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Fourier Analysis of JDST (DIREXION DAILY JUNIOR GOLD MINERS INDEX BEAR 3X SHARES DIREXION DAILY JUNIOR GOLD MINERS INDEX BEAR 3X SHARES)


JDST (DIREXION DAILY JUNIOR GOLD MINERS INDEX BEAR 3X SHARES DIREXION DAILY JUNIOR GOLD MINERS INDEX BEAR 3X SHARES) appears to have interesting cyclic behaviour every 23 weeks (2157.813*cosine), 23 weeks (2083.78*sine), and 20 weeks (1657.826*cosine).

JDST (DIREXION DAILY JUNIOR GOLD MINERS INDEX BEAR 3X SHARES DIREXION DAILY JUNIOR GOLD MINERS INDEX BEAR 3X SHARES) has an average price of 8,146.9 (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 1/16/2018 for JDST (DIREXION DAILY JUNIOR GOLD MINERS INDEX BEAR 3X SHARES DIREXION DAILY JUNIOR GOLD MINERS INDEX BEAR 3X SHARES), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
08,146.903   0 
15,720.857 8,060.794 (1*2π)/225225 weeks
24,095.798 4,110.103 (2*2π)/225113 weeks
32,395.613 4,546.003 (3*2π)/22575 weeks
42,670.932 4,233.013 (4*2π)/22556 weeks
5464.9643 4,598.477 (5*2π)/22545 weeks
6-143.6738 3,104.427 (6*2π)/22538 weeks
7384.5155 2,397.26 (7*2π)/22532 weeks
8144.5169 3,353.49 (8*2π)/22528 weeks
9-1,110.565 2,875.517 (9*2π)/22525 weeks
10-2,157.813 2,083.78 (10*2π)/22523 weeks
11-1,657.826 -32.58205 (11*2π)/22520 weeks
12-591.3893 355.8713 (12*2π)/22519 weeks
13-852.9781 -100.7522 (13*2π)/22517 weeks
14-80.29946 -432.1108 (14*2π)/22516 weeks
15303.2716 -69.16692 (15*2π)/22515 weeks
16261.0637 -45.72785 (16*2π)/22514 weeks
17460.4108 31.52878 (17*2π)/22513 weeks
18507.6939 -27.83004 (18*2π)/22513 weeks
19738.6752 201.9062 (19*2π)/22512 weeks
20720.7334 182.9498 (20*2π)/22511 weeks
21848.6274 559.9962 (21*2π)/22511 weeks
22536.1401 638.012 (22*2π)/22510 weeks
23294.9736 467.1164 (23*2π)/22510 weeks
24765.7239 234.2114 (24*2π)/2259 weeks
25570.7495 737.8581 (25*2π)/2259 weeks
26645.8563 515.4285 (26*2π)/2259 weeks
27444.9799 837.6162 (27*2π)/2258 weeks
28526.7863 681.7172 (28*2π)/2258 weeks
29171.7463 1,072.194 (29*2π)/2258 weeks
30-152.3194 552.59 (30*2π)/2258 weeks
31122.6394 366.8825 (31*2π)/2257 weeks
32211.0241 437.8719 (32*2π)/2257 weeks
33193.4684 517.8644 (33*2π)/2257 weeks
34-54.49096 477.3673 (34*2π)/2257 weeks
35154.1961 78.80863 (35*2π)/2256 weeks
36375.4113 473.58 (36*2π)/2256 weeks
3713.61971 416.537 (37*2π)/2256 weeks
3848.63874 148.2467 (38*2π)/2256 weeks
39396.3531 58.03365 (39*2π)/2256 weeks
40465.9774 383.1016 (40*2π)/2256 weeks
41320.4954 496.0184 (41*2π)/2255 weeks
42112.7277 382.9108 (42*2π)/2255 weeks
43310.037 315.9912 (43*2π)/2255 weeks
44228.8406 383.6413 (44*2π)/2255 weeks
45254.4919 490.3301 (45*2π)/2255 weeks
46-40.80781 347.9443 (46*2π)/2255 weeks
47244.0138 167.7539 (47*2π)/2255 weeks
48270.3729 326.502 (48*2π)/2255 weeks
49193.1854 428.9529 (49*2π)/2255 weeks
50.86402 248.2441 (50*2π)/2255 weeks
51275.1663 21.65754 (51*2π)/2254 weeks
52564.9317 339.1213 (52*2π)/2254 weeks
53227.3716 581.1034 (53*2π)/2254 weeks
54164.3898 416.5716 (54*2π)/2254 weeks
55117.5595 368.6639 (55*2π)/2254 weeks
56284.1049 406.9088 (56*2π)/2254 weeks
5734.95972 585.7682 (57*2π)/2254 weeks
58-66.95144 350.328 (58*2π)/2254 weeks
59-9.13502 259.5009 (59*2π)/2254 weeks
60114.6947 274.018 (60*2π)/2254 weeks
61-43.37413 384.9506 (61*2π)/2254 weeks
62-124.8661 95.40015 (62*2π)/2254 weeks
63187.7807 -12.71555 (63*2π)/2254 weeks
64334.5134 219.1084 (64*2π)/2254 weeks
65251.4247 383.1833 (65*2π)/2253 weeks
66126.299 443.3754 (66*2π)/2253 weeks
677.53749 425.6169 (67*2π)/2253 weeks
68-78.6537 341.6617 (68*2π)/2253 weeks
69-70.2898 265.8034 (69*2π)/2253 weeks
70-101.4933 242.5803 (70*2π)/2253 weeks
71-114.0236 103.6685 (71*2π)/2253 weeks
7256.72726 59.86612 (72*2π)/2253 weeks
7369.10081 218.3769 (73*2π)/2253 weeks
74-52.66555 163.9389 (74*2π)/2253 weeks
75-9.10295 98.02213 (75*2π)/2253 weeks
7642.8475 70.71651 (76*2π)/2253 weeks
7769.16573 123.5378 (77*2π)/2253 weeks
7876.71869 101.6726 (78*2π)/2253 weeks
7982.07802 163.5924 (79*2π)/2253 weeks
8075.90139 123.5397 (80*2π)/2253 weeks
81102.4937 221.7816 (81*2π)/2253 weeks
8214.13368 226.7148 (82*2π)/2253 weeks
83-46.42372 247.6288 (83*2π)/2253 weeks
84-78.89446 139.3989 (84*2π)/2253 weeks
85-112.9407 251.4945 (85*2π)/2253 weeks
86-264.2505 24.30872 (86*2π)/2253 weeks
87-119.023 -11.07937 (87*2π)/2253 weeks
88-143.2552 -81.68766 (88*2π)/2253 weeks
89-62.90255 -74.74799 (89*2π)/2253 weeks
90-95.4585 -120.5856 (90*2π)/2253 weeks
91-50.81053 -177.8982 (91*2π)/2252 weeks
9216.50349 -235.2997 (92*2π)/2252 weeks
93108.9043 -232.804 (93*2π)/2252 weeks
94164.1956 -179.3741 (94*2π)/2252 weeks
95135.8014 -230.6806 (95*2π)/2252 weeks
96358.5841 -226.5788 (96*2π)/2252 weeks
97348.6391 -33.86041 (97*2π)/2252 weeks
98309.7366 23.11178 (98*2π)/2252 weeks
99218.211 5.96151 (99*2π)/2252 weeks
100349.5127 -17.49777 (100*2π)/2252 weeks
101307.7464 168.2176 (101*2π)/2252 weeks
102183.1174 136.3858 (102*2π)/2252 weeks
103189.229 106.4341 (103*2π)/2252 weeks
104215.1514 108.8485 (104*2π)/2252 weeks
105222.304 221.5841 (105*2π)/2252 weeks
10611.33255 295.1539 (106*2π)/2252 weeks
107-96.41631 29.53298 (107*2π)/2252 weeks
108127.82 -9.56194 (108*2π)/2252 weeks
109107.4723 141.7803 (109*2π)/2252 weeks
110-74.96712 148.7137 (110*2π)/2252 weeks
111-93.39596 -119.2498 (111*2π)/2252 weeks
112169.6955 -115.9531 (112*2π)/2252 weeks
113169.6955 115.9531 (113*2π)/2252 weeks
114-93.39596 119.2498 (114*2π)/2252 weeks
115-74.96712 -148.7137 (115*2π)/2252 weeks
116107.4723 -141.7803 (116*2π)/2252 weeks
117127.82 9.56194 (117*2π)/2252 weeks
118-96.41631 -29.53298 (118*2π)/2252 weeks
11911.33255 -295.1539 (119*2π)/2252 weeks
120222.304 -221.5841 (120*2π)/2252 weeks
121215.1514 -108.8485 (121*2π)/2252 weeks
122189.229 -106.4341 (122*2π)/2252 weeks
123183.1174 -136.3858 (123*2π)/2252 weeks
124307.7464 -168.2176 (124*2π)/2252 weeks
125349.5127 17.49777 (125*2π)/2252 weeks
126218.211 -5.96151 (126*2π)/2252 weeks
127309.7366 -23.11178 (127*2π)/2252 weeks
128348.6391 33.86041 (128*2π)/2252 weeks
129358.5841 226.5788 (129*2π)/2252 weeks
130135.8014 230.6806 (130*2π)/2252 weeks
131164.1956 179.3741 (131*2π)/2252 weeks
132108.9043 232.804 (132*2π)/2252 weeks
13316.50349 235.2997 (133*2π)/2252 weeks
134-50.81053 177.8982 (134*2π)/2252 weeks
135-95.4585 120.5856 (135*2π)/2252 weeks
136-62.90255 74.74799 (136*2π)/2252 weeks
137-143.2552 81.68766 (137*2π)/2252 weeks
138-119.023 11.07937 (138*2π)/2252 weeks
139-264.2505 -24.30872 (139*2π)/2252 weeks
140-112.9407 -251.4945 (140*2π)/2252 weeks
141-78.89446 -139.3989 (141*2π)/2252 weeks
142-46.42372 -247.6288 (142*2π)/2252 weeks
14314.13368 -226.7148 (143*2π)/2252 weeks
144102.4937 -221.7816 (144*2π)/2252 weeks
14575.90139 -123.5397 (145*2π)/2252 weeks
14682.07802 -163.5924 (146*2π)/2252 weeks
14776.71869 -101.6726 (147*2π)/2252 weeks
14869.16573 -123.5378 (148*2π)/2252 weeks
14942.8475 -70.71651 (149*2π)/2252 weeks
150-9.10295 -98.02213 (150*2π)/2252 weeks
151-52.66555 -163.9389 (151*2π)/2251 weeks
15269.10081 -218.3769 (152*2π)/2251 weeks
15356.72726 -59.86612 (153*2π)/2251 weeks
154-114.0236 -103.6685 (154*2π)/2251 weeks
155-101.4933 -242.5803 (155*2π)/2251 weeks
156-70.2898 -265.8034 (156*2π)/2251 weeks
157-78.6537 -341.6617 (157*2π)/2251 weeks
1587.53749 -425.6169 (158*2π)/2251 weeks
159126.299 -443.3754 (159*2π)/2251 weeks
160251.4247 -383.1833 (160*2π)/2251 weeks
161334.5134 -219.1084 (161*2π)/2251 weeks
162187.7807 12.71555 (162*2π)/2251 weeks
163-124.8661 -95.40015 (163*2π)/2251 weeks
164-43.37413 -384.9506 (164*2π)/2251 weeks
165114.6947 -274.018 (165*2π)/2251 weeks
166-9.13502 -259.5009 (166*2π)/2251 weeks
167-66.95144 -350.328 (167*2π)/2251 weeks
16834.95972 -585.7682 (168*2π)/2251 weeks
169284.1049 -406.9088 (169*2π)/2251 weeks
170117.5595 -368.6639 (170*2π)/2251 weeks
171164.3898 -416.5716 (171*2π)/2251 weeks
172227.3716 -581.1034 (172*2π)/2251 weeks
173564.9317 -339.1213 (173*2π)/2251 weeks
174275.1663 -21.65754 (174*2π)/2251 weeks
175.86402 -248.2441 (175*2π)/2251 weeks
176193.1854 -428.9529 (176*2π)/2251 weeks
177270.3729 -326.502 (177*2π)/2251 weeks
178244.0138 -167.7539 (178*2π)/2251 weeks
179-40.80781 -347.9443 (179*2π)/2251 weeks
180254.4919 -490.3301 (180*2π)/2251 weeks
181228.8406 -383.6413 (181*2π)/2251 weeks
182310.037 -315.9912 (182*2π)/2251 weeks
183112.7277 -382.9108 (183*2π)/2251 weeks
184320.4954 -496.0184 (184*2π)/2251 weeks
185465.9774 -383.1016 (185*2π)/2251 weeks
186396.3531 -58.03365 (186*2π)/2251 weeks
18748.63874 -148.2467 (187*2π)/2251 weeks
18813.61971 -416.537 (188*2π)/2251 weeks
189375.4113 -473.58 (189*2π)/2251 weeks
190154.1961 -78.80863 (190*2π)/2251 weeks
191-54.49096 -477.3673 (191*2π)/2251 weeks
192193.4684 -517.8644 (192*2π)/2251 weeks
193211.0241 -437.8719 (193*2π)/2251 weeks
194122.6394 -366.8825 (194*2π)/2251 weeks
195-152.3194 -552.59 (195*2π)/2251 weeks
196171.7463 -1,072.194 (196*2π)/2251 weeks
197526.7863 -681.7172 (197*2π)/2251 weeks
198444.9799 -837.6162 (198*2π)/2251 weeks
199645.8563 -515.4285 (199*2π)/2251 weeks
200570.7495 -737.8581 (200*2π)/2251 weeks
201765.7239 -234.2114 (201*2π)/2251 weeks
202294.9736 -467.1164 (202*2π)/2251 weeks
203536.1401 -638.012 (203*2π)/2251 weeks
204848.6274 -559.9962 (204*2π)/2251 weeks
205720.7334 -182.9498 (205*2π)/2251 weeks
206738.6752 -201.9062 (206*2π)/2251 weeks
207507.6939 27.83004 (207*2π)/2251 weeks
208460.4108 -31.52878 (208*2π)/2251 weeks
209261.0637 45.72785 (209*2π)/2251 weeks
210303.2716 69.16692 (210*2π)/2251 weeks
211-80.29946 432.1108 (211*2π)/2251 weeks
212-852.9781 100.7522 (212*2π)/2251 weeks
213-591.3893 -355.8713 (213*2π)/2251 weeks
214-1,657.826 32.58205 (214*2π)/2251 weeks
215-2,157.813 -2,083.78 (215*2π)/2251 weeks
216-1,110.565 -2,875.517 (216*2π)/2251 weeks
217144.5169 -3,353.49 (217*2π)/2251 weeks
218384.5155 -2,397.26 (218*2π)/2251 weeks
219-143.6738 -3,104.427 (219*2π)/2251 weeks
220464.9643 -4,598.477 (220*2π)/2251 weeks
2212,670.932 -4,233.013 (221*2π)/2251 weeks
2222,395.613 -4,546.003 (222*2π)/2251 weeks
2234,095.798 -4,110.103 (223*2π)/2251 weeks



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