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Fourier Analysis of JNUG (Direxion Daily Junior Gold Mine)


JNUG (Direxion Daily Junior Gold Mine) appears to have interesting cyclic behaviour every 18 weeks (11.0071*sine), 17 weeks (9.65*sine), and 18 weeks (5.0577*cosine).

JNUG (Direxion Daily Junior Gold Mine) has an average price of 41.29 (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 JNUG (Direxion Daily Junior Gold Mine), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
041.29105   0 
135.41824 40.44901 (1*2π)/182182 weeks
2-8.229 27.26024 (2*2π)/18291 weeks
3-8.55782 7.71719 (3*2π)/18261 weeks
47.27866 6.07589 (4*2π)/18246 weeks
54.3796 10.88676 (5*2π)/18236 weeks
6-2.88467 2.5042 (6*2π)/18230 weeks
72.92588 -5.12491 (7*2π)/18226 weeks
811.58888 -.14101 (8*2π)/18223 weeks
910.03244 9.67744 (9*2π)/18220 weeks
105.05767 11.00708 (10*2π)/18218 weeks
111.06323 9.65001 (11*2π)/18217 weeks
12-1.25779 6.18026 (12*2π)/18215 weeks
13-.93764 5.02802 (13*2π)/18214 weeks
14-.52567 4.86285 (14*2π)/18213 weeks
15.05228 3.89401 (15*2π)/18212 weeks
16.37741 2.96838 (16*2π)/18211 weeks
17.28697 2.4431 (17*2π)/18211 weeks
181.54803 3.02854 (18*2π)/18210 weeks
191.7255 4.62172 (19*2π)/18210 weeks
20-.80762 4.35326 (20*2π)/1829 weeks
21-2.4568 2.73269 (21*2π)/1829 weeks
22-1.12725 .56389 (22*2π)/1828 weeks
23.92447 .10369 (23*2π)/1828 weeks
241.76132 1.35074 (24*2π)/1828 weeks
25.37471 2.23764 (25*2π)/1827 weeks
26.38607 1.49743 (26*2π)/1827 weeks
271.25834 1.38187 (27*2π)/1827 weeks
28.80725 1.9727 (28*2π)/1827 weeks
29-.23759 1.06797 (29*2π)/1826 weeks
30.82852 .74954 (30*2π)/1826 weeks
31.871 1.85979 (31*2π)/1826 weeks
32.12409 1.8387 (32*2π)/1826 weeks
33.01968 1.28662 (33*2π)/1826 weeks
34.17302 .26535 (34*2π)/1825 weeks
35.13212 -.45906 (35*2π)/1825 weeks
36.42258 -.3894 (36*2π)/1825 weeks
37.86961 .21973 (37*2π)/1825 weeks
38.85286 .55034 (38*2π)/1825 weeks
391.31349 .1103 (39*2π)/1825 weeks
401.745 .76527 (40*2π)/1825 weeks
41.59299 2.13209 (41*2π)/1824 weeks
42-.97282 1.28324 (42*2π)/1824 weeks
43-.4281 -.42285 (43*2π)/1824 weeks
44-.01072 -1.21746 (44*2π)/1824 weeks
45.55798 -1.46198 (45*2π)/1824 weeks
461.70456 -1.16976 (46*2π)/1824 weeks
472.2221 -.11492 (47*2π)/1824 weeks
481.91637 .05594 (48*2π)/1824 weeks
492.2635 -.06269 (49*2π)/1824 weeks
502.26779 1.30291 (50*2π)/1824 weeks
51.2517 2.04035 (51*2π)/1824 weeks
52-1.02083 .30831 (52*2π)/1824 weeks
53-.0709 -1.74322 (53*2π)/1823 weeks
541.75027 -2.04513 (54*2π)/1823 weeks
552.79995 -.80426 (55*2π)/1823 weeks
562.66494 .09988 (56*2π)/1823 weeks
572.39268 .32348 (57*2π)/1823 weeks
581.81196 .53972 (58*2π)/1823 weeks
591.39689 .44461 (59*2π)/1823 weeks
601.54182 .47946 (60*2π)/1823 weeks
611.73791 .38703 (61*2π)/1823 weeks
621.71819 .19668 (62*2π)/1823 weeks
631.71939 .06773 (63*2π)/1823 weeks
641.9441 .05316 (64*2π)/1823 weeks
651.86603 .5683 (65*2π)/1823 weeks
661.34202 .72991 (66*2π)/1823 weeks
671.53862 .39619 (67*2π)/1823 weeks
682.22863 .1328 (68*2π)/1823 weeks
692.53884 .31694 (69*2π)/1823 weeks
701.97616 1.13412 (70*2π)/1823 weeks
711.48635 1.26011 (71*2π)/1823 weeks
721.53809 .92031 (72*2π)/1823 weeks
731.78659 .87309 (73*2π)/1822 weeks
741.45414 1.28996 (74*2π)/1822 weeks
75.75059 1.33781 (75*2π)/1822 weeks
76.82439 .94838 (76*2π)/1822 weeks
771.18315 1.04612 (77*2π)/1822 weeks
78.79188 1.06812 (78*2π)/1822 weeks
79.44273 .66056 (79*2π)/1822 weeks
80.54148 .33868 (80*2π)/1822 weeks
81.40137 .21315 (81*2π)/1822 weeks
82.47543 .34185 (82*2π)/1822 weeks
83.26517 .37912 (83*2π)/1822 weeks
84.41193 -.27518 (84*2π)/1822 weeks
85.95657 -.66855 (85*2π)/1822 weeks
861.48532 -.23731 (86*2π)/1822 weeks
871.28366 .42154 (87*2π)/1822 weeks
881.02258 .16083 (88*2π)/1822 weeks
891.22374 .23949 (89*2π)/1822 weeks
90.59782 .77209 (90*2π)/1822 weeks
91-.12478   (91*2π)/1822 weeks
92.59782 -.77209 (92*2π)/1822 weeks
931.22374 -.23949 (93*2π)/1822 weeks
941.02258 -.16083 (94*2π)/1822 weeks
951.28366 -.42154 (95*2π)/1822 weeks
961.48532 .23731 (96*2π)/1822 weeks
97.95657 .66855 (97*2π)/1822 weeks
98.41193 .27518 (98*2π)/1822 weeks
99.26517 -.37912 (99*2π)/1822 weeks
100.47543 -.34185 (100*2π)/1822 weeks
101.40137 -.21315 (101*2π)/1822 weeks
102.54148 -.33868 (102*2π)/1822 weeks
103.44273 -.66056 (103*2π)/1822 weeks
104.79188 -1.06812 (104*2π)/1822 weeks
1051.18315 -1.04612 (105*2π)/1822 weeks
106.82439 -.94838 (106*2π)/1822 weeks
107.75059 -1.33781 (107*2π)/1822 weeks
1081.45414 -1.28996 (108*2π)/1822 weeks
1091.78659 -.87309 (109*2π)/1822 weeks
1101.53809 -.92031 (110*2π)/1822 weeks
1111.48635 -1.26011 (111*2π)/1822 weeks
1121.97616 -1.13412 (112*2π)/1822 weeks
1132.53884 -.31694 (113*2π)/1822 weeks
1142.22863 -.1328 (114*2π)/1822 weeks
1151.53862 -.39619 (115*2π)/1822 weeks
1161.34202 -.72991 (116*2π)/1822 weeks
1171.86603 -.5683 (117*2π)/1822 weeks
1181.9441 -.05316 (118*2π)/1822 weeks
1191.71939 -.06773 (119*2π)/1822 weeks
1201.71819 -.19668 (120*2π)/1822 weeks
1211.73791 -.38703 (121*2π)/1822 weeks
1221.54182 -.47946 (122*2π)/1821 weeks
1231.39689 -.44461 (123*2π)/1821 weeks
1241.81196 -.53972 (124*2π)/1821 weeks
1252.39268 -.32348 (125*2π)/1821 weeks
1262.66494 -.09988 (126*2π)/1821 weeks
1272.79995 .80426 (127*2π)/1821 weeks
1281.75027 2.04513 (128*2π)/1821 weeks
129-.0709 1.74322 (129*2π)/1821 weeks
130-1.02083 -.30831 (130*2π)/1821 weeks
131.2517 -2.04035 (131*2π)/1821 weeks
1322.26779 -1.30291 (132*2π)/1821 weeks
1332.2635 .06269 (133*2π)/1821 weeks
1341.91637 -.05594 (134*2π)/1821 weeks
1352.2221 .11492 (135*2π)/1821 weeks
1361.70456 1.16976 (136*2π)/1821 weeks
137.55798 1.46198 (137*2π)/1821 weeks
138-.01072 1.21746 (138*2π)/1821 weeks
139-.4281 .42285 (139*2π)/1821 weeks
140-.97282 -1.28324 (140*2π)/1821 weeks
141.59299 -2.13209 (141*2π)/1821 weeks
1421.745 -.76527 (142*2π)/1821 weeks
1431.31349 -.1103 (143*2π)/1821 weeks
144.85286 -.55034 (144*2π)/1821 weeks
145.86961 -.21973 (145*2π)/1821 weeks
146.42258 .3894 (146*2π)/1821 weeks
147.13212 .45906 (147*2π)/1821 weeks
148.17302 -.26535 (148*2π)/1821 weeks
149.01968 -1.28662 (149*2π)/1821 weeks
150.12409 -1.8387 (150*2π)/1821 weeks
151.871 -1.85979 (151*2π)/1821 weeks
152.82852 -.74954 (152*2π)/1821 weeks
153-.23759 -1.06797 (153*2π)/1821 weeks
154.80725 -1.9727 (154*2π)/1821 weeks
1551.25834 -1.38187 (155*2π)/1821 weeks
156.38607 -1.49743 (156*2π)/1821 weeks
157.37471 -2.23764 (157*2π)/1821 weeks
1581.76132 -1.35074 (158*2π)/1821 weeks
159.92447 -.10369 (159*2π)/1821 weeks
160-1.12725 -.56389 (160*2π)/1821 weeks
161-2.4568 -2.73269 (161*2π)/1821 weeks
162-.80762 -4.35326 (162*2π)/1821 weeks
1631.7255 -4.62172 (163*2π)/1821 weeks
1641.54803 -3.02854 (164*2π)/1821 weeks
165.28697 -2.4431 (165*2π)/1821 weeks
166.37741 -2.96838 (166*2π)/1821 weeks
167.05228 -3.89401 (167*2π)/1821 weeks
168-.52567 -4.86285 (168*2π)/1821 weeks
169-.93764 -5.02802 (169*2π)/1821 weeks
170-1.25779 -6.18026 (170*2π)/1821 weeks
1711.06323 -9.65001 (171*2π)/1821 weeks
1725.05767 -11.00708 (172*2π)/1821 weeks
17310.03244 -9.67744 (173*2π)/1821 weeks
17411.58888 .14101 (174*2π)/1821 weeks
1752.92588 5.12491 (175*2π)/1821 weeks
176-2.88467 -2.5042 (176*2π)/1821 weeks
1774.3796 -10.88676 (177*2π)/1821 weeks
1787.27866 -6.07589 (178*2π)/1821 weeks
179-8.55782 -7.71719 (179*2π)/1821 weeks
180-8.229 -27.26024 (180*2π)/1821 weeks

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