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Fourier Analysis of DUST (Direxion Daily Gold Miners Inde)


DUST (Direxion Daily Gold Miners Inde) appears to have interesting cyclic behaviour every 25 weeks (139.3546*sine), 21 weeks (104.3987*sine), and 27 weeks (86.7602*cosine).

DUST (Direxion Daily Gold Miners Inde) has an average price of 997.16 (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 1/17/2017 for DUST (Direxion Daily Gold Miners Inde), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0997.1645   0 
1-538.0923 216.9069 (1*2π)/320320 weeks
267.22854 48.75558 (2*2π)/320160 weeks
3-85.5621 354.2578 (3*2π)/320107 weeks
465.37199 -30.44451 (4*2π)/32080 weeks
5190.4116 178.8441 (5*2π)/32064 weeks
6-95.21632 4.36767 (6*2π)/32053 weeks
7-102.3272 -39.48603 (7*2π)/32046 weeks
8122.674 133.571 (8*2π)/32040 weeks
9-45.32408 -19.56454 (9*2π)/32036 weeks
1013.8712 37.84536 (10*2π)/32032 weeks
11-30.19613 83.53619 (11*2π)/32029 weeks
1286.76022 -65.95209 (12*2π)/32027 weeks
13-7.84358 139.3546 (13*2π)/32025 weeks
1417.3553 -80.50679 (14*2π)/32023 weeks
15-77.45193 104.3987 (15*2π)/32021 weeks
1628.13174 56.71266 (16*2π)/32020 weeks
1720.64653 -3.71042 (17*2π)/32019 weeks
18-11.6045 -12.72498 (18*2π)/32018 weeks
19-17.28457 37.17085 (19*2π)/32017 weeks
20-14.66673 39.86798 (20*2π)/32016 weeks
21-20.75451 -25.96382 (21*2π)/32015 weeks
2235.94897 4.85681 (22*2π)/32015 weeks
23-7.72395 19.77929 (23*2π)/32014 weeks
2423.688 28.88296 (24*2π)/32013 weeks
25-39.03327 12.86841 (25*2π)/32013 weeks
2642.05343 -10.47652 (26*2π)/32012 weeks
27-36.70797 39.12595 (27*2π)/32012 weeks
282.10592 -31.12835 (28*2π)/32011 weeks
297.82337 61.05779 (29*2π)/32011 weeks
308.59952 -34.17336 (30*2π)/32011 weeks
3123.75529 43.39492 (31*2π)/32010 weeks
32-37.57339 13.81991 (32*2π)/32010 weeks
3312.61122 -35.35421 (33*2π)/32010 weeks
34-30.76198 31.49491 (34*2π)/3209 weeks
3511.85911 9.73117 (35*2π)/3209 weeks
3623.96253 9.93157 (36*2π)/3209 weeks
375.91081 -5.26017 (37*2π)/3209 weeks
38-11.54225 -25.98855 (38*2π)/3208 weeks
396.38388 35.19952 (39*2π)/3208 weeks
40-22.22551 17.88919 (40*2π)/3208 weeks
4136.66111 8.29214 (41*2π)/3208 weeks
42-13.06486 -32.02059 (42*2π)/3208 weeks
43-1.18874 2.8727 (43*2π)/3207 weeks
4412.09826 22.09175 (44*2π)/3207 weeks
4510.3415 -8.15648 (45*2π)/3207 weeks
4618.66639 5.05591 (46*2π)/3207 weeks
476.6315 -2.71262 (47*2π)/3207 weeks
484.66436 33.60058 (48*2π)/3207 weeks
492.98184 22.31636 (49*2π)/3207 weeks
5011.72681 -18.32324 (50*2π)/3206 weeks
51-20.51625 11.79749 (51*2π)/3206 weeks
522.45735 4.50649 (52*2π)/3206 weeks
5318.69648 17.70399 (53*2π)/3206 weeks
54-21.59312 1.9555 (54*2π)/3206 weeks
5526.33302 -10.27431 (55*2π)/3206 weeks
56-7.23996 11.09276 (56*2π)/3206 weeks
574.57323 -7.35768 (57*2π)/3206 weeks
5822.74368 16.73133 (58*2π)/3206 weeks
59-30.01664 2.08301 (59*2π)/3205 weeks
6037.24447 1.35098 (60*2π)/3205 weeks
61-2.37762 32.77919 (61*2π)/3205 weeks
62-.92826 -21.87826 (62*2π)/3205 weeks
6312.86082 10.11983 (63*2π)/3205 weeks
64-27.42376 -7.35206 (64*2π)/3205 weeks
6530.13794 25.18714 (65*2π)/3205 weeks
66-1.54038 7.08772 (66*2π)/3205 weeks
674.92836 -18.31908 (67*2π)/3205 weeks
682.38371 13.08171 (68*2π)/3205 weeks
691.34767 -6.3846 (69*2π)/3205 weeks
702.70463 15.73394 (70*2π)/3205 weeks
717.98043 5.46931 (71*2π)/3205 weeks
728.34905 -10.49267 (72*2π)/3204 weeks
73-.61894 16.96813 (73*2π)/3204 weeks
7417.08699 16.69317 (74*2π)/3204 weeks
75-13.04285 -18.26333 (75*2π)/3204 weeks
767.7816 13.64705 (76*2π)/3204 weeks
77-5.44117 -2.25796 (77*2π)/3204 weeks
7822.00047 15.56517 (78*2π)/3204 weeks
79-4.42467 24.81491 (79*2π)/3204 weeks
801.77122 -19.42731 (80*2π)/3204 weeks
81-13.94762 12.89161 (81*2π)/3204 weeks
82-4.28209 -.60309 (82*2π)/3204 weeks
8314.75003 -5.38376 (83*2π)/3204 weeks
84.78005 12.87959 (84*2π)/3204 weeks
859.8552 -11.54303 (85*2π)/3204 weeks
86-.0989 8.23058 (86*2π)/3204 weeks
87-8.17978 8.73043 (87*2π)/3204 weeks
8822.63599 -.37563 (88*2π)/3204 weeks
89-8.83163 1.09657 (89*2π)/3204 weeks
90.23337 10.03363 (90*2π)/3204 weeks
9110.54747 .79708 (91*2π)/3204 weeks
92-10.58218 .77749 (92*2π)/3203 weeks
9320.20699 3.93548 (93*2π)/3203 weeks
94-18.07 1.25127 (94*2π)/3203 weeks
9517.20855 .29212 (95*2π)/3203 weeks
96-6.6282 12.75638 (96*2π)/3203 weeks
977.72549 -7.35122 (97*2π)/3203 weeks
98-1.79705 6.39158 (98*2π)/3203 weeks
995.93185 -5.52955 (99*2π)/3203 weeks
100-1.84164 14.23743 (100*2π)/3203 weeks
1018.79759 -2.61209 (101*2π)/3203 weeks
102-1.57791 -2.16253 (102*2π)/3203 weeks
103-4.1787 2.68373 (103*2π)/3203 weeks
10418.65376 7.54676 (104*2π)/3203 weeks
105-6.54439 -2.97955 (105*2π)/3203 weeks
1066.22165 .44282 (106*2π)/3203 weeks
107.54941 5.21616 (107*2π)/3203 weeks
1081.13576 -.50564 (108*2π)/3203 weeks
1091.82596 13.22413 (109*2π)/3203 weeks
1103.39818 -6.00523 (110*2π)/3203 weeks
1116.87419 -.51575 (111*2π)/3203 weeks
112-4.0847 4.97147 (112*2π)/3203 weeks
113-1.83264 .20924 (113*2π)/3203 weeks
114.50649 2.55711 (114*2π)/3203 weeks
11510.03533 -3.25979 (115*2π)/3203 weeks
1167.35498 1.1566 (116*2π)/3203 weeks
117-.7677 5.20974 (117*2π)/3203 weeks
118-3.44255 -.20228 (118*2π)/3203 weeks
119-1.83177 4.74745 (119*2π)/3203 weeks
12011.68004 -2.87681 (120*2π)/3203 weeks
12114.12152 -.89055 (121*2π)/3203 weeks
122-12.64151 -3.64884 (122*2π)/3203 weeks
1238.98874 9.08938 (123*2π)/3203 weeks
124-2.42282 7.51085 (124*2π)/3203 weeks
1254.5099 -.35691 (125*2π)/3203 weeks
1262.35868 -6.1124 (126*2π)/3203 weeks
1273.33072 .60176 (127*2π)/3203 weeks
128-2.71928 8.44465 (128*2π)/3203 weeks
1294.9042 -2.06064 (129*2π)/3202 weeks
130-5.43581 1.63561 (130*2π)/3202 weeks
1319.67406 -3.08188 (131*2π)/3202 weeks
132-9.73748 1.0426 (132*2π)/3202 weeks
13310.92092 -7.54156 (133*2π)/3202 weeks
1342.21691 6.26126 (134*2π)/3202 weeks
135-3.24222 -14.13431 (135*2π)/3202 weeks
13610.47718 17.97253 (136*2π)/3202 weeks
137-2.05623 -7.08028 (137*2π)/3202 weeks
1386.91128 -5.64806 (138*2π)/3202 weeks
1393.86262 .84311 (139*2π)/3202 weeks
1402.9604 -5.83065 (140*2π)/3202 weeks
1413.8209 6.79915 (141*2π)/3202 weeks
1424.57968 8.94879 (142*2π)/3202 weeks
14310.33611 -17.23793 (143*2π)/3202 weeks
144.25715 12.44184 (144*2π)/3202 weeks
1453.42431 -3.51119 (145*2π)/3202 weeks
1468.83975 8.91427 (146*2π)/3202 weeks
147-12.46363 1.03442 (147*2π)/3202 weeks
14815.68245 -11.69511 (148*2π)/3202 weeks
149.31513 6.646 (149*2π)/3202 weeks
1507.74338 2.88077 (150*2π)/3202 weeks
1512.98142 -3.46497 (151*2π)/3202 weeks
152-11.39906 6.71266 (152*2π)/3202 weeks
15316.66518 -2.69114 (153*2π)/3202 weeks
154-3.31031 2.2104 (154*2π)/3202 weeks
155-.79017 -6.18566 (155*2π)/3202 weeks
15616.36483 3.24542 (156*2π)/3202 weeks
157-9.17123 -9.8425 (157*2π)/3202 weeks
1588.44826 14.99645 (158*2π)/3202 weeks
1593.29822 -4.11806 (159*2π)/3202 weeks
160-1.02208   (160*2π)/3202 weeks
1613.29822 4.11806 (161*2π)/3202 weeks
1628.44826 -14.99645 (162*2π)/3202 weeks
163-9.17123 9.8425 (163*2π)/3202 weeks
16416.36483 -3.24542 (164*2π)/3202 weeks
165-.79017 6.18566 (165*2π)/3202 weeks
166-3.31031 -2.2104 (166*2π)/3202 weeks
16716.66518 2.69114 (167*2π)/3202 weeks
168-11.39906 -6.71266 (168*2π)/3202 weeks
1692.98142 3.46497 (169*2π)/3202 weeks
1707.74338 -2.88077 (170*2π)/3202 weeks
171.31513 -6.646 (171*2π)/3202 weeks
17215.68245 11.69511 (172*2π)/3202 weeks
173-12.46363 -1.03442 (173*2π)/3202 weeks
1748.83975 -8.91427 (174*2π)/3202 weeks
1753.42431 3.51119 (175*2π)/3202 weeks
176.25715 -12.44184 (176*2π)/3202 weeks
17710.33611 17.23793 (177*2π)/3202 weeks
1784.57968 -8.94879 (178*2π)/3202 weeks
1793.8209 -6.79915 (179*2π)/3202 weeks
1802.9604 5.83065 (180*2π)/3202 weeks
1813.86262 -.84311 (181*2π)/3202 weeks
1826.91128 5.64806 (182*2π)/3202 weeks
183-2.05623 7.08028 (183*2π)/3202 weeks
18410.47718 -17.97253 (184*2π)/3202 weeks
185-3.24222 14.13431 (185*2π)/3202 weeks
1862.21691 -6.26126 (186*2π)/3202 weeks
18710.92092 7.54156 (187*2π)/3202 weeks
188-9.73748 -1.0426 (188*2π)/3202 weeks
1899.67406 3.08188 (189*2π)/3202 weeks
190-5.43581 -1.63561 (190*2π)/3202 weeks
1914.9042 2.06064 (191*2π)/3202 weeks
192-2.71928 -8.44465 (192*2π)/3202 weeks
1933.33072 -.60176 (193*2π)/3202 weeks
1942.35868 6.1124 (194*2π)/3202 weeks
1954.5099 .35691 (195*2π)/3202 weeks
196-2.42282 -7.51085 (196*2π)/3202 weeks
1978.98874 -9.08938 (197*2π)/3202 weeks
198-12.64151 3.64884 (198*2π)/3202 weeks
19914.12152 .89055 (199*2π)/3202 weeks
20011.68004 2.87681 (200*2π)/3202 weeks
201-1.83177 -4.74745 (201*2π)/3202 weeks
202-3.44255 .20228 (202*2π)/3202 weeks
203-.7677 -5.20974 (203*2π)/3202 weeks
2047.35498 -1.1566 (204*2π)/3202 weeks
20510.03533 3.25979 (205*2π)/3202 weeks
206.50649 -2.55711 (206*2π)/3202 weeks
207-1.83264 -.20924 (207*2π)/3202 weeks
208-4.0847 -4.97147 (208*2π)/3202 weeks
2096.87419 .51575 (209*2π)/3202 weeks
2103.39818 6.00523 (210*2π)/3202 weeks
2111.82596 -13.22413 (211*2π)/3202 weeks
2121.13576 .50564 (212*2π)/3202 weeks
213.54941 -5.21616 (213*2π)/3202 weeks
2146.22165 -.44282 (214*2π)/3201 weeks
215-6.54439 2.97955 (215*2π)/3201 weeks
21618.65376 -7.54676 (216*2π)/3201 weeks
217-4.1787 -2.68373 (217*2π)/3201 weeks
218-1.57791 2.16253 (218*2π)/3201 weeks
2198.79759 2.61209 (219*2π)/3201 weeks
220-1.84164 -14.23743 (220*2π)/3201 weeks
2215.93185 5.52955 (221*2π)/3201 weeks
222-1.79705 -6.39158 (222*2π)/3201 weeks
2237.72549 7.35122 (223*2π)/3201 weeks
224-6.6282 -12.75638 (224*2π)/3201 weeks
22517.20855 -.29212 (225*2π)/3201 weeks
226-18.07 -1.25127 (226*2π)/3201 weeks
22720.20699 -3.93548 (227*2π)/3201 weeks
228-10.58218 -.77749 (228*2π)/3201 weeks
22910.54747 -.79708 (229*2π)/3201 weeks
230.23337 -10.03363 (230*2π)/3201 weeks
231-8.83163 -1.09657 (231*2π)/3201 weeks
23222.63599 .37563 (232*2π)/3201 weeks
233-8.17978 -8.73043 (233*2π)/3201 weeks
234-.0989 -8.23058 (234*2π)/3201 weeks
2359.8552 11.54303 (235*2π)/3201 weeks
236.78005 -12.87959 (236*2π)/3201 weeks
23714.75003 5.38376 (237*2π)/3201 weeks
238-4.28209 .60309 (238*2π)/3201 weeks
239-13.94762 -12.89161 (239*2π)/3201 weeks
2401.77122 19.42731 (240*2π)/3201 weeks
241-4.42467 -24.81491 (241*2π)/3201 weeks
24222.00047 -15.56517 (242*2π)/3201 weeks
243-5.44117 2.25796 (243*2π)/3201 weeks
2447.7816 -13.64705 (244*2π)/3201 weeks
245-13.04285 18.26333 (245*2π)/3201 weeks
24617.08699 -16.69317 (246*2π)/3201 weeks
247-.61894 -16.96813 (247*2π)/3201 weeks
2488.34905 10.49267 (248*2π)/3201 weeks
2497.98043 -5.46931 (249*2π)/3201 weeks
2502.70463 -15.73394 (250*2π)/3201 weeks
2511.34767 6.3846 (251*2π)/3201 weeks
2522.38371 -13.08171 (252*2π)/3201 weeks
2534.92836 18.31908 (253*2π)/3201 weeks
254-1.54038 -7.08772 (254*2π)/3201 weeks
25530.13794 -25.18714 (255*2π)/3201 weeks
256-27.42376 7.35206 (256*2π)/3201 weeks
25712.86082 -10.11983 (257*2π)/3201 weeks
258-.92826 21.87826 (258*2π)/3201 weeks
259-2.37762 -32.77919 (259*2π)/3201 weeks
26037.24447 -1.35098 (260*2π)/3201 weeks
261-30.01664 -2.08301 (261*2π)/3201 weeks
26222.74368 -16.73133 (262*2π)/3201 weeks
2634.57323 7.35768 (263*2π)/3201 weeks
264-7.23996 -11.09276 (264*2π)/3201 weeks
26526.33302 10.27431 (265*2π)/3201 weeks
266-21.59312 -1.9555 (266*2π)/3201 weeks
26718.69648 -17.70399 (267*2π)/3201 weeks
2682.45735 -4.50649 (268*2π)/3201 weeks
269-20.51625 -11.79749 (269*2π)/3201 weeks
27011.72681 18.32324 (270*2π)/3201 weeks
2712.98184 -22.31636 (271*2π)/3201 weeks
2724.66436 -33.60058 (272*2π)/3201 weeks
2736.6315 2.71262 (273*2π)/3201 weeks
27418.66639 -5.05591 (274*2π)/3201 weeks
27510.3415 8.15648 (275*2π)/3201 weeks
27612.09826 -22.09175 (276*2π)/3201 weeks
277-1.18874 -2.8727 (277*2π)/3201 weeks
278-13.06486 32.02059 (278*2π)/3201 weeks
27936.66111 -8.29214 (279*2π)/3201 weeks
280-22.22551 -17.88919 (280*2π)/3201 weeks
2816.38388 -35.19952 (281*2π)/3201 weeks
282-11.54225 25.98855 (282*2π)/3201 weeks
2835.91081 5.26017 (283*2π)/3201 weeks
28423.96253 -9.93157 (284*2π)/3201 weeks
28511.85911 -9.73117 (285*2π)/3201 weeks
286-30.76198 -31.49491 (286*2π)/3201 weeks
28712.61122 35.35421 (287*2π)/3201 weeks
288-37.57339 -13.81991 (288*2π)/3201 weeks
28923.75529 -43.39492 (289*2π)/3201 weeks
2908.59952 34.17336 (290*2π)/3201 weeks
2917.82337 -61.05779 (291*2π)/3201 weeks
2922.10592 31.12835 (292*2π)/3201 weeks
293-36.70797 -39.12595 (293*2π)/3201 weeks
29442.05343 10.47652 (294*2π)/3201 weeks
295-39.03327 -12.86841 (295*2π)/3201 weeks
29623.688 -28.88296 (296*2π)/3201 weeks
297-7.72395 -19.77929 (297*2π)/3201 weeks
29835.94897 -4.85681 (298*2π)/3201 weeks
299-20.75451 25.96382 (299*2π)/3201 weeks
300-14.66673 -39.86798 (300*2π)/3201 weeks
301-17.28457 -37.17085 (301*2π)/3201 weeks
302-11.6045 12.72498 (302*2π)/3201 weeks
30320.64653 3.71042 (303*2π)/3201 weeks
30428.13174 -56.71266 (304*2π)/3201 weeks
305-77.45193 -104.3987 (305*2π)/3201 weeks
30617.3553 80.50679 (306*2π)/3201 weeks
307-7.84358 -139.3546 (307*2π)/3201 weeks
30886.76022 65.95209 (308*2π)/3201 weeks
309-30.19613 -83.53619 (309*2π)/3201 weeks
31013.8712 -37.84536 (310*2π)/3201 weeks
311-45.32408 19.56454 (311*2π)/3201 weeks
312122.674 -133.571 (312*2π)/3201 weeks
313-102.3272 39.48603 (313*2π)/3201 weeks
314-95.21632 -4.36767 (314*2π)/3201 weeks
315190.4116 -178.8441 (315*2π)/3201 weeks
31665.37199 30.44451 (316*2π)/3201 weeks
317-85.5621 -354.2578 (317*2π)/3201 weeks
31867.22854 -48.75558 (318*2π)/3201 weeks

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