3581 weeks
342102.61 1.45654 (342*2π)/3581 weeks
343-86.46764 -61.10451 (343*2π)/3581 weeks
34499.57979 -81.01703 (344*2π)/3581 weeks
345-37.83136 60.46368 (345*2π)/3581 weeks
34618.79155 -65.17214 (346*2π)/3581 weeks
34720.16391 -36.93701 (347*2π)/3581 weeks
348-53.34323 8.54536 (348*2π)/3581 weeks
34994.88518 -131.849 (349*2π)/3581 weeks
350-53.00144 84.27477 (350*2π)/3581 weeks
351-11.75015 -17.43629 (351*2π)/3581 weeks
352-11.75941 -260.2646 (352*2π)/3581 weeks
35386.20903 2.75073 (353*2π)/3581 weeks
354-110.9169 58.65397 (354*2π)/3581 weeks
355176.0889 -269.0553 (355*2π)/3581 weeks
35674.21818 -72.43523 (356*2π)/3581 weeks



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