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Fourier Analysis of JNUG (Direxion Daily Jr Gld Mnrs Bull 3X ETF)


JNUG (Direxion Daily Jr Gld Mnrs Bull 3X ETF) appears to have interesting cyclic behaviour every 22 weeks (41.8299*cosine), 18 weeks (33.9569*sine), and 20 weeks (31.1461*sine).

JNUG (Direxion Daily Jr Gld Mnrs Bull 3X ETF) has an average price of 130.1 (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 4/16/2018 for JNUG (Direxion Daily Jr Gld Mnrs Bull 3X ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0130.0981   0 
1127.6138 110.7316 (1*2π)/238238 weeks
223.08559 142.8466 (2*2π)/238119 weeks
3-19.71029 58.60592 (3*2π)/23879 weeks
4-24.83523 19.07175 (4*2π)/23860 weeks
521.83741 10.86773 (5*2π)/23848 weeks
615.80172 24.29661 (6*2π)/23840 weeks
7-3.38625 35.166 (7*2π)/23834 weeks
8-6.44511 6.03818 (8*2π)/23830 weeks
93.29845 -13.68765 (9*2π)/23826 weeks
1028.9521 -4.98345 (10*2π)/23824 weeks
1141.82994 13.81689 (11*2π)/23822 weeks
1227.18432 31.14606 (12*2π)/23820 weeks
1316.57828 33.95694 (13*2π)/23818 weeks
145.91928 31.81237 (14*2π)/23817 weeks
15-.93182 27.58998 (15*2π)/23816 weeks
16-.98783 17.07738 (16*2π)/23815 weeks
17-2.51705 15.28626 (17*2π)/23814 weeks
18.68445 15.13913 (18*2π)/23813 weeks
19-.50919 10.58573 (19*2π)/23813 weeks
20-.91036 11.0307 (20*2π)/23812 weeks
211.43187 9.28658 (21*2π)/23811 weeks
22.82565 8.2692 (22*2π)/23811 weeks
234.51734 7.05337 (23*2π)/23810 weeks
244.6569 9.41945 (24*2π)/23810 weeks
254.10085 15.25911 (25*2π)/23810 weeks
26-1.91645 13.90927 (26*2π)/2389 weeks
27-5.4707 11.40868 (27*2π)/2389 weeks
28-6.57945 3.90797 (28*2π)/2389 weeks
29-2.91379 1.27919 (29*2π)/2388 weeks
302.74925 .20492 (30*2π)/2388 weeks
314.91515 2.60768 (31*2π)/2388 weeks
324.28274 6.73053 (32*2π)/2387 weeks
33.47845 5.77856 (33*2π)/2387 weeks
341.28865 4.72551 (34*2π)/2387 weeks
353.34527 3.01548 (35*2π)/2387 weeks
362.62223 5.32623 (36*2π)/2387 weeks
371.09042 6.6984 (37*2π)/2386 weeks
38-.58325 3.0621 (38*2π)/2386 weeks
392.02493 2.24214 (39*2π)/2386 weeks
403.79335 4.14266 (40*2π)/2386 weeks
411.33701 5.55359 (41*2π)/2386 weeks
42-.11531 5.69613 (42*2π)/2386 weeks
43.41549 3.6084 (43*2π)/2386 weeks
44-1.73352 1.06636 (44*2π)/2385 weeks
45-.63246 2.18229 (45*2π)/2385 weeks
461.55687 -.86634 (46*2π)/2385 weeks
47.86042 -.68515 (47*2π)/2385 weeks
483.38367 1.21474 (48*2π)/2385 weeks
493.85075 .89363 (49*2π)/2385 weeks
502.35517 1.08097 (50*2π)/2385 weeks
514.03142 .41242 (51*2π)/2385 weeks
525.01769 1.9224 (52*2π)/2385 weeks
535.18693 5.37103 (53*2π)/2384 weeks
54.35469 5.85931 (54*2π)/2384 weeks
55-3.21661 3.52041 (55*2π)/2384 weeks
56-1.9458 -1.17847 (56*2π)/2384 weeks
57-1.30634 -2.01275 (57*2π)/2384 weeks
581.4638 -3.43124 (58*2π)/2384 weeks
592.31641 -4.89386 (59*2π)/2384 weeks
605.01179 -3.65686 (60*2π)/2384 weeks
617.21815 -1.96953 (61*2π)/2384 weeks
625.82472 -.09589 (62*2π)/2384 weeks
635.62338 .32237 (63*2π)/2384 weeks
646.66027 -.22644 (64*2π)/2384 weeks
657.46439 3.00949 (65*2π)/2384 weeks
665.25577 6.24949 (66*2π)/2384 weeks
67-.53122 5.06019 (67*2π)/2384 weeks
68-3.12229 .92511 (68*2π)/2384 weeks
69-1.42481 -4.33594 (69*2π)/2383 weeks
702.74286 -6.31247 (70*2π)/2383 weeks
716.97734 -5.49427 (71*2π)/2383 weeks
728.61481 -2.24984 (72*2π)/2383 weeks
738.36419 -.22444 (73*2π)/2383 weeks
747.03187 .79311 (74*2π)/2383 weeks
757.00509 2.03967 (75*2π)/2383 weeks
765.68335 1.63255 (76*2π)/2383 weeks
774.52638 1.79007 (77*2π)/2383 weeks
785.54961 1.03107 (78*2π)/2383 weeks
794.63675 .38096 (79*2π)/2383 weeks
804.88812 1.26252 (80*2π)/2383 weeks
815.19859 .54301 (81*2π)/2383 weeks
824.83723 .43227 (82*2π)/2383 weeks
835.45674 .53381 (83*2π)/2383 weeks
846.49012 .5479 (84*2π)/2383 weeks
855.69364 1.78452 (85*2π)/2383 weeks
865.05649 2.69851 (86*2π)/2383 weeks
874.7261 .60341 (87*2π)/2383 weeks
884.25062 .38524 (88*2π)/2383 weeks
896.80295 .71002 (89*2π)/2383 weeks
907.07331 .58323 (90*2π)/2383 weeks
917.17431 3.63766 (91*2π)/2383 weeks
926.02985 3.57675 (92*2π)/2383 weeks
934.38296 3.60271 (93*2π)/2383 weeks
944.75866 2.71375 (94*2π)/2383 weeks
954.75258 2.35108 (95*2π)/2383 weeks
965.33001 3.79017 (96*2π)/2382 weeks
974.47406 4.08586 (97*2π)/2382 weeks
982.48053 4.25746 (98*2π)/2382 weeks
992.78599 2.88761 (99*2π)/2382 weeks
1002.88892 2.04107 (100*2π)/2382 weeks
1012.99902 3.59101 (101*2π)/2382 weeks
1022.43604 3.25787 (102*2π)/2382 weeks
1031.05627 2.34485 (103*2π)/2382 weeks
1041.11792 1.87971 (104*2π)/2382 weeks
1052.04648 1.51476 (105*2π)/2382 weeks
1061.39893 .51201 (106*2π)/2382 weeks
1071.65157 1.30566 (107*2π)/2382 weeks
1081.85346 1.13735 (108*2π)/2382 weeks
109.49477 .0778 (109*2π)/2382 weeks
1101.3631 -.9563 (110*2π)/2382 weeks
1112.60744 -2.10345 (111*2π)/2382 weeks
1124.11324 -1.2575 (112*2π)/2382 weeks
1134.75844 .23002 (113*2π)/2382 weeks
1143.58533 1.367 (114*2π)/2382 weeks
1153.15086 .48519 (115*2π)/2382 weeks
1163.38512 .51272 (116*2π)/2382 weeks
1173.59854 2.05525 (117*2π)/2382 weeks
1181.30029 2.08042 (118*2π)/2382 weeks
119-.35314   (119*2π)/2382 weeks
1201.30029 -2.08042 (120*2π)/2382 weeks
1213.59854 -2.05525 (121*2π)/2382 weeks
1223.38512 -.51272 (122*2π)/2382 weeks
1233.15086 -.48519 (123*2π)/2382 weeks
1243.58533 -1.367 (124*2π)/2382 weeks
1254.75844 -.23002 (125*2π)/2382 weeks
1264.11324 1.2575 (126*2π)/2382 weeks
1272.60744 2.10345 (127*2π)/2382 weeks
1281.3631 .9563 (128*2π)/2382 weeks
129.49477 -.0778 (129*2π)/2382 weeks
1301.85346 -1.13735 (130*2π)/2382 weeks
1311.65157 -1.30566 (131*2π)/2382 weeks
1321.39893 -.51201 (132*2π)/2382 weeks
1332.04648 -1.51476 (133*2π)/2382 weeks
1341.11792 -1.87971 (134*2π)/2382 weeks
1351.05627 -2.34485 (135*2π)/2382 weeks
1362.43604 -3.25787 (136*2π)/2382 weeks
1372.99902 -3.59101 (137*2π)/2382 weeks
1382.88892 -2.04107 (138*2π)/2382 weeks
1392.78599 -2.88761 (139*2π)/2382 weeks
1402.48053 -4.25746 (140*2π)/2382 weeks
1414.47406 -4.08586 (141*2π)/2382 weeks
1425.33001 -3.79017 (142*2π)/2382 weeks
1434.75258 -2.35108 (143*2π)/2382 weeks
1444.75866 -2.71375 (144*2π)/2382 weeks
1454.38296 -3.60271 (145*2π)/2382 weeks
1466.02985 -3.57675 (146*2π)/2382 weeks
1477.17431 -3.63766 (147*2π)/2382 weeks
1487.07331 -.58323 (148*2π)/2382 weeks
1496.80295 -.71002 (149*2π)/2382 weeks
1504.25062 -.38524 (150*2π)/2382 weeks
1514.7261 -.60341 (151*2π)/2382 weeks
1525.05649 -2.69851 (152*2π)/2382 weeks
1535.69364 -1.78452 (153*2π)/2382 weeks
1546.49012 -.5479 (154*2π)/2382 weeks
1555.45674 -.53381 (155*2π)/2382 weeks
1564.83723 -.43227 (156*2π)/2382 weeks
1575.19859 -.54301 (157*2π)/2382 weeks
1584.88812 -1.26252 (158*2π)/2382 weeks
1594.63675 -.38096 (159*2π)/2381 weeks
1605.54961 -1.03107 (160*2π)/2381 weeks
1614.52638 -1.79007 (161*2π)/2381 weeks
1625.68335 -1.63255 (162*2π)/2381 weeks
1637.00509 -2.03967 (163*2π)/2381 weeks
1647.03187 -.79311 (164*2π)/2381 weeks
1658.36419 .22444 (165*2π)/2381 weeks
1668.61481 2.24984 (166*2π)/2381 weeks
1676.97734 5.49427 (167*2π)/2381 weeks
1682.74286 6.31247 (168*2π)/2381 weeks
169-1.42481 4.33594 (169*2π)/2381 weeks
170-3.12229 -.92511 (170*2π)/2381 weeks
171-.53122 -5.06019 (171*2π)/2381 weeks
1725.25577 -6.24949 (172*2π)/2381 weeks
1737.46439 -3.00949 (173*2π)/2381 weeks
1746.66027 .22644 (174*2π)/2381 weeks
1755.62338 -.32237 (175*2π)/2381 weeks
1765.82472 .09589 (176*2π)/2381 weeks
1777.21815 1.96953 (177*2π)/2381 weeks
1785.01179 3.65686 (178*2π)/2381 weeks
1792.31641 4.89386 (179*2π)/2381 weeks
1801.4638 3.43124 (180*2π)/2381 weeks
181-1.30634 2.01275 (181*2π)/2381 weeks
182-1.9458 1.17847 (182*2π)/2381 weeks
183-3.21661 -3.52041 (183*2π)/2381 weeks
184.35469 -5.85931 (184*2π)/2381 weeks
1855.18693 -5.37103 (185*2π)/2381 weeks
1865.01769 -1.9224 (186*2π)/2381 weeks
1874.03142 -.41242 (187*2π)/2381 weeks
1882.35517 -1.08097 (188*2π)/2381 weeks
1893.85075 -.89363 (189*2π)/2381 weeks
1903.38367 -1.21474 (190*2π)/2381 weeks
191.86042 .68515 (191*2π)/2381 weeks
1921.55687 .86634 (192*2π)/2381 weeks
193-.63246 -2.18229 (193*2π)/2381 weeks
194-1.73352 -1.06636 (194*2π)/2381 weeks
195.41549 -3.6084 (195*2π)/2381 weeks
196-.11531 -5.69613 (196*2π)/2381 weeks
1971.33701 -5.55359 (197*2π)/2381 weeks
1983.79335 -4.14266 (198*2π)/2381 weeks
1992.02493 -2.24214 (199*2π)/2381 weeks
200-.58325 -3.0621 (200*2π)/2381 weeks
2011.09042 -6.6984 (201*2π)/2381 weeks
2022.62223 -5.32623 (202*2π)/2381 weeks
2033.34527 -3.01548 (203*2π)/2381 weeks
2041.28865 -4.72551 (204*2π)/2381 weeks
205.47845 -5.77856 (205*2π)/2381 weeks
2064.28274 -6.73053 (206*2π)/2381 weeks
2074.91515 -2.60768 (207*2π)/2381 weeks
2082.74925 -.20492 (208*2π)/2381 weeks
209-2.91379 -1.27919 (209*2π)/2381 weeks
210-6.57945 -3.90797 (210*2π)/2381 weeks
211-5.4707 -11.40868 (211*2π)/2381 weeks
212-1.91645 -13.90927 (212*2π)/2381 weeks
2134.10085 -15.25911 (213*2π)/2381 weeks
2144.6569 -9.41945 (214*2π)/2381 weeks
2154.51734 -7.05337 (215*2π)/2381 weeks
216.82565 -8.2692 (216*2π)/2381 weeks
2171.43187 -9.28658 (217*2π)/2381 weeks
218-.91036 -11.0307 (218*2π)/2381 weeks
219-.50919 -10.58573 (219*2π)/2381 weeks
220.68445 -15.13913 (220*2π)/2381 weeks
221-2.51705 -15.28626 (221*2π)/2381 weeks
222-.98783 -17.07738 (222*2π)/2381 weeks
223-.93182 -27.58998 (223*2π)/2381 weeks
2245.91928 -31.81237 (224*2π)/2381 weeks
22516.57828 -33.95694 (225*2π)/2381 weeks
22627.18432 -31.14606 (226*2π)/2381 weeks
22741.82994 -13.81689 (227*2π)/2381 weeks
22828.9521 4.98345 (228*2π)/2381 weeks
2293.29845 13.68765 (229*2π)/2381 weeks
230-6.44511 -6.03818 (230*2π)/2381 weeks
231-3.38625 -35.166 (231*2π)/2381 weeks
23215.80172 -24.29661 (232*2π)/2381 weeks
23321.83741 -10.86773 (233*2π)/2381 weeks
234-24.83523 -19.07175 (234*2π)/2381 weeks
235-19.71029 -58.60592 (235*2π)/2381 weeks
23623.08559 -142.8466 (236*2π)/2381 weeks



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