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


JDST (Direxion Daily Junior Gold Miners Index Bear 3x Shares ETF) appears to have interesting cyclic behaviour every 21 weeks (2373.476*cosine), 8 weeks (1132.162*sine), and 18 weeks (968.0917*cosine).

JDST (Direxion Daily Junior Gold Miners Index Bear 3x Shares ETF) has an average price of 8,683.54 (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 10/3/2013 to 10/9/2017 for JDST (Direxion Daily Junior Gold Miners Index Bear 3x Shares ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
08,683.544   0 
15,445.802 8,229.8 (1*2π)/211211 weeks
24,446.993 4,575.253 (2*2π)/211106 weeks
32,366.47 4,427.015 (3*2π)/21170 weeks
42,480.403 5,030.995 (4*2π)/21153 weeks
534.57943 4,276.129 (5*2π)/21142 weeks
6-92.03725 2,864.125 (6*2π)/21135 weeks
7671.5071 2,972.832 (7*2π)/21130 weeks
8-737.8832 3,474.516 (8*2π)/21126 weeks
9-1,723.326 2,741.919 (9*2π)/21123 weeks
10-2,373.476 559.8284 (10*2π)/21121 weeks
11-633.787 161.1358 (11*2π)/21119 weeks
12-968.0917 93.0426 (12*2π)/21118 weeks
13-195.5154 -478.1512 (13*2π)/21116 weeks
14323.031 -102.3106 (14*2π)/21115 weeks
15277.9047 -48.52954 (15*2π)/21114 weeks
16490.5258 43.47398 (16*2π)/21113 weeks
17589.1321 -38.35681 (17*2π)/21112 weeks
18751.4706 262.2563 (18*2π)/21112 weeks
19871.2776 232.5048 (19*2π)/21111 weeks
20775.9189 690.4487 (20*2π)/21111 weeks
21485.8127 666.029 (21*2π)/21110 weeks
22415.4453 231.7578 (22*2π)/21110 weeks
23892.1154 649.8259 (23*2π)/2119 weeks
24514.0834 553.4213 (24*2π)/2119 weeks
25656.611 870.3362 (25*2π)/2118 weeks
26460.2043 677.4301 (26*2π)/2118 weeks
27353.5399 1,132.162 (27*2π)/2118 weeks
28-183.2565 672.8327 (28*2π)/2118 weeks
29113.4747 388.3767 (29*2π)/2117 weeks
30224.5869 466.0211 (30*2π)/2117 weeks
31199.8304 558.8979 (31*2π)/2117 weeks
32-86.93534 455.7443 (32*2π)/2117 weeks
33282.6236 102.167 (33*2π)/2116 weeks
34286.0935 580.2794 (34*2π)/2116 weeks
35.3869 340.396 (35*2π)/2116 weeks
36152.0044 54.99118 (36*2π)/2116 weeks
37536.4279 227.5456 (37*2π)/2116 weeks
38412.8452 481.7652 (38*2π)/2116 weeks
39187.735 524.8568 (39*2π)/2115 weeks
40257.3442 279.3923 (40*2π)/2115 weeks
41262.3488 434.2482 (41*2π)/2115 weeks
42301.4642 468.8333 (42*2π)/2115 weeks
43-26.2563 442.0417 (43*2π)/2115 weeks
44236.5387 163.3545 (44*2π)/2115 weeks
45288.8567 347.1108 (45*2π)/2115 weeks
46193.4536 460.3465 (46*2π)/2115 weeks
477.90783 218.2742 (47*2π)/2114 weeks
48377.1003 37.87818 (48*2π)/2114 weeks
49563.6439 495.6199 (49*2π)/2114 weeks
50160.3307 544.101 (50*2π)/2114 weeks
51167.4366 454.0748 (51*2π)/2114 weeks
52193.3521 337.9276 (52*2π)/2114 weeks
53228.5625 603.6262 (53*2π)/2114 weeks
54-86.90764 470.0154 (54*2π)/2114 weeks
55-28.44076 308.3792 (55*2π)/2114 weeks
5687.72406 252.5167 (56*2π)/2114 weeks
5719.69956 421.337 (57*2π)/2114 weeks
58-155.3271 155.3091 (58*2π)/2114 weeks
59170.4418 -24.16584 (59*2π)/2114 weeks
60356.8246 228.6854 (60*2π)/2114 weeks
61262.2864 413.4989 (61*2π)/2113 weeks
62118.7315 473.8936 (62*2π)/2113 weeks
63-13.01961 444.0378 (63*2π)/2113 weeks
64-88.9641 335.5276 (64*2π)/2113 weeks
65-74.11835 277.5287 (65*2π)/2113 weeks
66-135.4391 217.8424 (66*2π)/2113 weeks
67-52.20609 53.93932 (67*2π)/2113 weeks
68113.1686 150.5958 (68*2π)/2113 weeks
69-25.00582 232.0415 (69*2π)/2113 weeks
70-26.42327 114.5215 (70*2π)/2113 weeks
7121.42714 79.23674 (71*2π)/2113 weeks
7282.16198 121.211 (72*2π)/2113 weeks
7370.58398 108.9482 (73*2π)/2113 weeks
7494.40807 170.9203 (74*2π)/2113 weeks
7578.56998 131.9755 (75*2π)/2113 weeks
76104.6572 240.9129 (76*2π)/2113 weeks
7712.87999 240.0615 (77*2π)/2113 weeks
78-75.51495 255.4479 (78*2π)/2113 weeks
79-52.05983 153.7744 (79*2π)/2113 weeks
80-218.8842 246.2108 (80*2π)/2113 weeks
81-201.9284 -43.66446 (81*2π)/2113 weeks
82-157.0151 -13.03204 (82*2π)/2113 weeks
83-88.20904 -110.1751 (83*2π)/2113 weeks
84-98.96705 -87.79447 (84*2π)/2113 weeks
85-69.4929 -172.6384 (85*2π)/2112 weeks
86-12.15928 -236.4352 (86*2π)/2112 weeks
8796.397 -253.0101 (87*2π)/2112 weeks
88174.1827 -204.2017 (88*2π)/2112 weeks
89137.8942 -229.6963 (89*2π)/2112 weeks
90376.6848 -248.3172 (90*2π)/2112 weeks
91368.2921 -33.49828 (91*2π)/2112 weeks
92322.6507 33.554 (92*2π)/2112 weeks
93236.9232 -18.48216 (93*2π)/2112 weeks
94397.0874 30.82446 (94*2π)/2112 weeks
95270.795 192.648 (95*2π)/2112 weeks
96194.5986 122.1441 (96*2π)/2112 weeks
97205.4933 109.9716 (97*2π)/2112 weeks
98252.4454 160.0332 (98*2π)/2112 weeks
99138.4449 316.0857 (99*2π)/2112 weeks
100-123.2959 154.5793 (100*2π)/2112 weeks
10176.19818 -49.98865 (101*2π)/2112 weeks
102139.3352 124.1797 (102*2π)/2112 weeks
103-40.81025 179.1492 (103*2π)/2112 weeks
104-121.2111 -100.7562 (104*2π)/2112 weeks
105174.5438 -130.45 (105*2π)/2112 weeks
106174.5438 130.45 (106*2π)/2112 weeks
107-121.2111 100.7562 (107*2π)/2112 weeks
108-40.81025 -179.1492 (108*2π)/2112 weeks
109139.3352 -124.1797 (109*2π)/2112 weeks
11076.19818 49.98865 (110*2π)/2112 weeks
111-123.2959 -154.5793 (111*2π)/2112 weeks
112138.4449 -316.0857 (112*2π)/2112 weeks
113252.4454 -160.0332 (113*2π)/2112 weeks
114205.4933 -109.9716 (114*2π)/2112 weeks
115194.5986 -122.1441 (115*2π)/2112 weeks
116270.795 -192.648 (116*2π)/2112 weeks
117397.0874 -30.82446 (117*2π)/2112 weeks
118236.9232 18.48216 (118*2π)/2112 weeks
119322.6507 -33.554 (119*2π)/2112 weeks
120368.2921 33.49828 (120*2π)/2112 weeks
121376.6848 248.3172 (121*2π)/2112 weeks
122137.8942 229.6963 (122*2π)/2112 weeks
123174.1827 204.2017 (123*2π)/2112 weeks
12496.397 253.0101 (124*2π)/2112 weeks
125-12.15928 236.4352 (125*2π)/2112 weeks
126-69.4929 172.6384 (126*2π)/2112 weeks
127-98.96705 87.79447 (127*2π)/2112 weeks
128-88.20904 110.1751 (128*2π)/2112 weeks
129-157.0151 13.03204 (129*2π)/2112 weeks
130-201.9284 43.66446 (130*2π)/2112 weeks
131-218.8842 -246.2108 (131*2π)/2112 weeks
132-52.05983 -153.7744 (132*2π)/2112 weeks
133-75.51495 -255.4479 (133*2π)/2112 weeks
13412.87999 -240.0615 (134*2π)/2112 weeks
135104.6572 -240.9129 (135*2π)/2112 weeks
13678.56998 -131.9755 (136*2π)/2112 weeks
13794.40807 -170.9203 (137*2π)/2112 weeks
13870.58398 -108.9482 (138*2π)/2112 weeks
13982.16198 -121.211 (139*2π)/2112 weeks
14021.42714 -79.23674 (140*2π)/2112 weeks
141-26.42327 -114.5215 (141*2π)/2111 weeks
142-25.00582 -232.0415 (142*2π)/2111 weeks
143113.1686 -150.5958 (143*2π)/2111 weeks
144-52.20609 -53.93932 (144*2π)/2111 weeks
145-135.4391 -217.8424 (145*2π)/2111 weeks
146-74.11835 -277.5287 (146*2π)/2111 weeks
147-88.9641 -335.5276 (147*2π)/2111 weeks
148-13.01961 -444.0378 (148*2π)/2111 weeks
149118.7315 -473.8936 (149*2π)/2111 weeks
150262.2864 -413.4989 (150*2π)/2111 weeks
151356.8246 -228.6854 (151*2π)/2111 weeks
152170.4418 24.16584 (152*2π)/2111 weeks
153-155.3271 -155.3091 (153*2π)/2111 weeks
15419.69956 -421.337 (154*2π)/2111 weeks
15587.72406 -252.5167 (155*2π)/2111 weeks
156-28.44076 -308.3792 (156*2π)/2111 weeks
157-86.90764 -470.0154 (157*2π)/2111 weeks
158228.5625 -603.6262 (158*2π)/2111 weeks
159193.3521 -337.9276 (159*2π)/2111 weeks
160167.4366 -454.0748 (160*2π)/2111 weeks
161160.3307 -544.101 (161*2π)/2111 weeks
162563.6439 -495.6199 (162*2π)/2111 weeks
163377.1003 -37.87818 (163*2π)/2111 weeks
1647.90783 -218.2742 (164*2π)/2111 weeks
165193.4536 -460.3465 (165*2π)/2111 weeks
166288.8567 -347.1108 (166*2π)/2111 weeks
167236.5387 -163.3545 (167*2π)/2111 weeks
168-26.2563 -442.0417 (168*2π)/2111 weeks
169301.4642 -468.8333 (169*2π)/2111 weeks
170262.3488 -434.2482 (170*2π)/2111 weeks
171257.3442 -279.3923 (171*2π)/2111 weeks
172187.735 -524.8568 (172*2π)/2111 weeks
173412.8452 -481.7652 (173*2π)/2111 weeks
174536.4279 -227.5456 (174*2π)/2111 weeks
175152.0044 -54.99118 (175*2π)/2111 weeks
176.3869 -340.396 (176*2π)/2111 weeks
177286.0935 -580.2794 (177*2π)/2111 weeks
178282.6236 -102.167 (178*2π)/2111 weeks
179-86.93534 -455.7443 (179*2π)/2111 weeks
180199.8304 -558.8979 (180*2π)/2111 weeks
181224.5869 -466.0211 (181*2π)/2111 weeks
182113.4747 -388.3767 (182*2π)/2111 weeks
183-183.2565 -672.8327 (183*2π)/2111 weeks
184353.5399 -1,132.162 (184*2π)/2111 weeks
185460.2043 -677.4301 (185*2π)/2111 weeks
186656.611 -870.3362 (186*2π)/2111 weeks
187514.0834 -553.4213 (187*2π)/2111 weeks
188892.1154 -649.8259 (188*2π)/2111 weeks
189415.4453 -231.7578 (189*2π)/2111 weeks
190485.8127 -666.029 (190*2π)/2111 weeks
191775.9189 -690.4487 (191*2π)/2111 weeks
192871.2776 -232.5048 (192*2π)/2111 weeks
193751.4706 -262.2563 (193*2π)/2111 weeks
194589.1321 38.35681 (194*2π)/2111 weeks
195490.5258 -43.47398 (195*2π)/2111 weeks
196277.9047 48.52954 (196*2π)/2111 weeks
197323.031 102.3106 (197*2π)/2111 weeks
198-195.5154 478.1512 (198*2π)/2111 weeks
199-968.0917 -93.0426 (199*2π)/2111 weeks
200-633.787 -161.1358 (200*2π)/2111 weeks
201-2,373.476 -559.8284 (201*2π)/2111 weeks
202-1,723.326 -2,741.919 (202*2π)/2111 weeks
203-737.8832 -3,474.516 (203*2π)/2111 weeks
204671.5071 -2,972.832 (204*2π)/2111 weeks
205-92.03725 -2,864.125 (205*2π)/2111 weeks
20634.57943 -4,276.129 (206*2π)/2111 weeks
2072,480.403 -5,030.995 (207*2π)/2111 weeks
2082,366.47 -4,427.015 (208*2π)/2111 weeks
2094,446.993 -4,575.253 (209*2π)/2111 weeks



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