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Fourier Analysis of BRZU (Direxion Daily Brazil Bull 3X S)


BRZU (Direxion Daily Brazil Bull 3X S) appears to have interesting cyclic behaviour every 17 weeks (16.0458*sine), 18 weeks (13.8811*sine), and 20 weeks (11.26*sine).

BRZU (Direxion Daily Brazil Bull 3X S) has an average price of 119.79 (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 4/10/2013 to 1/17/2017 for BRZU (Direxion Daily Brazil Bull 3X S), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0119.7948   0 
128.37395 117.1151 (1*2π)/198198 weeks
26.2813 9.99916 (2*2π)/19899 weeks
328.93427 27.17465 (3*2π)/19866 weeks
4-8.65113 33.64276 (4*2π)/19850 weeks
56.20517 -4.25972 (5*2π)/19840 weeks
620.21273 14.48915 (6*2π)/19833 weeks
716.08515 17.14109 (7*2π)/19828 weeks
812.4658 22.25202 (8*2π)/19825 weeks
95.30211 25.478 (9*2π)/19822 weeks
10-.23433 11.25995 (10*2π)/19820 weeks
116.04726 13.88114 (11*2π)/19818 weeks
12-1.13491 16.04581 (12*2π)/19817 weeks
13.41219 8.98559 (13*2π)/19815 weeks
144.12193 8.93649 (14*2π)/19814 weeks
153.09313 11.83221 (15*2π)/19813 weeks
16.55578 8.17772 (16*2π)/19812 weeks
17-.94288 11.14884 (17*2π)/19812 weeks
18-3.94063 2.80135 (18*2π)/19811 weeks
19.91879 6.64115 (19*2π)/19810 weeks
20-3.93376 4.34517 (20*2π)/19810 weeks
21-1.11327 1.08956 (21*2π)/1989 weeks
222.41653 2.83764 (22*2π)/1989 weeks
23-1.2029 3.40636 (23*2π)/1989 weeks
242.49085 1.4035 (24*2π)/1988 weeks
251.84212 3.41124 (25*2π)/1988 weeks
262.6982 2.61519 (26*2π)/1988 weeks
273.72229 2.31106 (27*2π)/1987 weeks
281.98643 5.89334 (28*2π)/1987 weeks
29-.81847 1.98338 (29*2π)/1987 weeks
304.12316 .74237 (30*2π)/1987 weeks
311.579 4.9144 (31*2π)/1986 weeks
32.9405 .32877 (32*2π)/1986 weeks
331.85936 4.22314 (33*2π)/1986 weeks
34-1.80241 -.1232 (34*2π)/1986 weeks
355.28897 -1.07658 (35*2π)/1986 weeks
363.81549 4.00908 (36*2π)/1986 weeks
37-.06662 2.90131 (37*2π)/1985 weeks
383.33011 .99183 (38*2π)/1985 weeks
392.28841 4.48289 (39*2π)/1985 weeks
40-.44237 2.01285 (40*2π)/1985 weeks
411.41495 -.20865 (41*2π)/1985 weeks
424.08576 1.30254 (42*2π)/1985 weeks
432.01471 2.23808 (43*2π)/1985 weeks
443.34909 1.07739 (44*2π)/1985 weeks
452.60127 3.51344 (45*2π)/1984 weeks
461.00874 1.80431 (46*2π)/1984 weeks
472.63879 1.88029 (47*2π)/1984 weeks
48.57301 1.09121 (48*2π)/1984 weeks
493.00617 .67781 (49*2π)/1984 weeks
501.38898 1.83695 (50*2π)/1984 weeks
512.13776 .58969 (51*2π)/1984 weeks
522.26346 1.59935 (52*2π)/1984 weeks
531.49782 1.2817 (53*2π)/1984 weeks
542.08552 .54503 (54*2π)/1984 weeks
552.64525 1.352 (55*2π)/1984 weeks
562.47424 1.93521 (56*2π)/1984 weeks
571.2377 1.36362 (57*2π)/1983 weeks
582.35989 1.16901 (58*2π)/1983 weeks
591.39818 .89598 (59*2π)/1983 weeks
602.7696 .32735 (60*2π)/1983 weeks
611.6716 1.7865 (61*2π)/1983 weeks
621.09974 -.72588 (62*2π)/1983 weeks
633.48253 .77473 (63*2π)/1983 weeks
641.54492 1.38155 (64*2π)/1983 weeks
652.97985 -.44901 (65*2π)/1983 weeks
662.26363 2.27784 (66*2π)/1983 weeks
67.78128 -.89241 (67*2π)/1983 weeks
684.26714 -1.15949 (68*2π)/1983 weeks
692.98485 2.60469 (69*2π)/1983 weeks
701.85743 -.4838 (70*2π)/1983 weeks
713.83454 2.0675 (71*2π)/1983 weeks
72.99684 1.09641 (72*2π)/1983 weeks
733.14288 .57597 (73*2π)/1983 weeks
742.21646 1.39701 (74*2π)/1983 weeks
752.31877 .92788 (75*2π)/1983 weeks
763.19354 1.71335 (76*2π)/1983 weeks
771.27355 2.38721 (77*2π)/1983 weeks
781.35748 .25901 (78*2π)/1983 weeks
791.47459 1.29249 (79*2π)/1983 weeks
801.56294 .36321 (80*2π)/1982 weeks
811.13193 .84363 (81*2π)/1982 weeks
821.72414 -.65612 (82*2π)/1982 weeks
832.27968 .98237 (83*2π)/1982 weeks
841.77754 .16497 (84*2π)/1982 weeks
852.12443 .49125 (85*2π)/1982 weeks
861.73898 .5654 (86*2π)/1982 weeks
872.17011 -.46903 (87*2π)/1982 weeks
881.74102 .18997 (88*2π)/1982 weeks
891.72041 -.88464 (89*2π)/1982 weeks
902.42646 -.11201 (90*2π)/1982 weeks
911.80403 .08139 (91*2π)/1982 weeks
922.45638 -.15733 (92*2π)/1982 weeks
932.24679 -.34184 (93*2π)/1982 weeks
942.92266 -.37796 (94*2π)/1982 weeks
952.56305 .71859 (95*2π)/1982 weeks
962.56737 .94289 (96*2π)/1982 weeks
972.35065 .79203 (97*2π)/1982 weeks
98.95334 1.36744 (98*2π)/1982 weeks
99.56837   (99*2π)/1982 weeks
100.95334 -1.36744 (100*2π)/1982 weeks
1012.35065 -.79203 (101*2π)/1982 weeks
1022.56737 -.94289 (102*2π)/1982 weeks
1032.56305 -.71859 (103*2π)/1982 weeks
1042.92266 .37796 (104*2π)/1982 weeks
1052.24679 .34184 (105*2π)/1982 weeks
1062.45638 .15733 (106*2π)/1982 weeks
1071.80403 -.08139 (107*2π)/1982 weeks
1082.42646 .11201 (108*2π)/1982 weeks
1091.72041 .88464 (109*2π)/1982 weeks
1101.74102 -.18997 (110*2π)/1982 weeks
1112.17011 .46903 (111*2π)/1982 weeks
1121.73898 -.5654 (112*2π)/1982 weeks
1132.12443 -.49125 (113*2π)/1982 weeks
1141.77754 -.16497 (114*2π)/1982 weeks
1152.27968 -.98237 (115*2π)/1982 weeks
1161.72414 .65612 (116*2π)/1982 weeks
1171.13193 -.84363 (117*2π)/1982 weeks
1181.56294 -.36321 (118*2π)/1982 weeks
1191.47459 -1.29249 (119*2π)/1982 weeks
1201.35748 -.25901 (120*2π)/1982 weeks
1211.27355 -2.38721 (121*2π)/1982 weeks
1223.19354 -1.71335 (122*2π)/1982 weeks
1232.31877 -.92788 (123*2π)/1982 weeks
1242.21646 -1.39701 (124*2π)/1982 weeks
1253.14288 -.57597 (125*2π)/1982 weeks
126.99684 -1.09641 (126*2π)/1982 weeks
1273.83454 -2.0675 (127*2π)/1982 weeks
1281.85743 .4838 (128*2π)/1982 weeks
1292.98485 -2.60469 (129*2π)/1982 weeks
1304.26714 1.15949 (130*2π)/1982 weeks
131.78128 .89241 (131*2π)/1982 weeks
1322.26363 -2.27784 (132*2π)/1982 weeks
1332.97985 .44901 (133*2π)/1981 weeks
1341.54492 -1.38155 (134*2π)/1981 weeks
1353.48253 -.77473 (135*2π)/1981 weeks
1361.09974 .72588 (136*2π)/1981 weeks
1371.6716 -1.7865 (137*2π)/1981 weeks
1382.7696 -.32735 (138*2π)/1981 weeks
1391.39818 -.89598 (139*2π)/1981 weeks
1402.35989 -1.16901 (140*2π)/1981 weeks
1411.2377 -1.36362 (141*2π)/1981 weeks
1422.47424 -1.93521 (142*2π)/1981 weeks
1432.64525 -1.352 (143*2π)/1981 weeks
1442.08552 -.54503 (144*2π)/1981 weeks
1451.49782 -1.2817 (145*2π)/1981 weeks
1462.26346 -1.59935 (146*2π)/1981 weeks
1472.13776 -.58969 (147*2π)/1981 weeks
1481.38898 -1.83695 (148*2π)/1981 weeks
1493.00617 -.67781 (149*2π)/1981 weeks
150.57301 -1.09121 (150*2π)/1981 weeks
1512.63879 -1.88029 (151*2π)/1981 weeks
1521.00874 -1.80431 (152*2π)/1981 weeks
1532.60127 -3.51344 (153*2π)/1981 weeks
1543.34909 -1.07739 (154*2π)/1981 weeks
1552.01471 -2.23808 (155*2π)/1981 weeks
1564.08576 -1.30254 (156*2π)/1981 weeks
1571.41495 .20865 (157*2π)/1981 weeks
158-.44237 -2.01285 (158*2π)/1981 weeks
1592.28841 -4.48289 (159*2π)/1981 weeks
1603.33011 -.99183 (160*2π)/1981 weeks
161-.06662 -2.90131 (161*2π)/1981 weeks
1623.81549 -4.00908 (162*2π)/1981 weeks
1635.28897 1.07658 (163*2π)/1981 weeks
164-1.80241 .1232 (164*2π)/1981 weeks
1651.85936 -4.22314 (165*2π)/1981 weeks
166.9405 -.32877 (166*2π)/1981 weeks
1671.579 -4.9144 (167*2π)/1981 weeks
1684.12316 -.74237 (168*2π)/1981 weeks
169-.81847 -1.98338 (169*2π)/1981 weeks
1701.98643 -5.89334 (170*2π)/1981 weeks
1713.72229 -2.31106 (171*2π)/1981 weeks
1722.6982 -2.61519 (172*2π)/1981 weeks
1731.84212 -3.41124 (173*2π)/1981 weeks
1742.49085 -1.4035 (174*2π)/1981 weeks
175-1.2029 -3.40636 (175*2π)/1981 weeks
1762.41653 -2.83764 (176*2π)/1981 weeks
177-1.11327 -1.08956 (177*2π)/1981 weeks
178-3.93376 -4.34517 (178*2π)/1981 weeks
179.91879 -6.64115 (179*2π)/1981 weeks
180-3.94063 -2.80135 (180*2π)/1981 weeks
181-.94288 -11.14884 (181*2π)/1981 weeks
182.55578 -8.17772 (182*2π)/1981 weeks
1833.09313 -11.83221 (183*2π)/1981 weeks
1844.12193 -8.93649 (184*2π)/1981 weeks
185.41219 -8.98559 (185*2π)/1981 weeks
186-1.13491 -16.04581 (186*2π)/1981 weeks
1876.04726 -13.88114 (187*2π)/1981 weeks
188-.23433 -11.25995 (188*2π)/1981 weeks
1895.30211 -25.478 (189*2π)/1981 weeks
19012.4658 -22.25202 (190*2π)/1981 weeks
19116.08515 -17.14109 (191*2π)/1981 weeks
19220.21273 -14.48915 (192*2π)/1981 weeks
1936.20517 4.25972 (193*2π)/1981 weeks
194-8.65113 -33.64276 (194*2π)/1981 weeks
19528.93427 -27.17465 (195*2π)/1981 weeks
1966.2813 -9.99916 (196*2π)/1981 weeks

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