Back to list of Stocks    See Also: Seasonal Analysis of DUSTGenetic Algorithms Stock Portfolio Generator, and Fourier Calculator

Fourier Analysis of DUST (Direxion Daily Gold Miners Inde)


DUST (Direxion Daily Gold Miners Inde) appears to have interesting cyclic behaviour every 25 weeks (114.575*sine), 22 weeks (114.4473*sine), and 24 weeks (96.4715*cosine).

DUST (Direxion Daily Gold Miners Inde) has an average price of 970.73 (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 3/20/2017 for DUST (Direxion Daily Gold Miners Inde), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0970.7324   0 
1-545.6692 274.4865 (1*2π)/329329 weeks
261.50967 60.51185 (2*2π)/329165 weeks
3-6.75 365.8712 (3*2π)/329110 weeks
441.46059 -57.1797 (4*2π)/32982 weeks
5194.2861 96.1104 (5*2π)/32966 weeks
6-146.4022 58.93554 (6*2π)/32955 weeks
7-98.20226 36.68981 (7*2π)/32947 weeks
8162.4946 36.63434 (8*2π)/32941 weeks
9-85.90456 36.61096 (9*2π)/32937 weeks
1029.93566 35.9136 (10*2π)/32933 weeks
1123.5615 67.30508 (11*2π)/32930 weeks
12-25.73773 -75.36082 (12*2π)/32927 weeks
1382.21163 114.575 (13*2π)/32925 weeks
14-96.47147 -2.75355 (14*2π)/32924 weeks
1580.72734 114.4473 (15*2π)/32922 weeks
16-2.33613 -34.12063 (16*2π)/32921 weeks
17-47.99343 13.00918 (17*2π)/32919 weeks
18-13.489 44.08403 (18*2π)/32918 weeks
1930.52501 25.84347 (19*2π)/32917 weeks
20-3.81418 14.16372 (20*2π)/32916 weeks
21-41.17687 16.22182 (21*2π)/32916 weeks
229.77657 -27.25736 (22*2π)/32915 weeks
2325.0663 27.73722 (23*2π)/32914 weeks
24.68941 2.94479 (24*2π)/32914 weeks
255.49078 44.84201 (25*2π)/32913 weeks
26-29.80591 -14.32747 (26*2π)/32913 weeks
2746.21517 24.90796 (27*2π)/32912 weeks
28-41.32184 11.78416 (28*2π)/32912 weeks
2923.3579 -27.92972 (29*2π)/32911 weeks
30-22.57221 52.7489 (30*2π)/32911 weeks
3125.28559 -24.90415 (31*2π)/32911 weeks
3214.27136 47.52088 (32*2π)/32910 weeks
33-35.8006 7.39285 (33*2π)/32910 weeks
3421.00601 -31.45249 (34*2π)/32910 weeks
35-33.37189 24.67083 (35*2π)/3299 weeks
3610.55976 9.98353 (36*2π)/3299 weeks
3723.42602 8.43605 (37*2π)/3299 weeks
383.09063 -6.3083 (38*2π)/3299 weeks
39-17.38212 -19.25086 (39*2π)/3298 weeks
4015.41292 35.03398 (40*2π)/3298 weeks
41-13.35969 21.09232 (41*2π)/3298 weeks
4231.85257 -13.71587 (42*2π)/3298 weeks
43-31.38373 -15.41936 (43*2π)/3298 weeks
448.16418 10.71588 (44*2π)/3297 weeks
4524.24639 10.28327 (45*2π)/3297 weeks
46-.9621 -8.92787 (46*2π)/3297 weeks
4714.47398 .63359 (47*2π)/3297 weeks
482.36817 9.97135 (48*2π)/3297 weeks
4926.77169 22.78931 (49*2π)/3297 weeks
501.10812 8.73096 (50*2π)/3297 weeks
51-22.28383 -3.51656 (51*2π)/3296 weeks
5210.36309 29.45576 (52*2π)/3296 weeks
534.14236 -6.69752 (53*2π)/3296 weeks
5410.04737 -5.16596 (54*2π)/3296 weeks
55-8.839 24.22031 (55*2π)/3296 weeks
56-7.91721 -20.49151 (56*2π)/3296 weeks
5718.14384 18.45152 (57*2π)/3296 weeks
58-4.41003 -1.07694 (58*2π)/3296 weeks
5914.9865 -6.34325 (59*2π)/3296 weeks
607.36184 29.92124 (60*2π)/3295 weeks
61-12.80753 -27.03072 (61*2π)/3295 weeks
6226.40634 20.46228 (62*2π)/3295 weeks
63-20.38061 25.07819 (63*2π)/3295 weeks
6414.76741 -12.27118 (64*2π)/3295 weeks
6510.97074 16.41878 (65*2π)/3295 weeks
66-14.67161 -25.97417 (66*2π)/3295 weeks
6713.24848 31.70736 (67*2π)/3295 weeks
68-2.60649 9.44509 (68*2π)/3295 weeks
6912.35916 -15.3546 (69*2π)/3295 weeks
70.61096 11.41582 (70*2π)/3295 weeks
713.25264 -6.88372 (71*2π)/3295 weeks
721.41265 14.93405 (72*2π)/3295 weeks
737.77827 5.45935 (73*2π)/3295 weeks
746.92915 -10.1928 (74*2π)/3294 weeks
751.58499 17.89832 (75*2π)/3294 weeks
7617.64724 11.13118 (76*2π)/3294 weeks
77-20.04143 -11.20689 (77*2π)/3294 weeks
7812.56315 12.29569 (78*2π)/3294 weeks
79-5.20854 3.22625 (79*2π)/3294 weeks
8024.4798 5.17652 (80*2π)/3294 weeks
811.70777 21.5305 (81*2π)/3294 weeks
82-18.08648 -13.15506 (82*2π)/3294 weeks
831.08161 21.23183 (83*2π)/3294 weeks
84-1.71746 -2.53909 (84*2π)/3294 weeks
855.5232 -12.40301 (85*2π)/3294 weeks
869.33015 10.0814 (86*2π)/3294 weeks
87-7.39187 -6.18676 (87*2π)/3294 weeks
8811.34166 12.11341 (88*2π)/3294 weeks
894.5179 7.96465 (89*2π)/3294 weeks
90-.34893 -14.42885 (90*2π)/3294 weeks
913.08303 20.32364 (91*2π)/3294 weeks
927.43929 -1.10765 (92*2π)/3294 weeks
93-3.9055 -1.63398 (93*2π)/3294 weeks
944.04308 12.5558 (94*2π)/3294 weeks
95-.36187 -11.63219 (95*2π)/3293 weeks
968.61021 20.57924 (96*2π)/3293 weeks
97-5.54106 -14.5123 (97*2π)/3293 weeks
9812.91398 10.21875 (98*2π)/3293 weeks
99-11.12574 3.11851 (99*2π)/3293 weeks
10011.16418 .48529 (100*2π)/3293 weeks
101-3.24116 2.36886 (101*2π)/3293 weeks
10210.48713 -2.93041 (102*2π)/3293 weeks
103-7.61276 9.10778 (103*2π)/3293 weeks
1049.22829 2.44396 (104*2π)/3293 weeks
1051.276 -3.24579 (105*2π)/3293 weeks
106-4.9718 -.59422 (106*2π)/3293 weeks
10716.50064 10.94983 (107*2π)/3293 weeks
108-5.13519 -3.86396 (108*2π)/3293 weeks
1096.16529 .50926 (109*2π)/3293 weeks
110.63783 5.13651 (110*2π)/3293 weeks
111.93386 -.17737 (111*2π)/3293 weeks
1124.10448 12.26612 (112*2π)/3293 weeks
1131.05301 -6.85978 (113*2π)/3293 weeks
1145.07595 -1.05259 (114*2π)/3293 weeks
115-2.49573 7.68208 (115*2π)/3293 weeks
116-.86892 1.34226 (116*2π)/3293 weeks
1173.36793 1.30176 (117*2π)/3293 weeks
1185.8935 -7.31687 (118*2π)/3293 weeks
1194.83588 1.08137 (119*2π)/3293 weeks
1201.66981 7.96247 (120*2π)/3293 weeks
121-1.78547 3.61165 (121*2π)/3293 weeks
1224.75179 1.32344 (122*2π)/3293 weeks
1232.35535 -10.72464 (123*2π)/3293 weeks
1243.24424 -1.59322 (124*2π)/3293 weeks
125-1.86188 17.36189 (125*2π)/3293 weeks
12613.10472 -6.43253 (126*2π)/3293 weeks
1271.71236 6.38325 (127*2π)/3293 weeks
128-4.60503 -2.32187 (128*2π)/3293 weeks
129-2.19699 2.51851 (129*2π)/3293 weeks
1307.06274 .59171 (130*2π)/3293 weeks
1317.08155 2.96399 (131*2π)/3293 weeks
132-5.73182 -.50931 (132*2π)/3292 weeks
1334.08622 3.92488 (133*2π)/3292 weeks
134-4.37917 -5.09341 (134*2π)/3292 weeks
1358.13284 5.63045 (135*2π)/3292 weeks
136-7.63735 -7.86254 (136*2π)/3292 weeks
13711.81987 -1.26974 (137*2π)/3292 weeks
138-1.22895 5.51023 (138*2π)/3292 weeks
1395.99514 -16.86396 (139*2π)/3292 weeks
140.05293 17.63115 (140*2π)/3292 weeks
141.32947 -6.34715 (141*2π)/3292 weeks
1427.88591 -4.24693 (142*2π)/3292 weeks
1433.61821 .63745 (143*2π)/3292 weeks
1444.00386 -6.24651 (144*2π)/3292 weeks
1452.96169 6.23083 (145*2π)/3292 weeks
1464.26544 8.81061 (146*2π)/3292 weeks
1478.81446 -17.10785 (147*2π)/3292 weeks
1481.82256 13.04618 (148*2π)/3292 weeks
1492.46519 -3.34971 (149*2π)/3292 weeks
1509.84809 6.65372 (150*2π)/3292 weeks
151-10.72404 4.8992 (151*2π)/3292 weeks
1529.75175 -15.81725 (152*2π)/3292 weeks
1534.22085 9.23766 (153*2π)/3292 weeks
1546.64933 -.75897 (154*2π)/3292 weeks
155-1.56756 -.16327 (155*2π)/3292 weeks
156-.29935 12.42754 (156*2π)/3292 weeks
1578.22955 -14.41315 (157*2π)/3292 weeks
158-.83582 7.92257 (158*2π)/3292 weeks
159-1.91375 -2.53278 (159*2π)/3292 weeks
16010.67359 -7.88784 (160*2π)/3292 weeks
161-6.29102 11.51609 (161*2π)/3292 weeks
16218.95297 -4.65995 (162*2π)/3292 weeks
163-6.74436 1.09186 (163*2π)/3292 weeks
1643.31118 2.91629 (164*2π)/3292 weeks
1653.31118 -2.91629 (165*2π)/3292 weeks
166-6.74436 -1.09186 (166*2π)/3292 weeks
16718.95297 4.65995 (167*2π)/3292 weeks
168-6.29102 -11.51609 (168*2π)/3292 weeks
16910.67359 7.88784 (169*2π)/3292 weeks
170-1.91375 2.53278 (170*2π)/3292 weeks
171-.83582 -7.92257 (171*2π)/3292 weeks
1728.22955 14.41315 (172*2π)/3292 weeks
173-.29935 -12.42754 (173*2π)/3292 weeks
174-1.56756 .16327 (174*2π)/3292 weeks
1756.64933 .75897 (175*2π)/3292 weeks
1764.22085 -9.23766 (176*2π)/3292 weeks
1779.75175 15.81725 (177*2π)/3292 weeks
178-10.72404 -4.8992 (178*2π)/3292 weeks
1799.84809 -6.65372 (179*2π)/3292 weeks
1802.46519 3.34971 (180*2π)/3292 weeks
1811.82256 -13.04618 (181*2π)/3292 weeks
1828.81446 17.10785 (182*2π)/3292 weeks
1834.26544 -8.81061 (183*2π)/3292 weeks
1842.96169 -6.23083 (184*2π)/3292 weeks
1854.00386 6.24651 (185*2π)/3292 weeks
1863.61821 -.63745 (186*2π)/3292 weeks
1877.88591 4.24693 (187*2π)/3292 weeks
188.32947 6.34715 (188*2π)/3292 weeks
189.05293 -17.63115 (189*2π)/3292 weeks
1905.99514 16.86396 (190*2π)/3292 weeks
191-1.22895 -5.51023 (191*2π)/3292 weeks
19211.81987 1.26974 (192*2π)/3292 weeks
193-7.63735 7.86254 (193*2π)/3292 weeks
1948.13284 -5.63045 (194*2π)/3292 weeks
195-4.37917 5.09341 (195*2π)/3292 weeks
1964.08622 -3.92488 (196*2π)/3292 weeks
197-5.73182 .50931 (197*2π)/3292 weeks
1987.08155 -2.96399 (198*2π)/3292 weeks
1997.06274 -.59171 (199*2π)/3292 weeks
200-2.19699 -2.51851 (200*2π)/3292 weeks
201-4.60503 2.32187 (201*2π)/3292 weeks
2021.71236 -6.38325 (202*2π)/3292 weeks
20313.10472 6.43253 (203*2π)/3292 weeks
204-1.86188 -17.36189 (204*2π)/3292 weeks
2053.24424 1.59322 (205*2π)/3292 weeks
2062.35535 10.72464 (206*2π)/3292 weeks
2074.75179 -1.32344 (207*2π)/3292 weeks
208-1.78547 -3.61165 (208*2π)/3292 weeks
2091.66981 -7.96247 (209*2π)/3292 weeks
2104.83588 -1.08137 (210*2π)/3292 weeks
2115.8935 7.31687 (211*2π)/3292 weeks
2123.36793 -1.30176 (212*2π)/3292 weeks
213-.86892 -1.34226 (213*2π)/3292 weeks
214-2.49573 -7.68208 (214*2π)/3292 weeks
2155.07595 1.05259 (215*2π)/3292 weeks
2161.05301 6.85978 (216*2π)/3292 weeks
2174.10448 -12.26612 (217*2π)/3292 weeks
218.93386 .17737 (218*2π)/3292 weeks
219.63783 -5.13651 (219*2π)/3292 weeks
2206.16529 -.50926 (220*2π)/3291 weeks
221-5.13519 3.86396 (221*2π)/3291 weeks
22216.50064 -10.94983 (222*2π)/3291 weeks
223-4.9718 .59422 (223*2π)/3291 weeks
2241.276 3.24579 (224*2π)/3291 weeks
2259.22829 -2.44396 (225*2π)/3291 weeks
226-7.61276 -9.10778 (226*2π)/3291 weeks
22710.48713 2.93041 (227*2π)/3291 weeks
228-3.24116 -2.36886 (228*2π)/3291 weeks
22911.16418 -.48529 (229*2π)/3291 weeks
230-11.12574 -3.11851 (230*2π)/3291 weeks
23112.91398 -10.21875 (231*2π)/3291 weeks
232-5.54106 14.5123 (232*2π)/3291 weeks
2338.61021 -20.57924 (233*2π)/3291 weeks
234-.36187 11.63219 (234*2π)/3291 weeks
2354.04308 -12.5558 (235*2π)/3291 weeks
236-3.9055 1.63398 (236*2π)/3291 weeks
2377.43929 1.10765 (237*2π)/3291 weeks
2383.08303 -20.32364 (238*2π)/3291 weeks
239-.34893 14.42885 (239*2π)/3291 weeks
2404.5179 -7.96465 (240*2π)/3291 weeks
24111.34166 -12.11341 (241*2π)/3291 weeks
242-7.39187 6.18676 (242*2π)/3291 weeks
2439.33015 -10.0814 (243*2π)/3291 weeks
2445.5232 12.40301 (244*2π)/3291 weeks
245-1.71746 2.53909 (245*2π)/3291 weeks
2461.08161 -21.23183 (246*2π)/3291 weeks
247-18.08648 13.15506 (247*2π)/3291 weeks
2481.70777 -21.5305 (248*2π)/3291 weeks
24924.4798 -5.17652 (249*2π)/3291 weeks
250-5.20854 -3.22625 (250*2π)/3291 weeks
25112.56315 -12.29569 (251*2π)/3291 weeks
252-20.04143 11.20689 (252*2π)/3291 weeks
25317.64724 -11.13118 (253*2π)/3291 weeks
2541.58499 -17.89832 (254*2π)/3291 weeks
2556.92915 10.1928 (255*2π)/3291 weeks
2567.77827 -5.45935 (256*2π)/3291 weeks
2571.41265 -14.93405 (257*2π)/3291 weeks
2583.25264 6.88372 (258*2π)/3291 weeks
259.61096 -11.41582 (259*2π)/3291 weeks
26012.35916 15.3546 (260*2π)/3291 weeks
261-2.60649 -9.44509 (261*2π)/3291 weeks
26213.24848 -31.70736 (262*2π)/3291 weeks
263-14.67161 25.97417 (263*2π)/3291 weeks
26410.97074 -16.41878 (264*2π)/3291 weeks
26514.76741 12.27118 (265*2π)/3291 weeks
266-20.38061 -25.07819 (266*2π)/3291 weeks
26726.40634 -20.46228 (267*2π)/3291 weeks
268-12.80753 27.03072 (268*2π)/3291 weeks
2697.36184 -29.92124 (269*2π)/3291 weeks
27014.9865 6.34325 (270*2π)/3291 weeks
271-4.41003 1.07694 (271*2π)/3291 weeks
27218.14384 -18.45152 (272*2π)/3291 weeks
273-7.91721 20.49151 (273*2π)/3291 weeks
274-8.839 -24.22031 (274*2π)/3291 weeks
27510.04737 5.16596 (275*2π)/3291 weeks
2764.14236 6.69752 (276*2π)/3291 weeks
27710.36309 -29.45576 (277*2π)/3291 weeks
278-22.28383 3.51656 (278*2π)/3291 weeks
2791.10812 -8.73096 (279*2π)/3291 weeks
28026.77169 -22.78931 (280*2π)/3291 weeks
2812.36817 -9.97135 (281*2π)/3291 weeks
28214.47398 -.63359 (282*2π)/3291 weeks
283-.9621 8.92787 (283*2π)/3291 weeks
28424.24639 -10.28327 (284*2π)/3291 weeks
2858.16418 -10.71588 (285*2π)/3291 weeks
286-31.38373 15.41936 (286*2π)/3291 weeks
28731.85257 13.71587 (287*2π)/3291 weeks
288-13.35969 -21.09232 (288*2π)/3291 weeks
28915.41292 -35.03398 (289*2π)/3291 weeks
290-17.38212 19.25086 (290*2π)/3291 weeks
2913.09063 6.3083 (291*2π)/3291 weeks
29223.42602 -8.43605 (292*2π)/3291 weeks
29310.55976 -9.98353 (293*2π)/3291 weeks
294-33.37189 -24.67083 (294*2π)/3291 weeks
29521.00601 31.45249 (295*2π)/3291 weeks
296-35.8006 -7.39285 (296*2π)/3291 weeks
29714.27136 -47.52088 (297*2π)/3291 weeks
29825.28559 24.90415 (298*2π)/3291 weeks
299-22.57221 -52.7489 (299*2π)/3291 weeks
30023.3579 27.92972 (300*2π)/3291 weeks
301-41.32184 -11.78416 (301*2π)/3291 weeks
30246.21517 -24.90796 (302*2π)/3291 weeks
303-29.80591 14.32747 (303*2π)/3291 weeks
3045.49078 -44.84201 (304*2π)/3291 weeks
305.68941 -2.94479 (305*2π)/3291 weeks
30625.0663 -27.73722 (306*2π)/3291 weeks
3079.77657 27.25736 (307*2π)/3291 weeks
308-41.17687 -16.22182 (308*2π)/3291 weeks
309-3.81418 -14.16372 (309*2π)/3291 weeks
31030.52501 -25.84347 (310*2π)/3291 weeks
311-13.489 -44.08403 (311*2π)/3291 weeks
312-47.99343 -13.00918 (312*2π)/3291 weeks
313-2.33613 34.12063 (313*2π)/3291 weeks
31480.72734 -114.4473 (314*2π)/3291 weeks
315-96.47147 2.75355 (315*2π)/3291 weeks
31682.21163 -114.575 (316*2π)/3291 weeks
317-25.73773 75.36082 (317*2π)/3291 weeks
31823.5615 -67.30508 (318*2π)/3291 weeks
31929.93566 -35.9136 (319*2π)/3291 weeks
320-85.90456 -36.61096 (320*2π)/3291 weeks
321162.4946 -36.63434 (321*2π)/3291 weeks
322-98.20226 -36.68981 (322*2π)/3291 weeks
323-146.4022 -58.93554 (323*2π)/3291 weeks
324194.2861 -96.1104 (324*2π)/3291 weeks
32541.46059 57.1797 (325*2π)/3291 weeks
326-6.75 -365.8712 (326*2π)/3291 weeks
32761.50967 -60.51185 (327*2π)/3291 weeks

Problems, Comments, Suggestions? Click here to contact Greg Thatcher

Please read my Disclaimer





Copyright (c) 2013 Thatcher Development Software, LLC. All rights reserved. No claim to original U.S. Gov't works.