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Fourier Analysis of JDST (Direxion Daily Junior Gold Mine)


JDST (Direxion Daily Junior Gold Mine) appears to have interesting cyclic behaviour every 8 weeks (280.2317*sine), 11 weeks (260.2173*cosine), and 8 weeks (240.8249*sine).

JDST (Direxion Daily Junior Gold Mine) has an average price of 2,506.04 (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 3/20/2017 for JDST (Direxion Daily Junior Gold Mine), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
02,506.038   0 
11,219.091 2,047.821 (1*2π)/182182 weeks
21,146.215 1,492.475 (2*2π)/18291 weeks
3797.9925 1,170.179 (3*2π)/18261 weeks
4175.736 1,441.179 (4*2π)/18246 weeks
5-42.1018 894.4984 (5*2π)/18236 weeks
6194.2617 840.3269 (6*2π)/18230 weeks
7-257.9169 970.5674 (7*2π)/18226 weeks
8-619.2522 696.9135 (8*2π)/18223 weeks
9-431.5851 -38.36109 (9*2π)/18220 weeks
10-240.7694 121.8847 (10*2π)/18218 weeks
11-123.5343 -134.1666 (11*2π)/18217 weeks
1291.26617 -40.86953 (12*2π)/18215 weeks
1384.38026 -17.56741 (13*2π)/18214 weeks
14137.7561 18.07924 (14*2π)/18213 weeks
15217.1237 10.38822 (15*2π)/18212 weeks
16203.4773 61.82816 (16*2π)/18211 weeks
17260.2173 174.1839 (17*2π)/18211 weeks
18150.3777 194.2635 (18*2π)/18210 weeks
19124.7137 62.88187 (19*2π)/18210 weeks
20227.7174 219.2013 (20*2π)/1829 weeks
21194.1107 155.4035 (21*2π)/1829 weeks
22115.1569 240.8249 (22*2π)/1828 weeks
23163.4729 280.2317 (23*2π)/1828 weeks
24-51.92353 230.7634 (24*2π)/1828 weeks
2531.57007 111.8484 (25*2π)/1827 weeks
2665.62848 137.5853 (26*2π)/1827 weeks
2740.42 171.1705 (27*2π)/1827 weeks
28-12.91691 55.33402 (28*2π)/1827 weeks
29127.7272 124.7755 (29*2π)/1826 weeks
301.37581 119.6041 (30*2π)/1826 weeks
3137.42962 19.84901 (31*2π)/1826 weeks
32156.3669 78.15389 (32*2π)/1826 weeks
33108.2001 146.8726 (33*2π)/1826 weeks
3434.68689 114.5932 (34*2π)/1825 weeks
3595.21358 115.9403 (35*2π)/1825 weeks
3683.96252 118.3028 (36*2π)/1825 weeks
37.14782 141.1036 (37*2π)/1825 weeks
3873.41576 50.35747 (38*2π)/1825 weeks
3981.8922 105.0299 (39*2π)/1825 weeks
4023.91105 125.6748 (40*2π)/1825 weeks
4145.86534 13.66614 (41*2π)/1824 weeks
42173.5276 91.94253 (42*2π)/1824 weeks
4355.0581 168.7527 (43*2π)/1824 weeks
4448.12861 131.1035 (44*2π)/1824 weeks
4568.61031 99.94335 (45*2π)/1824 weeks
4625.85407 183.9011 (46*2π)/1824 weeks
47-17.97405 103.3347 (47*2π)/1824 weeks
487.74415 71.73911 (48*2π)/1824 weeks
4921.63597 116.8734 (49*2π)/1824 weeks
50-45.81377 48.60186 (50*2π)/1824 weeks
5162.35717 -1.80947 (51*2π)/1824 weeks
5298.91957 86.37576 (52*2π)/1824 weeks
5358.23972 130.8229 (53*2π)/1823 weeks
5410.4704 133.7185 (54*2π)/1823 weeks
55-24.15522 105.1368 (55*2π)/1823 weeks
56-21.03596 80.40742 (56*2π)/1823 weeks
57-40.24496 59.04903 (57*2π)/1823 weeks
58.42477 13.03446 (58*2π)/1823 weeks
5923.97598 65.35475 (59*2π)/1823 weeks
60-15.5899 43.68471 (60*2π)/1823 weeks
611.29504 26.19825 (61*2π)/1823 weeks
6224.13101 32.44658 (62*2π)/1823 weeks
6321.02168 31.22415 (63*2π)/1823 weeks
6422.45477 50.79069 (64*2π)/1823 weeks
6533.84748 43.21843 (65*2π)/1823 weeks
6610.89227 73.89706 (66*2π)/1823 weeks
67-7.50049 75.97401 (67*2π)/1823 weeks
68-21.68423 42.39561 (68*2π)/1823 weeks
69-62.85793 71.45175 (69*2π)/1823 weeks
70-47.97462 -13.63945 (70*2π)/1823 weeks
71-48.28004 -15.8763 (71*2π)/1823 weeks
72-19.56798 -22.9201 (72*2π)/1823 weeks
73-26.16055 -43.40363 (73*2π)/1822 weeks
74-8.67806 -63.74368 (74*2π)/1822 weeks
7526.32208 -73.33181 (75*2π)/1822 weeks
7650.71921 -56.21041 (76*2π)/1822 weeks
7749.63742 -80.01633 (77*2π)/1822 weeks
78120.6188 -37.23985 (78*2π)/1822 weeks
7998.70439 -.9721 (79*2π)/1822 weeks
8067.9248 5.8276 (80*2π)/1822 weeks
81112.3274 2.2952 (81*2π)/1822 weeks
8274.59271 55.17587 (82*2π)/1822 weeks
8357.3047 33.46407 (83*2π)/1822 weeks
8463.60921 31.92348 (84*2π)/1822 weeks
8566.11552 71.98147 (85*2π)/1822 weeks
86-22.01826 73.63042 (86*2π)/1822 weeks
8710.64341 -16.20449 (87*2π)/1822 weeks
8839.71904 36.6946 (88*2π)/1822 weeks
89-24.86183 44.58554 (89*2π)/1822 weeks
90-7.36385 -50.57554 (90*2π)/1822 weeks
9166.00233   (91*2π)/1822 weeks
92-7.36385 50.57554 (92*2π)/1822 weeks
93-24.86183 -44.58554 (93*2π)/1822 weeks
9439.71904 -36.6946 (94*2π)/1822 weeks
9510.64341 16.20449 (95*2π)/1822 weeks
96-22.01826 -73.63042 (96*2π)/1822 weeks
9766.11552 -71.98147 (97*2π)/1822 weeks
9863.60921 -31.92348 (98*2π)/1822 weeks
9957.3047 -33.46407 (99*2π)/1822 weeks
10074.59271 -55.17587 (100*2π)/1822 weeks
101112.3274 -2.2952 (101*2π)/1822 weeks
10267.9248 -5.8276 (102*2π)/1822 weeks
10398.70439 .9721 (103*2π)/1822 weeks
104120.6188 37.23985 (104*2π)/1822 weeks
10549.63742 80.01633 (105*2π)/1822 weeks
10650.71921 56.21041 (106*2π)/1822 weeks
10726.32208 73.33181 (107*2π)/1822 weeks
108-8.67806 63.74368 (108*2π)/1822 weeks
109-26.16055 43.40363 (109*2π)/1822 weeks
110-19.56798 22.9201 (110*2π)/1822 weeks
111-48.28004 15.8763 (111*2π)/1822 weeks
112-47.97462 13.63945 (112*2π)/1822 weeks
113-62.85793 -71.45175 (113*2π)/1822 weeks
114-21.68423 -42.39561 (114*2π)/1822 weeks
115-7.50049 -75.97401 (115*2π)/1822 weeks
11610.89227 -73.89706 (116*2π)/1822 weeks
11733.84748 -43.21843 (117*2π)/1822 weeks
11822.45477 -50.79069 (118*2π)/1822 weeks
11921.02168 -31.22415 (119*2π)/1822 weeks
12024.13101 -32.44658 (120*2π)/1822 weeks
1211.29504 -26.19825 (121*2π)/1822 weeks
122-15.5899 -43.68471 (122*2π)/1821 weeks
12323.97598 -65.35475 (123*2π)/1821 weeks
124.42477 -13.03446 (124*2π)/1821 weeks
125-40.24496 -59.04903 (125*2π)/1821 weeks
126-21.03596 -80.40742 (126*2π)/1821 weeks
127-24.15522 -105.1368 (127*2π)/1821 weeks
12810.4704 -133.7185 (128*2π)/1821 weeks
12958.23972 -130.8229 (129*2π)/1821 weeks
13098.91957 -86.37576 (130*2π)/1821 weeks
13162.35717 1.80947 (131*2π)/1821 weeks
132-45.81377 -48.60186 (132*2π)/1821 weeks
13321.63597 -116.8734 (133*2π)/1821 weeks
1347.74415 -71.73911 (134*2π)/1821 weeks
135-17.97405 -103.3347 (135*2π)/1821 weeks
13625.85407 -183.9011 (136*2π)/1821 weeks
13768.61031 -99.94335 (137*2π)/1821 weeks
13848.12861 -131.1035 (138*2π)/1821 weeks
13955.0581 -168.7527 (139*2π)/1821 weeks
140173.5276 -91.94253 (140*2π)/1821 weeks
14145.86534 -13.66614 (141*2π)/1821 weeks
14223.91105 -125.6748 (142*2π)/1821 weeks
14381.8922 -105.0299 (143*2π)/1821 weeks
14473.41576 -50.35747 (144*2π)/1821 weeks
145.14782 -141.1036 (145*2π)/1821 weeks
14683.96252 -118.3028 (146*2π)/1821 weeks
14795.21358 -115.9403 (147*2π)/1821 weeks
14834.68689 -114.5932 (148*2π)/1821 weeks
149108.2001 -146.8726 (149*2π)/1821 weeks
150156.3669 -78.15389 (150*2π)/1821 weeks
15137.42962 -19.84901 (151*2π)/1821 weeks
1521.37581 -119.6041 (152*2π)/1821 weeks
153127.7272 -124.7755 (153*2π)/1821 weeks
154-12.91691 -55.33402 (154*2π)/1821 weeks
15540.42 -171.1705 (155*2π)/1821 weeks
15665.62848 -137.5853 (156*2π)/1821 weeks
15731.57007 -111.8484 (157*2π)/1821 weeks
158-51.92353 -230.7634 (158*2π)/1821 weeks
159163.4729 -280.2317 (159*2π)/1821 weeks
160115.1569 -240.8249 (160*2π)/1821 weeks
161194.1107 -155.4035 (161*2π)/1821 weeks
162227.7174 -219.2013 (162*2π)/1821 weeks
163124.7137 -62.88187 (163*2π)/1821 weeks
164150.3777 -194.2635 (164*2π)/1821 weeks
165260.2173 -174.1839 (165*2π)/1821 weeks
166203.4773 -61.82816 (166*2π)/1821 weeks
167217.1237 -10.38822 (167*2π)/1821 weeks
168137.7561 -18.07924 (168*2π)/1821 weeks
16984.38026 17.56741 (169*2π)/1821 weeks
17091.26617 40.86953 (170*2π)/1821 weeks
171-123.5343 134.1666 (171*2π)/1821 weeks
172-240.7694 -121.8847 (172*2π)/1821 weeks
173-431.5851 38.36109 (173*2π)/1821 weeks
174-619.2522 -696.9135 (174*2π)/1821 weeks
175-257.9169 -970.5674 (175*2π)/1821 weeks
176194.2617 -840.3269 (176*2π)/1821 weeks
177-42.1018 -894.4984 (177*2π)/1821 weeks
178175.736 -1,441.179 (178*2π)/1821 weeks
179797.9925 -1,170.179 (179*2π)/1821 weeks
1801,146.215 -1,492.475 (180*2π)/1821 weeks

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