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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 21 weeks (15.479*sine), 17 weeks (15.4087*sine), and 19 weeks (10.1259*sine).

BRZU (Direxion Daily Brazil Bull 3X S) has an average price of 116.87 (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 3/13/2017 for BRZU (Direxion Daily Brazil Bull 3X S), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0116.874   0 
135.54937 114.7965 (1*2π)/206206 weeks
21.59755 10.88649 (2*2π)/206103 weeks
328.07289 22.66743 (3*2π)/20669 weeks
4-1.44958 37.97104 (4*2π)/20652 weeks
5-.78864 -2.05326 (5*2π)/20641 weeks
622.38996 9.7612 (6*2π)/20634 weeks
716.5373 14.92235 (7*2π)/20629 weeks
814.91809 18.94166 (8*2π)/20626 weeks
99.39064 21.11897 (9*2π)/20623 weeks
10-3.44191 15.47896 (10*2π)/20621 weeks
114.59932 10.12585 (11*2π)/20619 weeks
123.14772 15.40869 (12*2π)/20617 weeks
13-2.70381 9.42562 (13*2π)/20616 weeks
14.5298 7.03113 (14*2π)/20615 weeks
152.46164 9.6348 (15*2π)/20614 weeks
16-.71489 11.74577 (16*2π)/20613 weeks
17.97142 9.33921 (17*2π)/20612 weeks
18-3.71028 10.72536 (18*2π)/20611 weeks
19-.90124 2.451 (19*2π)/20611 weeks
20-.17105 7.32513 (20*2π)/20610 weeks
21-3.39199 3.13603 (21*2π)/20610 weeks
22-.55104 .81029 (22*2π)/2069 weeks
232.19256 3.20085 (23*2π)/2069 weeks
24-1.36542 2.88528 (24*2π)/2069 weeks
252.33758 1.51567 (25*2π)/2068 weeks
261.71498 3.37837 (26*2π)/2068 weeks
272.5351 2.4897 (27*2π)/2068 weeks
283.21759 2.08398 (28*2π)/2067 weeks
292.48747 5.54709 (29*2π)/2067 weeks
30-1.05822 2.7468 (30*2π)/2067 weeks
312.66758 -.05633 (31*2π)/2067 weeks
322.58534 4.70675 (32*2π)/2066 weeks
33-.66615 1.73614 (33*2π)/2066 weeks
343.00774 3.18965 (34*2π)/2066 weeks
35-1.54411 2.87247 (35*2π)/2066 weeks
362.39331 -2.3579 (36*2π)/2066 weeks
375.36407 2.91743 (37*2π)/2066 weeks
382.02851 4.47564 (38*2π)/2065 weeks
391.26955 .52281 (39*2π)/2065 weeks
403.93895 2.53043 (40*2π)/2065 weeks
41.58906 3.80385 (41*2π)/2065 weeks
42.00678 .66679 (42*2π)/2065 weeks
432.27747 -.45834 (43*2π)/2065 weeks
443.48345 2.16128 (44*2π)/2065 weeks
451.73438 1.66007 (45*2π)/2065 weeks
463.58828 1.57398 (46*2π)/2064 weeks
471.96371 3.40725 (47*2π)/2064 weeks
481.1018 1.51639 (48*2π)/2064 weeks
492.49744 2.12514 (49*2π)/2064 weeks
50.66675 .88241 (50*2π)/2064 weeks
512.9599 .70413 (51*2π)/2064 weeks
521.38972 1.7985 (52*2π)/2064 weeks
531.98295 .55657 (53*2π)/2064 weeks
542.27513 1.51587 (54*2π)/2064 weeks
551.53286 1.39594 (55*2π)/2064 weeks
561.89097 .60127 (56*2π)/2064 weeks
572.72304 1.11533 (57*2π)/2064 weeks
582.58685 1.53473 (58*2π)/2064 weeks
591.42648 1.68609 (59*2π)/2063 weeks
602.00702 .55918 (60*2π)/2063 weeks
611.45392 1.22927 (61*2π)/2063 weeks
621.72984 .07381 (62*2π)/2063 weeks
632.46022 1.5334 (63*2π)/2063 weeks
64.57456 .93765 (64*2π)/2063 weeks
652.79542 -.73685 (65*2π)/2063 weeks
662.64735 1.51163 (66*2π)/2063 weeks
671.13858 .31186 (67*2π)/2063 weeks
683.50763 .66657 (68*2π)/2063 weeks
69.91914 1.92898 (69*2π)/2063 weeks
701.66331 -1.31399 (70*2π)/2063 weeks
714.84392 -.08573 (71*2π)/2063 weeks
722.10649 2.33244 (72*2π)/2063 weeks
732.58049 -.68009 (73*2π)/2063 weeks
743.36464 2.29271 (74*2π)/2063 weeks
751.06615 .73814 (75*2π)/2063 weeks
763.10039 .64984 (76*2π)/2063 weeks
772.18367 1.32767 (77*2π)/2063 weeks
782.29048 .89202 (78*2π)/2063 weeks
793.16875 1.46746 (79*2π)/2063 weeks
801.52696 2.338 (80*2π)/2063 weeks
811.01482 .321 (81*2π)/2063 weeks
821.75513 1.17759 (82*2π)/2063 weeks
831.31638 .33293 (83*2π)/2062 weeks
841.50432 .82172 (84*2π)/2062 weeks
851.1206 -.44871 (85*2π)/2062 weeks
862.69293 .22142 (86*2π)/2062 weeks
871.46332 .25837 (87*2π)/2062 weeks
881.9537 .05824 (88*2π)/2062 weeks
891.66869 .34348 (89*2π)/2062 weeks
901.05334 -.06478 (90*2π)/2062 weeks
912.01012 .33286 (91*2π)/2062 weeks
921.35692 .11549 (92*2π)/2062 weeks
932.37077 -.59574 (93*2π)/2062 weeks
942.35194 .08814 (94*2π)/2062 weeks
951.7997 -.32511 (95*2π)/2062 weeks
962.24073 -.00686 (96*2π)/2062 weeks
972.29454 -.37105 (97*2π)/2062 weeks
983.03591 -.19201 (98*2π)/2062 weeks
992.35296 .54555 (99*2π)/2062 weeks
1002.31086 .94407 (100*2π)/2062 weeks
1012.26254 .8365 (101*2π)/2062 weeks
102.825 1.25336 (102*2π)/2062 weeks
103.51562   (103*2π)/2062 weeks
104.825 -1.25336 (104*2π)/2062 weeks
1052.26254 -.8365 (105*2π)/2062 weeks
1062.31086 -.94407 (106*2π)/2062 weeks
1072.35296 -.54555 (107*2π)/2062 weeks
1083.03591 .19201 (108*2π)/2062 weeks
1092.29454 .37105 (109*2π)/2062 weeks
1102.24073 .00686 (110*2π)/2062 weeks
1111.7997 .32511 (111*2π)/2062 weeks
1122.35194 -.08814 (112*2π)/2062 weeks
1132.37077 .59574 (113*2π)/2062 weeks
1141.35692 -.11549 (114*2π)/2062 weeks
1152.01012 -.33286 (115*2π)/2062 weeks
1161.05334 .06478 (116*2π)/2062 weeks
1171.66869 -.34348 (117*2π)/2062 weeks
1181.9537 -.05824 (118*2π)/2062 weeks
1191.46332 -.25837 (119*2π)/2062 weeks
1202.69293 -.22142 (120*2π)/2062 weeks
1211.1206 .44871 (121*2π)/2062 weeks
1221.50432 -.82172 (122*2π)/2062 weeks
1231.31638 -.33293 (123*2π)/2062 weeks
1241.75513 -1.17759 (124*2π)/2062 weeks
1251.01482 -.321 (125*2π)/2062 weeks
1261.52696 -2.338 (126*2π)/2062 weeks
1273.16875 -1.46746 (127*2π)/2062 weeks
1282.29048 -.89202 (128*2π)/2062 weeks
1292.18367 -1.32767 (129*2π)/2062 weeks
1303.10039 -.64984 (130*2π)/2062 weeks
1311.06615 -.73814 (131*2π)/2062 weeks
1323.36464 -2.29271 (132*2π)/2062 weeks
1332.58049 .68009 (133*2π)/2062 weeks
1342.10649 -2.33244 (134*2π)/2062 weeks
1354.84392 .08573 (135*2π)/2062 weeks
1361.66331 1.31399 (136*2π)/2062 weeks
137.91914 -1.92898 (137*2π)/2062 weeks
1383.50763 -.66657 (138*2π)/2061 weeks
1391.13858 -.31186 (139*2π)/2061 weeks
1402.64735 -1.51163 (140*2π)/2061 weeks
1412.79542 .73685 (141*2π)/2061 weeks
142.57456 -.93765 (142*2π)/2061 weeks
1432.46022 -1.5334 (143*2π)/2061 weeks
1441.72984 -.07381 (144*2π)/2061 weeks
1451.45392 -1.22927 (145*2π)/2061 weeks
1462.00702 -.55918 (146*2π)/2061 weeks
1471.42648 -1.68609 (147*2π)/2061 weeks
1482.58685 -1.53473 (148*2π)/2061 weeks
1492.72304 -1.11533 (149*2π)/2061 weeks
1501.89097 -.60127 (150*2π)/2061 weeks
1511.53286 -1.39594 (151*2π)/2061 weeks
1522.27513 -1.51587 (152*2π)/2061 weeks
1531.98295 -.55657 (153*2π)/2061 weeks
1541.38972 -1.7985 (154*2π)/2061 weeks
1552.9599 -.70413 (155*2π)/2061 weeks
156.66675 -.88241 (156*2π)/2061 weeks
1572.49744 -2.12514 (157*2π)/2061 weeks
1581.1018 -1.51639 (158*2π)/2061 weeks
1591.96371 -3.40725 (159*2π)/2061 weeks
1603.58828 -1.57398 (160*2π)/2061 weeks
1611.73438 -1.66007 (161*2π)/2061 weeks
1623.48345 -2.16128 (162*2π)/2061 weeks
1632.27747 .45834 (163*2π)/2061 weeks
164.00678 -.66679 (164*2π)/2061 weeks
165.58906 -3.80385 (165*2π)/2061 weeks
1663.93895 -2.53043 (166*2π)/2061 weeks
1671.26955 -.52281 (167*2π)/2061 weeks
1682.02851 -4.47564 (168*2π)/2061 weeks
1695.36407 -2.91743 (169*2π)/2061 weeks
1702.39331 2.3579 (170*2π)/2061 weeks
171-1.54411 -2.87247 (171*2π)/2061 weeks
1723.00774 -3.18965 (172*2π)/2061 weeks
173-.66615 -1.73614 (173*2π)/2061 weeks
1742.58534 -4.70675 (174*2π)/2061 weeks
1752.66758 .05633 (175*2π)/2061 weeks
176-1.05822 -2.7468 (176*2π)/2061 weeks
1772.48747 -5.54709 (177*2π)/2061 weeks
1783.21759 -2.08398 (178*2π)/2061 weeks
1792.5351 -2.4897 (179*2π)/2061 weeks
1801.71498 -3.37837 (180*2π)/2061 weeks
1812.33758 -1.51567 (181*2π)/2061 weeks
182-1.36542 -2.88528 (182*2π)/2061 weeks
1832.19256 -3.20085 (183*2π)/2061 weeks
184-.55104 -.81029 (184*2π)/2061 weeks
185-3.39199 -3.13603 (185*2π)/2061 weeks
186-.17105 -7.32513 (186*2π)/2061 weeks
187-.90124 -2.451 (187*2π)/2061 weeks
188-3.71028 -10.72536 (188*2π)/2061 weeks
189.97142 -9.33921 (189*2π)/2061 weeks
190-.71489 -11.74577 (190*2π)/2061 weeks
1912.46164 -9.6348 (191*2π)/2061 weeks
192.5298 -7.03113 (192*2π)/2061 weeks
193-2.70381 -9.42562 (193*2π)/2061 weeks
1943.14772 -15.40869 (194*2π)/2061 weeks
1954.59932 -10.12585 (195*2π)/2061 weeks
196-3.44191 -15.47896 (196*2π)/2061 weeks
1979.39064 -21.11897 (197*2π)/2061 weeks
19814.91809 -18.94166 (198*2π)/2061 weeks
19916.5373 -14.92235 (199*2π)/2061 weeks
20022.38996 -9.7612 (200*2π)/2061 weeks
201-.78864 2.05326 (201*2π)/2061 weeks
202-1.44958 -37.97104 (202*2π)/2061 weeks
20328.07289 -22.66743 (203*2π)/2061 weeks
2041.59755 -10.88649 (204*2π)/2061 weeks

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