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Fourier Analysis of JDST (Direxion Daily Jr Gld Mnrs Bear 3X ETF)


JDST (Direxion Daily Jr Gld Mnrs Bear 3X ETF) appears to have interesting cyclic behaviour every 24 weeks (2507.186*sine), 22 weeks (2275.362*cosine), and 22 weeks (1107.52*sine).

JDST (Direxion Daily Jr Gld Mnrs Bear 3X ETF) has an average price of 7,704.93 (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 4/16/2018 for JDST (Direxion Daily Jr Gld Mnrs Bear 3X ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
07,704.927   0 
15,950.178 7,839.422 (1*2π)/238238 weeks
23,729.594 3,838.607 (2*2π)/238119 weeks
32,578.805 4,551.849 (3*2π)/23879 weeks
42,504.688 3,666.571 (4*2π)/23860 weeks
51,048.073 4,666.694 (5*2π)/23848 weeks
6-103.4674 3,297.584 (6*2π)/23840 weeks
736.37566 2,359.903 (7*2π)/23834 weeks
8572.6724 2,753.549 (8*2π)/23830 weeks
9-626.0825 3,096.556 (9*2π)/23826 weeks
10-1,371.069 2,507.186 (10*2π)/23824 weeks
11-2,275.362 1,107.52 (11*2π)/23822 weeks
12-945.2003 -124.1279 (12*2π)/23820 weeks
13-698.6143 390.3951 (13*2π)/23818 weeks
14-669.3868 -268.5051 (14*2π)/23817 weeks
1539.0235 -371.0449 (15*2π)/23816 weeks
16280.0757 -28.38058 (16*2π)/23815 weeks
17259.7152 -52.02847 (17*2π)/23814 weeks
18435.0794 32.64394 (18*2π)/23813 weeks
19469.0658 -22.00603 (19*2π)/23813 weeks
20706.4147 161.6683 (20*2π)/23812 weeks
21640.4764 181.8923 (21*2π)/23811 weeks
22845.38 440.6645 (22*2π)/23811 weeks
23557.6812 617.004 (23*2π)/23810 weeks
24349.1494 553.3473 (24*2π)/23810 weeks
25474.9667 155.8147 (25*2π)/23810 weeks
26770.6849 607.475 (26*2π)/2389 weeks
27439.7599 511.8452 (27*2π)/2389 weeks
28647.5009 698.8569 (28*2π)/2389 weeks
29337.77 663.7298 (29*2π)/2388 weeks
30518.2792 820.631 (30*2π)/2388 weeks
31-38.96176 919.0389 (31*2π)/2388 weeks
32-83.54607 422.7039 (32*2π)/2387 weeks
33147.8076 357.5306 (33*2π)/2387 weeks
34201.1043 422.7397 (34*2π)/2387 weeks
35173.7847 499.2415 (35*2π)/2387 weeks
36-59.44028 439.6141 (36*2π)/2387 weeks
37133.9265 75.6034 (37*2π)/2386 weeks
38376.313 416.5891 (38*2π)/2386 weeks
3932.39651 433.2306 (39*2π)/2386 weeks
4025.55273 185.5501 (40*2π)/2386 weeks
41279.4065 20.33255 (41*2π)/2386 weeks
42474.5839 287.4799 (42*2π)/2386 weeks
43350.4208 438.1005 (43*2π)/2386 weeks
44164.2918 464.1173 (44*2π)/2385 weeks
45197.8872 247.4673 (45*2π)/2385 weeks
46265.6676 383.0307 (46*2π)/2385 weeks
47251.8121 355.4948 (47*2π)/2385 weeks
48125.8504 503.3604 (48*2π)/2385 weeks
493.00731 195.0557 (49*2π)/2385 weeks
50271.372 215.782 (50*2π)/2385 weeks
51252.3319 322.6042 (51*2π)/2385 weeks
52146.0698 410.076 (52*2π)/2385 weeks
535.60519 198.2028 (53*2π)/2384 weeks
54280.184 22.12267 (54*2π)/2384 weeks
55534.0458 318.6239 (55*2π)/2384 weeks
56235.4932 557.298 (56*2π)/2384 weeks
57149.4215 395.5144 (57*2π)/2384 weeks
58112.3613 373.8198 (58*2π)/2384 weeks
59240.8061 329.3269 (59*2π)/2384 weeks
60133.0933 564.0103 (60*2π)/2384 weeks
61-78.22407 395.5952 (61*2π)/2384 weeks
62-26.38762 276.0244 (62*2π)/2384 weeks
6355.11792 216.7319 (63*2π)/2384 weeks
6480.47173 349.6976 (64*2π)/2384 weeks
65-132.6911 266.9899 (65*2π)/2384 weeks
66-21.42445 -3.91675 (66*2π)/2384 weeks
67261.9863 49.17952 (67*2π)/2384 weeks
68304.1239 265.7985 (68*2π)/2384 weeks
69212.5451 382.2795 (69*2π)/2383 weeks
7097.72548 420.3238 (70*2π)/2383 weeks
71-5.52148 396.7297 (71*2π)/2383 weeks
72-76.38271 315.7983 (72*2π)/2383 weeks
73-66.35165 250.9245 (73*2π)/2383 weeks
74-93.1164 231.7249 (74*2π)/2383 weeks
75-115.8167 112.8528 (75*2π)/2383 weeks
7627.74585 45.07359 (76*2π)/2383 weeks
7788.82198 180.9987 (77*2π)/2383 weeks
78-38.67014 188.4881 (78*2π)/2383 weeks
79-21.34098 100.3421 (79*2π)/2383 weeks
8014.14353 72.87937 (80*2π)/2383 weeks
8173.65269 94.30022 (81*2π)/2383 weeks
8251.39264 107.7473 (82*2π)/2383 weeks
8396.12512 120.0989 (83*2π)/2383 weeks
8452.34832 146.9648 (84*2π)/2383 weeks
85104.1288 132.4935 (85*2π)/2383 weeks
8663.95584 228.0799 (86*2π)/2383 weeks
879.54851 213.1992 (87*2π)/2383 weeks
88-69.15678 224.9722 (88*2π)/2383 weeks
89-57.75312 130.6584 (89*2π)/2383 weeks
90-130.1828 238.6318 (90*2π)/2383 weeks
91-245.7861 15.23988 (91*2π)/2383 weeks
92-112.2795 -12.28699 (92*2π)/2383 weeks
93-141.7588 -68.03152 (93*2π)/2383 weeks
94-58.37134 -78.11411 (94*2π)/2383 weeks
95-92.83754 -97.25505 (95*2π)/2383 weeks
96-56.89245 -157.6858 (96*2π)/2382 weeks
97-11.21894 -209.3085 (97*2π)/2382 weeks
9875.30482 -226.0132 (98*2π)/2382 weeks
99144.6107 -197.707 (99*2π)/2382 weeks
100128.4939 -162.0599 (100*2π)/2382 weeks
101216.3847 -269.2083 (101*2π)/2382 weeks
102370.8842 -114.2446 (102*2π)/2382 weeks
103308.6126 -15.96428 (103*2π)/2382 weeks
104266.3983 42.16998 (104*2π)/2382 weeks
105217.0434 -27.53413 (105*2π)/2382 weeks
106350.6751 21.90665 (106*2π)/2382 weeks
107264.6705 168.5368 (107*2π)/2382 weeks
108171.4406 121.8973 (108*2π)/2382 weeks
109179.043 100.4205 (109*2π)/2382 weeks
110202.9744 102.56 (110*2π)/2382 weeks
111214.748 200.1841 (111*2π)/2382 weeks
11242.8994 286.9073 (112*2π)/2382 weeks
113-108.6978 77.14999 (113*2π)/2382 weeks
11482.89705 -38.45786 (114*2π)/2382 weeks
115127.3656 104.2432 (115*2π)/2382 weeks
116-.59773 166.8221 (116*2π)/2382 weeks
117-137.0104 -7.02184 (117*2π)/2382 weeks
11859.45699 -163.4085 (118*2π)/2382 weeks
119202.437   (119*2π)/2382 weeks
12059.45699 163.4085 (120*2π)/2382 weeks
121-137.0104 7.02184 (121*2π)/2382 weeks
122-.59773 -166.8221 (122*2π)/2382 weeks
123127.3656 -104.2432 (123*2π)/2382 weeks
12482.89705 38.45786 (124*2π)/2382 weeks
125-108.6978 -77.14999 (125*2π)/2382 weeks
12642.8994 -286.9073 (126*2π)/2382 weeks
127214.748 -200.1841 (127*2π)/2382 weeks
128202.9744 -102.56 (128*2π)/2382 weeks
129179.043 -100.4205 (129*2π)/2382 weeks
130171.4406 -121.8973 (130*2π)/2382 weeks
131264.6705 -168.5368 (131*2π)/2382 weeks
132350.6751 -21.90665 (132*2π)/2382 weeks
133217.0434 27.53413 (133*2π)/2382 weeks
134266.3983 -42.16998 (134*2π)/2382 weeks
135308.6126 15.96428 (135*2π)/2382 weeks
136370.8842 114.2446 (136*2π)/2382 weeks
137216.3847 269.2083 (137*2π)/2382 weeks
138128.4939 162.0599 (138*2π)/2382 weeks
139144.6107 197.707 (139*2π)/2382 weeks
14075.30482 226.0132 (140*2π)/2382 weeks
141-11.21894 209.3085 (141*2π)/2382 weeks
142-56.89245 157.6858 (142*2π)/2382 weeks
143-92.83754 97.25505 (143*2π)/2382 weeks
144-58.37134 78.11411 (144*2π)/2382 weeks
145-141.7588 68.03152 (145*2π)/2382 weeks
146-112.2795 12.28699 (146*2π)/2382 weeks
147-245.7861 -15.23988 (147*2π)/2382 weeks
148-130.1828 -238.6318 (148*2π)/2382 weeks
149-57.75312 -130.6584 (149*2π)/2382 weeks
150-69.15678 -224.9722 (150*2π)/2382 weeks
1519.54851 -213.1992 (151*2π)/2382 weeks
15263.95584 -228.0799 (152*2π)/2382 weeks
153104.1288 -132.4935 (153*2π)/2382 weeks
15452.34832 -146.9648 (154*2π)/2382 weeks
15596.12512 -120.0989 (155*2π)/2382 weeks
15651.39264 -107.7473 (156*2π)/2382 weeks
15773.65269 -94.30022 (157*2π)/2382 weeks
15814.14353 -72.87937 (158*2π)/2382 weeks
159-21.34098 -100.3421 (159*2π)/2381 weeks
160-38.67014 -188.4881 (160*2π)/2381 weeks
16188.82198 -180.9987 (161*2π)/2381 weeks
16227.74585 -45.07359 (162*2π)/2381 weeks
163-115.8167 -112.8528 (163*2π)/2381 weeks
164-93.1164 -231.7249 (164*2π)/2381 weeks
165-66.35165 -250.9245 (165*2π)/2381 weeks
166-76.38271 -315.7983 (166*2π)/2381 weeks
167-5.52148 -396.7297 (167*2π)/2381 weeks
16897.72548 -420.3238 (168*2π)/2381 weeks
169212.5451 -382.2795 (169*2π)/2381 weeks
170304.1239 -265.7985 (170*2π)/2381 weeks
171261.9863 -49.17952 (171*2π)/2381 weeks
172-21.42445 3.91675 (172*2π)/2381 weeks
173-132.6911 -266.9899 (173*2π)/2381 weeks
17480.47173 -349.6976 (174*2π)/2381 weeks
17555.11792 -216.7319 (175*2π)/2381 weeks
176-26.38762 -276.0244 (176*2π)/2381 weeks
177-78.22407 -395.5952 (177*2π)/2381 weeks
178133.0933 -564.0103 (178*2π)/2381 weeks
179240.8061 -329.3269 (179*2π)/2381 weeks
180112.3613 -373.8198 (180*2π)/2381 weeks
181149.4215 -395.5144 (181*2π)/2381 weeks
182235.4932 -557.298 (182*2π)/2381 weeks
183534.0458 -318.6239 (183*2π)/2381 weeks
184280.184 -22.12267 (184*2π)/2381 weeks
1855.60519 -198.2028 (185*2π)/2381 weeks
186146.0698 -410.076 (186*2π)/2381 weeks
187252.3319 -322.6042 (187*2π)/2381 weeks
188271.372 -215.782 (188*2π)/2381 weeks
1893.00731 -195.0557 (189*2π)/2381 weeks
190125.8504 -503.3604 (190*2π)/2381 weeks
191251.8121 -355.4948 (191*2π)/2381 weeks
192265.6676 -383.0307 (192*2π)/2381 weeks
193197.8872 -247.4673 (193*2π)/2381 weeks
194164.2918 -464.1173 (194*2π)/2381 weeks
195350.4208 -438.1005 (195*2π)/2381 weeks
196474.5839 -287.4799 (196*2π)/2381 weeks
197279.4065 -20.33255 (197*2π)/2381 weeks
19825.55273 -185.5501 (198*2π)/2381 weeks
19932.39651 -433.2306 (199*2π)/2381 weeks
200376.313 -416.5891 (200*2π)/2381 weeks
201133.9265 -75.6034 (201*2π)/2381 weeks
202-59.44028 -439.6141 (202*2π)/2381 weeks
203173.7847 -499.2415 (203*2π)/2381 weeks
204201.1043 -422.7397 (204*2π)/2381 weeks
205147.8076 -357.5306 (205*2π)/2381 weeks
206-83.54607 -422.7039 (206*2π)/2381 weeks
207-38.96176 -919.0389 (207*2π)/2381 weeks
208518.2792 -820.631 (208*2π)/2381 weeks
209337.77 -663.7298 (209*2π)/2381 weeks
210647.5009 -698.8569 (210*2π)/2381 weeks
211439.7599 -511.8452 (211*2π)/2381 weeks
212770.6849 -607.475 (212*2π)/2381 weeks
213474.9667 -155.8147 (213*2π)/2381 weeks
214349.1494 -553.3473 (214*2π)/2381 weeks
215557.6812 -617.004 (215*2π)/2381 weeks
216845.38 -440.6645 (216*2π)/2381 weeks
217640.4764 -181.8923 (217*2π)/2381 weeks
218706.4147 -161.6683 (218*2π)/2381 weeks
219469.0658 22.00603 (219*2π)/2381 weeks
220435.0794 -32.64394 (220*2π)/2381 weeks
221259.7152 52.02847 (221*2π)/2381 weeks
222280.0757 28.38058 (222*2π)/2381 weeks
22339.0235 371.0449 (223*2π)/2381 weeks
224-669.3868 268.5051 (224*2π)/2381 weeks
225-698.6143 -390.3951 (225*2π)/2381 weeks
226-945.2003 124.1279 (226*2π)/2381 weeks
227-2,275.362 -1,107.52 (227*2π)/2381 weeks
228-1,371.069 -2,507.186 (228*2π)/2381 weeks
229-626.0825 -3,096.556 (229*2π)/2381 weeks
230572.6724 -2,753.549 (230*2π)/2381 weeks
23136.37566 -2,359.903 (231*2π)/2381 weeks
232-103.4674 -3,297.584 (232*2π)/2381 weeks
2331,048.073 -4,666.694 (233*2π)/2381 weeks
2342,504.688 -3,666.571 (234*2π)/2381 weeks
2352,578.805 -4,551.849 (235*2π)/2381 weeks
2363,729.594 -3,838.607 (236*2π)/2381 weeks



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