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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 (345.2149*sine), 11 weeks (283.3286*cosine), and 17 weeks (264.345*cosine).

JDST (Direxion Daily Junior Gold Mine) has an average price of 2,650.79 (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 1/9/2017 for JDST (Direxion Daily Junior Gold Mine), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
02,650.79   0 
11,196.7 2,011.984 (1*2π)/172172 weeks
21,086.392 1,609.63 (2*2π)/17286 weeks
3876.981 1,333.021 (3*2π)/17257 weeks
439.26518 1,362.189 (4*2π)/17243 weeks
5-3.4443 831.8385 (5*2π)/17234 weeks
6117.1552 1,056.19 (6*2π)/17229 weeks
7-393.0347 905.7516 (7*2π)/17225 weeks
8-778.4047 327.0064 (8*2π)/17222 weeks
9-188.7061 62.0004 (9*2π)/17219 weeks
10-264.345 -56.11148 (10*2π)/17217 weeks
1152.10843 -105.1328 (11*2π)/17216 weeks
1276.31096 -.18077 (12*2π)/17214 weeks
13150.1221 9.82643 (13*2π)/17213 weeks
14203.6757 -7.64217 (14*2π)/17212 weeks
15210.1724 74.00201 (15*2π)/17211 weeks
16283.3286 172.3391 (16*2π)/17211 weeks
17160.0459 205.7264 (17*2π)/17210 weeks
18143.4328 60.07527 (18*2π)/17210 weeks
19214.5842 241.7361 (19*2π)/1729 weeks
20225.6406 188.744 (20*2π)/1729 weeks
21117.8384 222.3263 (21*2π)/1728 weeks
22110.9726 345.2149 (22*2π)/1728 weeks
23-44.10541 166.1655 (23*2π)/1727 weeks
2458.5813 127.664 (24*2π)/1727 weeks
2568.23793 158.543 (25*2π)/1727 weeks
26-19.25096 153.9269 (26*2π)/1727 weeks
27108.2467 43.14896 (27*2π)/1726 weeks
2833.32701 170.955 (28*2π)/1726 weeks
2912.62599 53.41154 (29*2π)/1726 weeks
30153.6513 43.25787 (30*2π)/1726 weeks
31124.6445 147.8933 (31*2π)/1726 weeks
3239.66747 138.8772 (32*2π)/1725 weeks
33102.7774 115.7242 (33*2π)/1725 weeks
3487.86269 123.8527 (34*2π)/1725 weeks
35-3.53405 143.8285 (35*2π)/1725 weeks
3686.17701 60.95308 (36*2π)/1725 weeks
3785.69617 116.6843 (37*2π)/1725 weeks
387.53744 112.7905 (38*2π)/1725 weeks
3992.10933 7.00179 (39*2π)/1724 weeks
40165.1975 161.7708 (40*2π)/1724 weeks
4146.31886 143.712 (41*2π)/1724 weeks
4237.9472 123.3575 (42*2π)/1724 weeks
4389.81514 159.4465 (43*2π)/1724 weeks
44-26.15236 145.7097 (44*2π)/1724 weeks
45-5.70238 88.51197 (45*2π)/1724 weeks
4638.82896 99.94617 (46*2π)/1724 weeks
47-46.95986 88.63425 (47*2π)/1724 weeks
4837.89581 -10.00022 (48*2π)/1724 weeks
49107.8655 78.66795 (49*2π)/1724 weeks
5066.23077 135.9732 (50*2π)/1723 weeks
5112.58037 141.8989 (51*2π)/1723 weeks
52-25.93238 110.1699 (52*2π)/1723 weeks
53-22.57992 84.72233 (53*2π)/1723 weeks
54-43.48091 53.50283 (54*2π)/1723 weeks
5515.53507 17.75553 (55*2π)/1723 weeks
568.70001 75.95574 (56*2π)/1723 weeks
57-9.79227 35.86525 (57*2π)/1723 weeks
5810.52266 22.9557 (58*2π)/1723 weeks
5919.76965 40.65764 (59*2π)/1723 weeks
6033.14927 41.75369 (60*2π)/1723 weeks
6119.46314 42.2677 (61*2π)/1723 weeks
6229.68611 75.29612 (62*2π)/1723 weeks
632.04088 74.75995 (63*2π)/1723 weeks
64-33.81281 54.42945 (64*2π)/1723 weeks
65-39.54991 82.35433 (65*2π)/1723 weeks
66-64.28773 -12.63987 (66*2π)/1723 weeks
67-51.10036 -10.99943 (67*2π)/1723 weeks
68-20.29498 -25.19687 (68*2π)/1723 weeks
69-27.43826 -46.22948 (69*2π)/1722 weeks
70-7.27359 -69.279 (70*2π)/1722 weeks
7132.11267 -76.72418 (71*2π)/1722 weeks
7251.67263 -54.87246 (72*2π)/1722 weeks
7375.35839 -92.79901 (73*2π)/1722 weeks
74119.4303 -17.2605 (74*2π)/1722 weeks
7598.4873 10.40951 (75*2π)/1722 weeks
7680.83798 -14.4319 (76*2π)/1722 weeks
77114.0812 42.97353 (77*2π)/1722 weeks
7859.33979 43.60307 (78*2π)/1722 weeks
7962.0658 33.96096 (79*2π)/1722 weeks
8077.29288 54.97795 (80*2π)/1722 weeks
817.49291 97.38494 (81*2π)/1722 weeks
82-13.61439 -9.82144 (82*2π)/1722 weeks
8347.10957 29.30303 (83*2π)/1722 weeks
84-16.06701 53.33826 (84*2π)/1722 weeks
85-14.54678 -50.63061 (85*2π)/1722 weeks
8669.81851   (86*2π)/1722 weeks
87-14.54678 50.63061 (87*2π)/1722 weeks
88-16.06701 -53.33826 (88*2π)/1722 weeks
8947.10957 -29.30303 (89*2π)/1722 weeks
90-13.61439 9.82144 (90*2π)/1722 weeks
917.49291 -97.38494 (91*2π)/1722 weeks
9277.29288 -54.97795 (92*2π)/1722 weeks
9362.0658 -33.96096 (93*2π)/1722 weeks
9459.33979 -43.60307 (94*2π)/1722 weeks
95114.0812 -42.97353 (95*2π)/1722 weeks
9680.83798 14.4319 (96*2π)/1722 weeks
9798.4873 -10.40951 (97*2π)/1722 weeks
98119.4303 17.2605 (98*2π)/1722 weeks
9975.35839 92.79901 (99*2π)/1722 weeks
10051.67263 54.87246 (100*2π)/1722 weeks
10132.11267 76.72418 (101*2π)/1722 weeks
102-7.27359 69.279 (102*2π)/1722 weeks
103-27.43826 46.22948 (103*2π)/1722 weeks
104-20.29498 25.19687 (104*2π)/1722 weeks
105-51.10036 10.99943 (105*2π)/1722 weeks
106-64.28773 12.63987 (106*2π)/1722 weeks
107-39.54991 -82.35433 (107*2π)/1722 weeks
108-33.81281 -54.42945 (108*2π)/1722 weeks
1092.04088 -74.75995 (109*2π)/1722 weeks
11029.68611 -75.29612 (110*2π)/1722 weeks
11119.46314 -42.2677 (111*2π)/1722 weeks
11233.14927 -41.75369 (112*2π)/1722 weeks
11319.76965 -40.65764 (113*2π)/1722 weeks
11410.52266 -22.9557 (114*2π)/1722 weeks
115-9.79227 -35.86525 (115*2π)/1721 weeks
1168.70001 -75.95574 (116*2π)/1721 weeks
11715.53507 -17.75553 (117*2π)/1721 weeks
118-43.48091 -53.50283 (118*2π)/1721 weeks
119-22.57992 -84.72233 (119*2π)/1721 weeks
120-25.93238 -110.1699 (120*2π)/1721 weeks
12112.58037 -141.8989 (121*2π)/1721 weeks
12266.23077 -135.9732 (122*2π)/1721 weeks
123107.8655 -78.66795 (123*2π)/1721 weeks
12437.89581 10.00022 (124*2π)/1721 weeks
125-46.95986 -88.63425 (125*2π)/1721 weeks
12638.82896 -99.94617 (126*2π)/1721 weeks
127-5.70238 -88.51197 (127*2π)/1721 weeks
128-26.15236 -145.7097 (128*2π)/1721 weeks
12989.81514 -159.4465 (129*2π)/1721 weeks
13037.9472 -123.3575 (130*2π)/1721 weeks
13146.31886 -143.712 (131*2π)/1721 weeks
132165.1975 -161.7708 (132*2π)/1721 weeks
13392.10933 -7.00179 (133*2π)/1721 weeks
1347.53744 -112.7905 (134*2π)/1721 weeks
13585.69617 -116.6843 (135*2π)/1721 weeks
13686.17701 -60.95308 (136*2π)/1721 weeks
137-3.53405 -143.8285 (137*2π)/1721 weeks
13887.86269 -123.8527 (138*2π)/1721 weeks
139102.7774 -115.7242 (139*2π)/1721 weeks
14039.66747 -138.8772 (140*2π)/1721 weeks
141124.6445 -147.8933 (141*2π)/1721 weeks
142153.6513 -43.25787 (142*2π)/1721 weeks
14312.62599 -53.41154 (143*2π)/1721 weeks
14433.32701 -170.955 (144*2π)/1721 weeks
145108.2467 -43.14896 (145*2π)/1721 weeks
146-19.25096 -153.9269 (146*2π)/1721 weeks
14768.23793 -158.543 (147*2π)/1721 weeks
14858.5813 -127.664 (148*2π)/1721 weeks
149-44.10541 -166.1655 (149*2π)/1721 weeks
150110.9726 -345.2149 (150*2π)/1721 weeks
151117.8384 -222.3263 (151*2π)/1721 weeks
152225.6406 -188.744 (152*2π)/1721 weeks
153214.5842 -241.7361 (153*2π)/1721 weeks
154143.4328 -60.07527 (154*2π)/1721 weeks
155160.0459 -205.7264 (155*2π)/1721 weeks
156283.3286 -172.3391 (156*2π)/1721 weeks
157210.1724 -74.00201 (157*2π)/1721 weeks
158203.6757 7.64217 (158*2π)/1721 weeks
159150.1221 -9.82643 (159*2π)/1721 weeks
16076.31096 .18077 (160*2π)/1721 weeks
16152.10843 105.1328 (161*2π)/1721 weeks
162-264.345 56.11148 (162*2π)/1721 weeks
163-188.7061 -62.0004 (163*2π)/1721 weeks
164-778.4047 -327.0064 (164*2π)/1721 weeks
165-393.0347 -905.7516 (165*2π)/1721 weeks
166117.1552 -1,056.19 (166*2π)/1721 weeks
167-3.4443 -831.8385 (167*2π)/1721 weeks
16839.26518 -1,362.189 (168*2π)/1721 weeks
169876.981 -1,333.021 (169*2π)/1721 weeks
1701,086.392 -1,609.63 (170*2π)/1721 weeks

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