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Fourier Analysis of JNUG (Direxion Daily Junior Gold Miners Index Bull 3x Shares ETF)


JNUG (Direxion Daily Junior Gold Miners Index Bull 3x Shares ETF) appears to have interesting cyclic behaviour every 18 weeks (40.3767*sine), 20 weeks (36.595*sine), and 20 weeks (33.2752*cosine).

JNUG (Direxion Daily Junior Gold Miners Index Bull 3x Shares ETF) has an average price of 152.36 (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 7/17/2017 for JNUG (Direxion Daily Junior Gold Miners Index Bull 3x Shares ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0152.3577   0 
1138.1809 140.6397 (1*2π)/199199 weeks
2-22.07104 128.2247 (2*2π)/199100 weeks
3-28.07986 50.9721 (3*2π)/19966 weeks
418.82023 3.12789 (4*2π)/19950 weeks
518.67962 28.52478 (5*2π)/19940 weeks
6-11.51878 35.74118 (6*2π)/19933 weeks
7-6.70979 2.65002 (7*2π)/19928 weeks
827.61847 -14.33763 (8*2π)/19925 weeks
948.54021 7.43864 (9*2π)/19922 weeks
1033.27518 36.59499 (10*2π)/19920 weeks
1117.66301 40.37672 (11*2π)/19918 weeks
124.30841 35.45578 (12*2π)/19917 weeks
13-5.13243 24.79607 (13*2π)/19915 weeks
14-2.44344 20.93115 (14*2π)/19914 weeks
151.13749 17.98623 (15*2π)/19913 weeks
16.30151 12.79006 (16*2π)/19912 weeks
17-.638 11.2346 (17*2π)/19912 weeks
181.15043 11.17595 (18*2π)/19911 weeks
193.70603 7.7937 (19*2π)/19910 weeks
205.51717 11.34067 (20*2π)/19910 weeks
213.82312 18.63239 (21*2π)/1999 weeks
22-3.43093 15.74707 (22*2π)/1999 weeks
23-8.96835 9.74524 (23*2π)/1999 weeks
24-4.09802 2.41722 (24*2π)/1998 weeks
252.62104 -.2072 (25*2π)/1998 weeks
266.08418 3.5704 (26*2π)/1998 weeks
273.67431 8.77838 (27*2π)/1997 weeks
281.42706 5.34536 (28*2π)/1997 weeks
292.08993 3.35937 (29*2π)/1997 weeks
303.23044 6.55881 (30*2π)/1997 weeks
31.87251 8.06715 (31*2π)/1996 weeks
32.24305 2.94521 (32*2π)/1996 weeks
333.62821 3.22581 (33*2π)/1996 weeks
342.65421 7.05293 (34*2π)/1996 weeks
35.45617 6.90066 (35*2π)/1996 weeks
36.33298 4.55424 (36*2π)/1996 weeks
37-.49506 .62556 (37*2π)/1995 weeks
38-1.55638 -.065 (38*2π)/1995 weeks
391.23004 .78853 (39*2π)/1995 weeks
404.5621 .7408 (40*2π)/1995 weeks
414.59814 1.05163 (41*2π)/1995 weeks
423.05152 .6375 (42*2π)/1995 weeks
435.59942 1.13537 (43*2π)/1995 weeks
446.81757 4.06824 (44*2π)/1995 weeks
451.07757 7.38824 (45*2π)/1994 weeks
46-3.92199 4.11664 (46*2π)/1994 weeks
47-1.62489 -1.55256 (47*2π)/1994 weeks
48-.67025 -4.12812 (48*2π)/1994 weeks
491.49908 -4.39953 (49*2π)/1994 weeks
505.8726 -4.54116 (50*2π)/1994 weeks
518.71428 -2.33156 (51*2π)/1994 weeks
527.02367 -.16726 (52*2π)/1994 weeks
536.60104 .0222 (53*2π)/1994 weeks
549.36091 1.76654 (54*2π)/1994 weeks
557.36738 6.43014 (55*2π)/1994 weeks
56-.54493 6.1705 (56*2π)/1994 weeks
57-3.85932 -.12943 (57*2π)/1993 weeks
58.05878 -6.5656 (58*2π)/1993 weeks
596.14383 -7.55845 (59*2π)/1993 weeks
6010.20857 -3.58452 (60*2π)/1993 weeks
6110.0086 -.37645 (61*2π)/1993 weeks
628.42865 .84983 (62*2π)/1993 weeks
637.32969 2.67057 (63*2π)/1993 weeks
646.51509 2.46576 (64*2π)/1993 weeks
656.22586 .71968 (65*2π)/1993 weeks
665.37421 .64997 (66*2π)/1993 weeks
675.59927 1.41792 (67*2π)/1993 weeks
686.17053 1.02913 (68*2π)/1993 weeks
696.43619 .35453 (69*2π)/1993 weeks
707.15465 .24485 (70*2π)/1993 weeks
716.88139 2.18643 (71*2π)/1993 weeks
725.59769 3.16267 (72*2π)/1993 weeks
736.12409 1.17979 (73*2π)/1993 weeks
746.90024 -.73021 (74*2π)/1993 weeks
757.50022 .82577 (75*2π)/1993 weeks
768.88737 4.08288 (76*2π)/1993 weeks
777.06084 4.37392 (77*2π)/1993 weeks
785.00013 3.68837 (78*2π)/1993 weeks
795.43222 3.37528 (79*2π)/1993 weeks
806.69698 3.76144 (80*2π)/1992 weeks
815.32695 4.76777 (81*2π)/1992 weeks
822.77649 4.91337 (82*2π)/1992 weeks
833.15574 3.55123 (83*2π)/1992 weeks
844.44669 3.13504 (84*2π)/1992 weeks
852.86898 3.65532 (85*2π)/1992 weeks
861.20037 3.19681 (86*2π)/1992 weeks
871.27507 2.16163 (87*2π)/1992 weeks
882.0226 2.1766 (88*2π)/1992 weeks
892.66161 .97165 (89*2π)/1992 weeks
902.12302 .88855 (90*2π)/1992 weeks
91.56387 .57944 (91*2π)/1992 weeks
921.61214 -1.16325 (92*2π)/1992 weeks
933.73515 -2.4116 (93*2π)/1992 weeks
945.43391 -.95593 (94*2π)/1992 weeks
955.02378 1.35974 (95*2π)/1992 weeks
963.56385 .67863 (96*2π)/1992 weeks
974.01986 .63483 (97*2π)/1992 weeks
983.69278 2.86721 (98*2π)/1992 weeks
99.63097 2.00313 (99*2π)/1992 weeks
100.63097 -2.00313 (100*2π)/1992 weeks
1013.69278 -2.86721 (101*2π)/1992 weeks
1024.01986 -.63483 (102*2π)/1992 weeks
1033.56385 -.67863 (103*2π)/1992 weeks
1045.02378 -1.35974 (104*2π)/1992 weeks
1055.43391 .95593 (105*2π)/1992 weeks
1063.73515 2.4116 (106*2π)/1992 weeks
1071.61214 1.16325 (107*2π)/1992 weeks
108.56387 -.57944 (108*2π)/1992 weeks
1092.12302 -.88855 (109*2π)/1992 weeks
1102.66161 -.97165 (110*2π)/1992 weeks
1112.0226 -2.1766 (111*2π)/1992 weeks
1121.27507 -2.16163 (112*2π)/1992 weeks
1131.20037 -3.19681 (113*2π)/1992 weeks
1142.86898 -3.65532 (114*2π)/1992 weeks
1154.44669 -3.13504 (115*2π)/1992 weeks
1163.15574 -3.55123 (116*2π)/1992 weeks
1172.77649 -4.91337 (117*2π)/1992 weeks
1185.32695 -4.76777 (118*2π)/1992 weeks
1196.69698 -3.76144 (119*2π)/1992 weeks
1205.43222 -3.37528 (120*2π)/1992 weeks
1215.00013 -3.68837 (121*2π)/1992 weeks
1227.06084 -4.37392 (122*2π)/1992 weeks
1238.88737 -4.08288 (123*2π)/1992 weeks
1247.50022 -.82577 (124*2π)/1992 weeks
1256.90024 .73021 (125*2π)/1992 weeks
1266.12409 -1.17979 (126*2π)/1992 weeks
1275.59769 -3.16267 (127*2π)/1992 weeks
1286.88139 -2.18643 (128*2π)/1992 weeks
1297.15465 -.24485 (129*2π)/1992 weeks
1306.43619 -.35453 (130*2π)/1992 weeks
1316.17053 -1.02913 (131*2π)/1992 weeks
1325.59927 -1.41792 (132*2π)/1992 weeks
1335.37421 -.64997 (133*2π)/1991 weeks
1346.22586 -.71968 (134*2π)/1991 weeks
1356.51509 -2.46576 (135*2π)/1991 weeks
1367.32969 -2.67057 (136*2π)/1991 weeks
1378.42865 -.84983 (137*2π)/1991 weeks
13810.0086 .37645 (138*2π)/1991 weeks
13910.20857 3.58452 (139*2π)/1991 weeks
1406.14383 7.55845 (140*2π)/1991 weeks
141.05878 6.5656 (141*2π)/1991 weeks
142-3.85932 .12943 (142*2π)/1991 weeks
143-.54493 -6.1705 (143*2π)/1991 weeks
1447.36738 -6.43014 (144*2π)/1991 weeks
1459.36091 -1.76654 (145*2π)/1991 weeks
1466.60104 -.0222 (146*2π)/1991 weeks
1477.02367 .16726 (147*2π)/1991 weeks
1488.71428 2.33156 (148*2π)/1991 weeks
1495.8726 4.54116 (149*2π)/1991 weeks
1501.49908 4.39953 (150*2π)/1991 weeks
151-.67025 4.12812 (151*2π)/1991 weeks
152-1.62489 1.55256 (152*2π)/1991 weeks
153-3.92199 -4.11664 (153*2π)/1991 weeks
1541.07757 -7.38824 (154*2π)/1991 weeks
1556.81757 -4.06824 (155*2π)/1991 weeks
1565.59942 -1.13537 (156*2π)/1991 weeks
1573.05152 -.6375 (157*2π)/1991 weeks
1584.59814 -1.05163 (158*2π)/1991 weeks
1594.5621 -.7408 (159*2π)/1991 weeks
1601.23004 -.78853 (160*2π)/1991 weeks
161-1.55638 .065 (161*2π)/1991 weeks
162-.49506 -.62556 (162*2π)/1991 weeks
163.33298 -4.55424 (163*2π)/1991 weeks
164.45617 -6.90066 (164*2π)/1991 weeks
1652.65421 -7.05293 (165*2π)/1991 weeks
1663.62821 -3.22581 (166*2π)/1991 weeks
167.24305 -2.94521 (167*2π)/1991 weeks
168.87251 -8.06715 (168*2π)/1991 weeks
1693.23044 -6.55881 (169*2π)/1991 weeks
1702.08993 -3.35937 (170*2π)/1991 weeks
1711.42706 -5.34536 (171*2π)/1991 weeks
1723.67431 -8.77838 (172*2π)/1991 weeks
1736.08418 -3.5704 (173*2π)/1991 weeks
1742.62104 .2072 (174*2π)/1991 weeks
175-4.09802 -2.41722 (175*2π)/1991 weeks
176-8.96835 -9.74524 (176*2π)/1991 weeks
177-3.43093 -15.74707 (177*2π)/1991 weeks
1783.82312 -18.63239 (178*2π)/1991 weeks
1795.51717 -11.34067 (179*2π)/1991 weeks
1803.70603 -7.7937 (180*2π)/1991 weeks
1811.15043 -11.17595 (181*2π)/1991 weeks
182-.638 -11.2346 (182*2π)/1991 weeks
183.30151 -12.79006 (183*2π)/1991 weeks
1841.13749 -17.98623 (184*2π)/1991 weeks
185-2.44344 -20.93115 (185*2π)/1991 weeks
186-5.13243 -24.79607 (186*2π)/1991 weeks
1874.30841 -35.45578 (187*2π)/1991 weeks
18817.66301 -40.37672 (188*2π)/1991 weeks
18933.27518 -36.59499 (189*2π)/1991 weeks
19048.54021 -7.43864 (190*2π)/1991 weeks
19127.61847 14.33763 (191*2π)/1991 weeks
192-6.70979 -2.65002 (192*2π)/1991 weeks
193-11.51878 -35.74118 (193*2π)/1991 weeks
19418.67962 -28.52478 (194*2π)/1991 weeks
19518.82023 -3.12789 (195*2π)/1991 weeks
196-28.07986 -50.9721 (196*2π)/1991 weeks
197-22.07104 -128.2247 (197*2π)/1991 weeks



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