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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 17 weeks (11.0503*sine), 16 weeks (8.5794*sine), and 3 weeks (2.9695*cosine).

JNUG (Direxion Daily Junior Gold Mine) has an average price of 43.33 (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 JNUG (Direxion Daily Junior Gold Mine), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
043.32786   0 
135.12511 44.39898 (1*2π)/172172 weeks
2-8.78476 24.28491 (2*2π)/17286 weeks
3-7.2561 3.08004 (3*2π)/17257 weeks
45.89542 7.99339 (4*2π)/17243 weeks
5-.37376 12.26253 (5*2π)/17234 weeks
6-2.14503 .77346 (6*2π)/17229 weeks
78.70355 -3.75478 (7*2π)/17225 weeks
814.46099 5.18313 (8*2π)/17222 weeks
97.64256 10.91274 (9*2π)/17219 weeks
102.40586 11.05025 (10*2π)/17217 weeks
11-1.19562 8.57943 (11*2π)/17216 weeks
12-.46203 6.08978 (12*2π)/17214 weeks
13.22189 5.11513 (13*2π)/17213 weeks
14.26412 3.79508 (14*2π)/17212 weeks
15.32817 2.93233 (15*2π)/17211 weeks
16.2916 2.5613 (16*2π)/17211 weeks
171.70565 3.05911 (17*2π)/17210 weeks
181.75957 4.90556 (18*2π)/17210 weeks
19-.91466 4.39881 (19*2π)/1729 weeks
20-2.57838 2.12724 (20*2π)/1729 weeks
21-.90106 .19745 (21*2π)/1728 weeks
221.35262 .43921 (22*2π)/1728 weeks
231.77937 2.09051 (23*2π)/1727 weeks
24.30454 1.68695 (24*2π)/1727 weeks
25.56611 1.03363 (25*2π)/1727 weeks
26.97667 1.88865 (26*2π)/1727 weeks
27-.10917 2.08016 (27*2π)/1726 weeks
28.57071 .76237 (28*2π)/1726 weeks
291.35091 1.6224 (29*2π)/1726 weeks
30.44043 1.88403 (30*2π)/1726 weeks
31.047 1.18572 (31*2π)/1726 weeks
32-.11353 .18985 (32*2π)/1725 weeks
33-.1128 -.37698 (33*2π)/1725 weeks
34.39325 -.32937 (34*2π)/1725 weeks
35.91155 .25168 (35*2π)/1725 weeks
36.80749 .55593 (36*2π)/1725 weeks
371.47963 .2481 (37*2π)/1725 weeks
381.92459 1.16817 (38*2π)/1725 weeks
39.08334 2.09704 (39*2π)/1724 weeks
40-1.35818 .52567 (40*2π)/1724 weeks
41-.48302 -.4664 (41*2π)/1724 weeks
42.449 -1.13645 (42*2π)/1724 weeks
431.47848 -1.58108 (43*2π)/1724 weeks
442.43215 -.869 (44*2π)/1724 weeks
452.00057 -.08137 (45*2π)/1724 weeks
461.97603 -.13826 (46*2π)/1724 weeks
472.54545 1.02313 (47*2π)/1724 weeks
48.85342 2.34246 (48*2π)/1724 weeks
49-.95802 .671 (49*2π)/1724 weeks
50-.24594 -1.75153 (50*2π)/1723 weeks
511.78932 -2.19935 (51*2π)/1723 weeks
522.96954 -.83086 (52*2π)/1723 weeks
532.77508 .17127 (53*2π)/1723 weeks
542.54762 .47014 (54*2π)/1723 weeks
551.97189 .54946 (55*2π)/1723 weeks
561.61116 .21575 (56*2π)/1723 weeks
571.53199 .23846 (57*2π)/1723 weeks
581.57732 .35562 (58*2π)/1723 weeks
591.67897 .29663 (59*2π)/1723 weeks
601.87348 .19291 (60*2π)/1723 weeks
612.24721 .52822 (61*2π)/1723 weeks
621.92216 .85295 (62*2π)/1723 weeks
631.71735 .26262 (63*2π)/1723 weeks
642.04385 -.19819 (64*2π)/1723 weeks
652.34787 .16478 (65*2π)/1723 weeks
662.14934 1.25282 (66*2π)/1723 weeks
671.63962 1.38225 (67*2π)/1723 weeks
681.60214 .96168 (68*2π)/1723 weeks
691.86794 .92997 (69*2π)/1722 weeks
701.50734 1.37198 (70*2π)/1722 weeks
71.71636 1.25729 (71*2π)/1722 weeks
72.8055 .88276 (72*2π)/1722 weeks
73.99635 1.23883 (73*2π)/1722 weeks
74.56753 1.19932 (74*2π)/1722 weeks
75.42324 .7098 (75*2π)/1722 weeks
76.60703 .58835 (76*2π)/1722 weeks
77.74902 .32198 (77*2π)/1722 weeks
78.63592 .32893 (78*2π)/1722 weeks
79.25901 -.20793 (79*2π)/1722 weeks
80.65716 -.66908 (80*2π)/1722 weeks
811.45328 -.42178 (81*2π)/1722 weeks
821.52255 .32937 (82*2π)/1722 weeks
831.03356 .18925 (83*2π)/1722 weeks
841.2377 .19985 (84*2π)/1722 weeks
85.69167 .83837 (85*2π)/1722 weeks
86-.13187   (86*2π)/1722 weeks
87.69167 -.83837 (87*2π)/1722 weeks
881.2377 -.19985 (88*2π)/1722 weeks
891.03356 -.18925 (89*2π)/1722 weeks
901.52255 -.32937 (90*2π)/1722 weeks
911.45328 .42178 (91*2π)/1722 weeks
92.65716 .66908 (92*2π)/1722 weeks
93.25901 .20793 (93*2π)/1722 weeks
94.63592 -.32893 (94*2π)/1722 weeks
95.74902 -.32198 (95*2π)/1722 weeks
96.60703 -.58835 (96*2π)/1722 weeks
97.42324 -.7098 (97*2π)/1722 weeks
98.56753 -1.19932 (98*2π)/1722 weeks
99.99635 -1.23883 (99*2π)/1722 weeks
100.8055 -.88276 (100*2π)/1722 weeks
101.71636 -1.25729 (101*2π)/1722 weeks
1021.50734 -1.37198 (102*2π)/1722 weeks
1031.86794 -.92997 (103*2π)/1722 weeks
1041.60214 -.96168 (104*2π)/1722 weeks
1051.63962 -1.38225 (105*2π)/1722 weeks
1062.14934 -1.25282 (106*2π)/1722 weeks
1072.34787 -.16478 (107*2π)/1722 weeks
1082.04385 .19819 (108*2π)/1722 weeks
1091.71735 -.26262 (109*2π)/1722 weeks
1101.92216 -.85295 (110*2π)/1722 weeks
1112.24721 -.52822 (111*2π)/1722 weeks
1121.87348 -.19291 (112*2π)/1722 weeks
1131.67897 -.29663 (113*2π)/1722 weeks
1141.57732 -.35562 (114*2π)/1722 weeks
1151.53199 -.23846 (115*2π)/1721 weeks
1161.61116 -.21575 (116*2π)/1721 weeks
1171.97189 -.54946 (117*2π)/1721 weeks
1182.54762 -.47014 (118*2π)/1721 weeks
1192.77508 -.17127 (119*2π)/1721 weeks
1202.96954 .83086 (120*2π)/1721 weeks
1211.78932 2.19935 (121*2π)/1721 weeks
122-.24594 1.75153 (122*2π)/1721 weeks
123-.95802 -.671 (123*2π)/1721 weeks
124.85342 -2.34246 (124*2π)/1721 weeks
1252.54545 -1.02313 (125*2π)/1721 weeks
1261.97603 .13826 (126*2π)/1721 weeks
1272.00057 .08137 (127*2π)/1721 weeks
1282.43215 .869 (128*2π)/1721 weeks
1291.47848 1.58108 (129*2π)/1721 weeks
130.449 1.13645 (130*2π)/1721 weeks
131-.48302 .4664 (131*2π)/1721 weeks
132-1.35818 -.52567 (132*2π)/1721 weeks
133.08334 -2.09704 (133*2π)/1721 weeks
1341.92459 -1.16817 (134*2π)/1721 weeks
1351.47963 -.2481 (135*2π)/1721 weeks
136.80749 -.55593 (136*2π)/1721 weeks
137.91155 -.25168 (137*2π)/1721 weeks
138.39325 .32937 (138*2π)/1721 weeks
139-.1128 .37698 (139*2π)/1721 weeks
140-.11353 -.18985 (140*2π)/1721 weeks
141.047 -1.18572 (141*2π)/1721 weeks
142.44043 -1.88403 (142*2π)/1721 weeks
1431.35091 -1.6224 (143*2π)/1721 weeks
144.57071 -.76237 (144*2π)/1721 weeks
145-.10917 -2.08016 (145*2π)/1721 weeks
146.97667 -1.88865 (146*2π)/1721 weeks
147.56611 -1.03363 (147*2π)/1721 weeks
148.30454 -1.68695 (148*2π)/1721 weeks
1491.77937 -2.09051 (149*2π)/1721 weeks
1501.35262 -.43921 (150*2π)/1721 weeks
151-.90106 -.19745 (151*2π)/1721 weeks
152-2.57838 -2.12724 (152*2π)/1721 weeks
153-.91466 -4.39881 (153*2π)/1721 weeks
1541.75957 -4.90556 (154*2π)/1721 weeks
1551.70565 -3.05911 (155*2π)/1721 weeks
156.2916 -2.5613 (156*2π)/1721 weeks
157.32817 -2.93233 (157*2π)/1721 weeks
158.26412 -3.79508 (158*2π)/1721 weeks
159.22189 -5.11513 (159*2π)/1721 weeks
160-.46203 -6.08978 (160*2π)/1721 weeks
161-1.19562 -8.57943 (161*2π)/1721 weeks
1622.40586 -11.05025 (162*2π)/1721 weeks
1637.64256 -10.91274 (163*2π)/1721 weeks
16414.46099 -5.18313 (164*2π)/1721 weeks
1658.70355 3.75478 (165*2π)/1721 weeks
166-2.14503 -.77346 (166*2π)/1721 weeks
167-.37376 -12.26253 (167*2π)/1721 weeks
1685.89542 -7.99339 (168*2π)/1721 weeks
169-7.2561 -3.08004 (169*2π)/1721 weeks
170-8.78476 -24.28491 (170*2π)/1721 weeks

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