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Fourier Analysis of JNUG (DIREXION DAILY JUNIOR GOLD MINERS INDEX BULL 3X SHARES DIREXION DAILY JUNIOR GOLD MINERS INDEX BULL 3X SHARES)


JNUG (DIREXION DAILY JUNIOR GOLD MINERS INDEX BULL 3X SHARES DIREXION DAILY JUNIOR GOLD MINERS INDEX BULL 3X SHARES) appears to have interesting cyclic behaviour every 23 weeks (40.1462*cosine), 20 weeks (35.4899*cosine), and 20 weeks (30.1906*sine).

JNUG (DIREXION DAILY JUNIOR GOLD MINERS INDEX BULL 3X SHARES DIREXION DAILY JUNIOR GOLD MINERS INDEX BULL 3X SHARES) has an average price of 136.8 (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 1/16/2018 for JNUG (DIREXION DAILY JUNIOR GOLD MINERS INDEX BULL 3X SHARES DIREXION DAILY JUNIOR GOLD MINERS INDEX BULL 3X SHARES), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0136.8006   0 
1131.2705 118.7945 (1*2π)/225225 weeks
28.00874 143.0042 (2*2π)/225113 weeks
3-18.80724 56.9379 (3*2π)/22575 weeks
4-16.84628 6.01853 (4*2π)/22556 weeks
522.8986 21.45783 (5*2π)/22545 weeks
617.22728 30.6685 (6*2π)/22538 weeks
7-14.0716 22.18941 (7*2π)/22532 weeks
8-5.95939 .80317 (8*2π)/22528 weeks
923.34616 -13.28248 (9*2π)/22525 weeks
1040.14624 1.99127 (10*2π)/22523 weeks
1135.48994 30.19061 (11*2π)/22520 weeks
1221.12477 34.73689 (12*2π)/22519 weeks
138.64387 34.68613 (13*2π)/22517 weeks
14.83776 29.92435 (14*2π)/22516 weeks
15-2.38472 18.35608 (15*2π)/22515 weeks
16-2.80266 16.88101 (16*2π)/22514 weeks
17.74966 15.97142 (17*2π)/22513 weeks
18-.31677 11.18141 (18*2π)/22513 weeks
19-1.04819 11.13286 (19*2π)/22512 weeks
201.46936 10.05 (20*2π)/22511 weeks
211.17411 8.09826 (21*2π)/22511 weeks
225.59969 8.86185 (22*2π)/22510 weeks
236.40778 10.71395 (23*2π)/22510 weeks
24.99184 16.23731 (24*2π)/2259 weeks
25-3.54087 13.46733 (25*2π)/2259 weeks
26-7.96073 8.53164 (26*2π)/2259 weeks
27-4.01994 2.16028 (27*2π)/2258 weeks
28.27578 -.90714 (28*2π)/2258 weeks
294.12881 1.98298 (29*2π)/2258 weeks
305.25961 6.18627 (30*2π)/2258 weeks
31.87577 7.04023 (31*2π)/2257 weeks
321.54225 4.9703 (32*2π)/2257 weeks
333.03852 2.92941 (33*2π)/2257 weeks
342.75409 5.66311 (34*2π)/2257 weeks
351.02296 7.08295 (35*2π)/2256 weeks
36-.40168 2.96092 (36*2π)/2256 weeks
372.43735 2.40989 (37*2π)/2256 weeks
383.82789 5.09658 (38*2π)/2256 weeks
391.21022 5.45888 (39*2π)/2256 weeks
40-1.24428 4.82574 (40*2π)/2256 weeks
41-.86876 4.7327 (41*2π)/2255 weeks
42.48786 1.02937 (42*2π)/2255 weeks
43-1.16331 -.20243 (43*2π)/2255 weeks
441.53771 .8839 (44*2π)/2255 weeks
454.06473 -.53695 (45*2π)/2255 weeks
463.22635 .25795 (46*2π)/2255 weeks
472.66251 1.74891 (47*2π)/2255 weeks
483.7388 .26481 (48*2π)/2255 weeks
495.17047 1.76811 (49*2π)/2255 weeks
505.78185 5.05234 (50*2π)/2255 weeks
51.48368 6.29134 (51*2π)/2254 weeks
52-3.46285 3.70871 (52*2π)/2254 weeks
53-1.88641 -1.30023 (53*2π)/2254 weeks
54-1.35151 -2.56194 (54*2π)/2254 weeks
551.58788 -3.31492 (55*2π)/2254 weeks
563.64883 -5.22647 (56*2π)/2254 weeks
575.83513 -3.7932 (57*2π)/2254 weeks
587.46327 -.68504 (58*2π)/2254 weeks
596.26765 -.14689 (59*2π)/2254 weeks
605.86776 -.15151 (60*2π)/2254 weeks
618.2186 1.25036 (61*2π)/2254 weeks
626.962 4.83863 (62*2π)/2254 weeks
631.06301 6.73566 (63*2π)/2254 weeks
64-2.66125 2.65067 (64*2π)/2254 weeks
65-2.38087 -3.52907 (65*2π)/2253 weeks
662.06636 -6.56682 (66*2π)/2253 weeks
676.82854 -6.18914 (67*2π)/2253 weeks
689.0755 -2.62845 (68*2π)/2253 weeks
698.81623 -.29008 (69*2π)/2253 weeks
707.39296 .78531 (70*2π)/2253 weeks
717.10585 2.28668 (71*2π)/2253 weeks
726.01717 1.77148 (72*2π)/2253 weeks
734.54087 1.32878 (73*2π)/2253 weeks
745.47054 1.63781 (74*2π)/2253 weeks
755.65992 .47631 (75*2π)/2253 weeks
764.85616 .78726 (76*2π)/2253 weeks
775.371 .92087 (77*2π)/2253 weeks
785.69725 .27678 (78*2π)/2253 weeks
796.05311 .19933 (79*2π)/2253 weeks
806.57151 1.90839 (80*2π)/2253 weeks
816.14169 2.33511 (81*2π)/2253 weeks
824.29778 .89614 (82*2π)/2253 weeks
834.59935 1.0237 (83*2π)/2253 weeks
847.146 .22511 (84*2π)/2253 weeks
857.16248 .529 (85*2π)/2253 weeks
867.64646 3.7516 (86*2π)/2253 weeks
876.3127 3.77771 (87*2π)/2253 weeks
884.50012 3.628 (88*2π)/2253 weeks
894.99501 2.93451 (89*2π)/2253 weeks
905.34199 2.44946 (90*2π)/2253 weeks
915.12573 4.2061 (91*2π)/2252 weeks
924.35791 4.75638 (92*2π)/2252 weeks
932.30866 3.5318 (93*2π)/2252 weeks
942.64088 3.02682 (94*2π)/2252 weeks
953.94855 2.83665 (95*2π)/2252 weeks
962.49388 3.2777 (96*2π)/2252 weeks
971.34216 3.40796 (97*2π)/2252 weeks
981.50161 2.20485 (98*2π)/2252 weeks
991.94259 1.13824 (99*2π)/2252 weeks
1001.0811 1.00267 (100*2π)/2252 weeks
1012.00546 1.43208 (101*2π)/2252 weeks
1022.00318 1.04663 (102*2π)/2252 weeks
103.483 .19941 (103*2π)/2252 weeks
1041.41799 -1.02226 (104*2π)/2252 weeks
1052.90643 -2.22625 (105*2π)/2252 weeks
1064.45777 -1.22243 (106*2π)/2252 weeks
1074.8996 .56466 (107*2π)/2252 weeks
1083.32481 1.31856 (108*2π)/2252 weeks
1093.44603 .60004 (109*2π)/2252 weeks
1103.96306 .75449 (110*2π)/2252 weeks
1112.68555 2.6531 (111*2π)/2252 weeks
112.42304 1.65322 (112*2π)/2252 weeks
113.42304 -1.65322 (113*2π)/2252 weeks
1142.68555 -2.6531 (114*2π)/2252 weeks
1153.96306 -.75449 (115*2π)/2252 weeks
1163.44603 -.60004 (116*2π)/2252 weeks
1173.32481 -1.31856 (117*2π)/2252 weeks
1184.8996 -.56466 (118*2π)/2252 weeks
1194.45777 1.22243 (119*2π)/2252 weeks
1202.90643 2.22625 (120*2π)/2252 weeks
1211.41799 1.02226 (121*2π)/2252 weeks
122.483 -.19941 (122*2π)/2252 weeks
1232.00318 -1.04663 (123*2π)/2252 weeks
1242.00546 -1.43208 (124*2π)/2252 weeks
1251.0811 -1.00267 (125*2π)/2252 weeks
1261.94259 -1.13824 (126*2π)/2252 weeks
1271.50161 -2.20485 (127*2π)/2252 weeks
1281.34216 -3.40796 (128*2π)/2252 weeks
1292.49388 -3.2777 (129*2π)/2252 weeks
1303.94855 -2.83665 (130*2π)/2252 weeks
1312.64088 -3.02682 (131*2π)/2252 weeks
1322.30866 -3.5318 (132*2π)/2252 weeks
1334.35791 -4.75638 (133*2π)/2252 weeks
1345.12573 -4.2061 (134*2π)/2252 weeks
1355.34199 -2.44946 (135*2π)/2252 weeks
1364.99501 -2.93451 (136*2π)/2252 weeks
1374.50012 -3.628 (137*2π)/2252 weeks
1386.3127 -3.77771 (138*2π)/2252 weeks
1397.64646 -3.7516 (139*2π)/2252 weeks
1407.16248 -.529 (140*2π)/2252 weeks
1417.146 -.22511 (141*2π)/2252 weeks
1424.59935 -1.0237 (142*2π)/2252 weeks
1434.29778 -.89614 (143*2π)/2252 weeks
1446.14169 -2.33511 (144*2π)/2252 weeks
1456.57151 -1.90839 (145*2π)/2252 weeks
1466.05311 -.19933 (146*2π)/2252 weeks
1475.69725 -.27678 (147*2π)/2252 weeks
1485.371 -.92087 (148*2π)/2252 weeks
1494.85616 -.78726 (149*2π)/2252 weeks
1505.65992 -.47631 (150*2π)/2252 weeks
1515.47054 -1.63781 (151*2π)/2251 weeks
1524.54087 -1.32878 (152*2π)/2251 weeks
1536.01717 -1.77148 (153*2π)/2251 weeks
1547.10585 -2.28668 (154*2π)/2251 weeks
1557.39296 -.78531 (155*2π)/2251 weeks
1568.81623 .29008 (156*2π)/2251 weeks
1579.0755 2.62845 (157*2π)/2251 weeks
1586.82854 6.18914 (158*2π)/2251 weeks
1592.06636 6.56682 (159*2π)/2251 weeks
160-2.38087 3.52907 (160*2π)/2251 weeks
161-2.66125 -2.65067 (161*2π)/2251 weeks
1621.06301 -6.73566 (162*2π)/2251 weeks
1636.962 -4.83863 (163*2π)/2251 weeks
1648.2186 -1.25036 (164*2π)/2251 weeks
1655.86776 .15151 (165*2π)/2251 weeks
1666.26765 .14689 (166*2π)/2251 weeks
1677.46327 .68504 (167*2π)/2251 weeks
1685.83513 3.7932 (168*2π)/2251 weeks
1693.64883 5.22647 (169*2π)/2251 weeks
1701.58788 3.31492 (170*2π)/2251 weeks
171-1.35151 2.56194 (171*2π)/2251 weeks
172-1.88641 1.30023 (172*2π)/2251 weeks
173-3.46285 -3.70871 (173*2π)/2251 weeks
174.48368 -6.29134 (174*2π)/2251 weeks
1755.78185 -5.05234 (175*2π)/2251 weeks
1765.17047 -1.76811 (176*2π)/2251 weeks
1773.7388 -.26481 (177*2π)/2251 weeks
1782.66251 -1.74891 (178*2π)/2251 weeks
1793.22635 -.25795 (179*2π)/2251 weeks
1804.06473 .53695 (180*2π)/2251 weeks
1811.53771 -.8839 (181*2π)/2251 weeks
182-1.16331 .20243 (182*2π)/2251 weeks
183.48786 -1.02937 (183*2π)/2251 weeks
184-.86876 -4.7327 (184*2π)/2251 weeks
185-1.24428 -4.82574 (185*2π)/2251 weeks
1861.21022 -5.45888 (186*2π)/2251 weeks
1873.82789 -5.09658 (187*2π)/2251 weeks
1882.43735 -2.40989 (188*2π)/2251 weeks
189-.40168 -2.96092 (189*2π)/2251 weeks
1901.02296 -7.08295 (190*2π)/2251 weeks
1912.75409 -5.66311 (191*2π)/2251 weeks
1923.03852 -2.92941 (192*2π)/2251 weeks
1931.54225 -4.9703 (193*2π)/2251 weeks
194.87577 -7.04023 (194*2π)/2251 weeks
1955.25961 -6.18627 (195*2π)/2251 weeks
1964.12881 -1.98298 (196*2π)/2251 weeks
197.27578 .90714 (197*2π)/2251 weeks
198-4.01994 -2.16028 (198*2π)/2251 weeks
199-7.96073 -8.53164 (199*2π)/2251 weeks
200-3.54087 -13.46733 (200*2π)/2251 weeks
201.99184 -16.23731 (201*2π)/2251 weeks
2026.40778 -10.71395 (202*2π)/2251 weeks
2035.59969 -8.86185 (203*2π)/2251 weeks
2041.17411 -8.09826 (204*2π)/2251 weeks
2051.46936 -10.05 (205*2π)/2251 weeks
206-1.04819 -11.13286 (206*2π)/2251 weeks
207-.31677 -11.18141 (207*2π)/2251 weeks
208.74966 -15.97142 (208*2π)/2251 weeks
209-2.80266 -16.88101 (209*2π)/2251 weeks
210-2.38472 -18.35608 (210*2π)/2251 weeks
211.83776 -29.92435 (211*2π)/2251 weeks
2128.64387 -34.68613 (212*2π)/2251 weeks
21321.12477 -34.73689 (213*2π)/2251 weeks
21435.48994 -30.19061 (214*2π)/2251 weeks
21540.14624 -1.99127 (215*2π)/2251 weeks
21623.34616 13.28248 (216*2π)/2251 weeks
217-5.95939 -.80317 (217*2π)/2251 weeks
218-14.0716 -22.18941 (218*2π)/2251 weeks
21917.22728 -30.6685 (219*2π)/2251 weeks
22022.8986 -21.45783 (220*2π)/2251 weeks
221-16.84628 -6.01853 (221*2π)/2251 weeks
222-18.80724 -56.9379 (222*2π)/2251 weeks
2238.00874 -143.0042 (223*2π)/2251 weeks



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