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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 20 weeks (1203.402*cosine), 8 weeks (1043.008*sine), and 11 weeks (958.1335*cosine).

JDST (Direxion Daily Junior Gold Miners Index Bear 3x Shares ETF) has an average price of 9,203.86 (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 7/17/2017 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
09,203.862   0 
15,205.858 8,295.889 (1*2π)/199199 weeks
24,640.635 5,114.247 (2*2π)/199100 weeks
32,577.062 4,353.329 (3*2π)/19966 weeks
41,904.02 5,624.46 (4*2π)/19950 weeks
5-119.0229 3,972.072 (5*2π)/19940 weeks
6201.8165 2,721.773 (6*2π)/19933 weeks
7307.5881 3,728.054 (7*2π)/19928 weeks
8-1,286.574 3,218.684 (8*2π)/19925 weeks
9-2,638.563 1,945.65 (9*2π)/19922 weeks
10-1,203.402 -160.2827 (10*2π)/19920 weeks
11-929.3071 411.7289 (11*2π)/19918 weeks
12-486.1432 -483.3138 (12*2π)/19917 weeks
13307.1001 -218.9657 (13*2π)/19915 weeks
14271.3203 -22.53264 (14*2π)/19914 weeks
15519.8598 26.92764 (15*2π)/19913 weeks
16608.6514 -39.71408 (16*2π)/19912 weeks
17790.1224 281.7023 (17*2π)/19912 weeks
18958.1335 279.6021 (18*2π)/19911 weeks
19756.007 745.3041 (19*2π)/19910 weeks
20443.4834 679.3472 (20*2π)/19910 weeks
21659.7995 179.1069 (21*2π)/1999 weeks
22730.5512 839.4209 (22*2π)/1999 weeks
23732.1487 583.8032 (23*2π)/1999 weeks
24443.4407 908.2875 (24*2π)/1998 weeks
25634.0024 917.9102 (25*2π)/1998 weeks
26-98.94154 1,043.008 (26*2π)/1998 weeks
27-1.72163 433.4275 (27*2π)/1997 weeks
28225.7705 467.3918 (28*2π)/1997 weeks
29234.0668 559.5555 (29*2π)/1997 weeks
30-36.63273 569.2108 (30*2π)/1997 weeks
31208.0925 88.6061 (31*2π)/1996 weeks
32342.5845 599.8062 (32*2π)/1996 weeks
33.39105 364.0391 (33*2π)/1996 weeks
34183.0156 46.98243 (34*2π)/1996 weeks
35573.7462 291.3059 (35*2π)/1996 weeks
36411.93 529.0673 (36*2π)/1996 weeks
37141.7964 491.7845 (37*2π)/1995 weeks
38346.6773 348.5773 (38*2π)/1995 weeks
39262.5179 424.7307 (39*2π)/1995 weeks
40214.9822 596.7839 (40*2π)/1995 weeks
4114.77416 220.6491 (41*2π)/1995 weeks
42329.4701 309.1984 (42*2π)/1995 weeks
43284.9619 436.8059 (43*2π)/1995 weeks
4419.10201 379.049 (44*2π)/1995 weeks
45254.0795 26.77988 (45*2π)/1994 weeks
46638.261 389.2408 (46*2π)/1994 weeks
47208.0915 625.6995 (47*2π)/1994 weeks
48185.4504 478.9046 (48*2π)/1994 weeks
49192.8485 359.7916 (49*2π)/1994 weeks
50236.3587 643.83 (50*2π)/1994 weeks
51-93.95284 474.1996 (51*2π)/1994 weeks
52-23.44016 313.7627 (52*2π)/1994 weeks
53122.5639 295.4467 (53*2π)/1994 weeks
54-66.47787 426.8708 (54*2π)/1994 weeks
55-95.48318 46.47359 (55*2π)/1994 weeks
56307.6647 52.4738 (56*2π)/1994 weeks
57348.9767 351.0515 (57*2π)/1993 weeks
58205.5985 484.4547 (58*2π)/1993 weeks
5944.97758 493.0622 (59*2π)/1993 weeks
60-80.58815 406.6045 (60*2π)/1993 weeks
61-80.20158 301.3925 (61*2π)/1993 weeks
62-123.4142 265.7488 (62*2π)/1993 weeks
63-96.27756 80.27083 (63*2π)/1993 weeks
64113.6254 128.0601 (64*2π)/1993 weeks
65-13.08376 254.1707 (65*2π)/1993 weeks
66-29.4177 122.2384 (66*2π)/1993 weeks
6726.10794 82.56763 (67*2π)/1993 weeks
6883.56676 134.932 (68*2π)/1993 weeks
6987.96797 115.0836 (69*2π)/1993 weeks
7080.29417 186.4473 (70*2π)/1993 weeks
71116.634 150.4784 (71*2π)/1993 weeks
7262.26486 274.4816 (72*2π)/1993 weeks
73.72735 266.0014 (73*2π)/1993 weeks
74-119.5583 197.6448 (74*2π)/1993 weeks
75-72.3821 261.7044 (75*2π)/1993 weeks
76-308.3674 50.73548 (76*2π)/1993 weeks
77-136.5854 -8.52202 (77*2π)/1993 weeks
78-137.6722 -112.0797 (78*2π)/1993 weeks
79-89.34071 -78.94164 (79*2π)/1993 weeks
80-84.20194 -173.1351 (80*2π)/1992 weeks
81-23.99322 -242.1155 (81*2π)/1992 weeks
8296.63628 -269.3262 (82*2π)/1992 weeks
83184.8367 -216.0524 (83*2π)/1992 weeks
84151.1181 -256.256 (84*2π)/1992 weeks
85423.9103 -228.0917 (85*2π)/1992 weeks
86375.4605 -24.89487 (86*2π)/1992 weeks
87312.3727 52.11097 (87*2π)/1992 weeks
88295.3033 -55.6743 (88*2π)/1992 weeks
89408.8983 128.7032 (89*2π)/1992 weeks
90220.9824 176.8254 (90*2π)/1992 weeks
91213.3971 120.7938 (91*2π)/1992 weeks
92244.424 124.0521 (92*2π)/1992 weeks
93233.4137 276.8213 (93*2π)/1992 weeks
94-71.60324 280.2665 (94*2π)/1992 weeks
95-4.10624 -52.83968 (95*2π)/1992 weeks
96165.2095 96.44525 (96*2π)/1992 weeks
97-2.9918 199.2233 (97*2π)/1992 weeks
98-145.7755 -76.28101 (98*2π)/1992 weeks
99178.1472 -145.0296 (99*2π)/1992 weeks
100178.1472 145.0296 (100*2π)/1992 weeks
101-145.7755 76.28101 (101*2π)/1992 weeks
102-2.9918 -199.2233 (102*2π)/1992 weeks
103165.2095 -96.44525 (103*2π)/1992 weeks
104-4.10624 52.83968 (104*2π)/1992 weeks
105-71.60324 -280.2665 (105*2π)/1992 weeks
106233.4137 -276.8213 (106*2π)/1992 weeks
107244.424 -124.0521 (107*2π)/1992 weeks
108213.3971 -120.7938 (108*2π)/1992 weeks
109220.9824 -176.8254 (109*2π)/1992 weeks
110408.8983 -128.7032 (110*2π)/1992 weeks
111295.3033 55.6743 (111*2π)/1992 weeks
112312.3727 -52.11097 (112*2π)/1992 weeks
113375.4605 24.89487 (113*2π)/1992 weeks
114423.9103 228.0917 (114*2π)/1992 weeks
115151.1181 256.256 (115*2π)/1992 weeks
116184.8367 216.0524 (116*2π)/1992 weeks
11796.63628 269.3262 (117*2π)/1992 weeks
118-23.99322 242.1155 (118*2π)/1992 weeks
119-84.20194 173.1351 (119*2π)/1992 weeks
120-89.34071 78.94164 (120*2π)/1992 weeks
121-137.6722 112.0797 (121*2π)/1992 weeks
122-136.5854 8.52202 (122*2π)/1992 weeks
123-308.3674 -50.73548 (123*2π)/1992 weeks
124-72.3821 -261.7044 (124*2π)/1992 weeks
125-119.5583 -197.6448 (125*2π)/1992 weeks
126.72735 -266.0014 (126*2π)/1992 weeks
12762.26486 -274.4816 (127*2π)/1992 weeks
128116.634 -150.4784 (128*2π)/1992 weeks
12980.29417 -186.4473 (129*2π)/1992 weeks
13087.96797 -115.0836 (130*2π)/1992 weeks
13183.56676 -134.932 (131*2π)/1992 weeks
13226.10794 -82.56763 (132*2π)/1992 weeks
133-29.4177 -122.2384 (133*2π)/1991 weeks
134-13.08376 -254.1707 (134*2π)/1991 weeks
135113.6254 -128.0601 (135*2π)/1991 weeks
136-96.27756 -80.27083 (136*2π)/1991 weeks
137-123.4142 -265.7488 (137*2π)/1991 weeks
138-80.20158 -301.3925 (138*2π)/1991 weeks
139-80.58815 -406.6045 (139*2π)/1991 weeks
14044.97758 -493.0622 (140*2π)/1991 weeks
141205.5985 -484.4547 (141*2π)/1991 weeks
142348.9767 -351.0515 (142*2π)/1991 weeks
143307.6647 -52.4738 (143*2π)/1991 weeks
144-95.48318 -46.47359 (144*2π)/1991 weeks
145-66.47787 -426.8708 (145*2π)/1991 weeks
146122.5639 -295.4467 (146*2π)/1991 weeks
147-23.44016 -313.7627 (147*2π)/1991 weeks
148-93.95284 -474.1996 (148*2π)/1991 weeks
149236.3587 -643.83 (149*2π)/1991 weeks
150192.8485 -359.7916 (150*2π)/1991 weeks
151185.4504 -478.9046 (151*2π)/1991 weeks
152208.0915 -625.6995 (152*2π)/1991 weeks
153638.261 -389.2408 (153*2π)/1991 weeks
154254.0795 -26.77988 (154*2π)/1991 weeks
15519.10201 -379.049 (155*2π)/1991 weeks
156284.9619 -436.8059 (156*2π)/1991 weeks
157329.4701 -309.1984 (157*2π)/1991 weeks
15814.77416 -220.6491 (158*2π)/1991 weeks
159214.9822 -596.7839 (159*2π)/1991 weeks
160262.5179 -424.7307 (160*2π)/1991 weeks
161346.6773 -348.5773 (161*2π)/1991 weeks
162141.7964 -491.7845 (162*2π)/1991 weeks
163411.93 -529.0673 (163*2π)/1991 weeks
164573.7462 -291.3059 (164*2π)/1991 weeks
165183.0156 -46.98243 (165*2π)/1991 weeks
166.39105 -364.0391 (166*2π)/1991 weeks
167342.5845 -599.8062 (167*2π)/1991 weeks
168208.0925 -88.6061 (168*2π)/1991 weeks
169-36.63273 -569.2108 (169*2π)/1991 weeks
170234.0668 -559.5555 (170*2π)/1991 weeks
171225.7705 -467.3918 (171*2π)/1991 weeks
172-1.72163 -433.4275 (172*2π)/1991 weeks
173-98.94154 -1,043.008 (173*2π)/1991 weeks
174634.0024 -917.9102 (174*2π)/1991 weeks
175443.4407 -908.2875 (175*2π)/1991 weeks
176732.1487 -583.8032 (176*2π)/1991 weeks
177730.5512 -839.4209 (177*2π)/1991 weeks
178659.7995 -179.1069 (178*2π)/1991 weeks
179443.4834 -679.3472 (179*2π)/1991 weeks
180756.007 -745.3041 (180*2π)/1991 weeks
181958.1335 -279.6021 (181*2π)/1991 weeks
182790.1224 -281.7023 (182*2π)/1991 weeks
183608.6514 39.71408 (183*2π)/1991 weeks
184519.8598 -26.92764 (184*2π)/1991 weeks
185271.3203 22.53264 (185*2π)/1991 weeks
186307.1001 218.9657 (186*2π)/1991 weeks
187-486.1432 483.3138 (187*2π)/1991 weeks
188-929.3071 -411.7289 (188*2π)/1991 weeks
189-1,203.402 160.2827 (189*2π)/1991 weeks
190-2,638.563 -1,945.65 (190*2π)/1991 weeks
191-1,286.574 -3,218.684 (191*2π)/1991 weeks
192307.5881 -3,728.054 (192*2π)/1991 weeks
193201.8165 -2,721.773 (193*2π)/1991 weeks
194-119.0229 -3,972.072 (194*2π)/1991 weeks
1951,904.02 -5,624.46 (195*2π)/1991 weeks
1962,577.062 -4,353.329 (196*2π)/1991 weeks
1974,640.635 -5,114.247 (197*2π)/1991 weeks



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