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Fourier Analysis of BRZU (DIREXION DAILY MSCI BRAZIL BULL 3X SHARES DIREXION DAILY MSCI BRAZIL BULL 3X SHARES)


BRZU (DIREXION DAILY MSCI BRAZIL BULL 3X SHARES DIREXION DAILY MSCI BRAZIL BULL 3X SHARES) appears to have interesting cyclic behaviour every 22 weeks (20.7464*sine), 24 weeks (17.1533*sine), and 24 weeks (7.4589*cosine).

BRZU (DIREXION DAILY MSCI BRAZIL BULL 3X SHARES DIREXION DAILY MSCI BRAZIL BULL 3X SHARES) has an average price of 105.69 (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 11/6/2017 for BRZU (DIREXION DAILY MSCI BRAZIL BULL 3X SHARES DIREXION DAILY MSCI BRAZIL BULL 3X SHARES), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0105.6895   0 
155.18317 100.2474 (1*2π)/240240 weeks
2-14.04285 23.97326 (2*2π)/240120 weeks
320.12287 12.84848 (3*2π)/24080 weeks
420.87567 31.1651 (4*2π)/24060 weeks
5-8.67895 22.65617 (5*2π)/24048 weeks
64.99713 -3.82363 (6*2π)/24040 weeks
719.98204 7.44599 (7*2π)/24034 weeks
814.24588 10.90768 (8*2π)/24030 weeks
912.29427 13.40978 (9*2π)/24027 weeks
107.45891 17.15329 (10*2π)/24024 weeks
112.12739 20.74638 (11*2π)/24022 weeks
12-1.7123 9.85169 (12*2π)/24020 weeks
134.21036 9.66449 (13*2π)/24018 weeks
142.18667 13.56628 (14*2π)/24017 weeks
15-3.09958 9.73669 (15*2π)/24016 weeks
16-.01473 7.61016 (16*2π)/24015 weeks
173.41994 7.77375 (17*2π)/24014 weeks
182.93775 8.8396 (18*2π)/24013 weeks
19-1.34447 7.53482 (19*2π)/24013 weeks
20.24566 8.22837 (20*2π)/24012 weeks
21-3.79216 9.10661 (21*2π)/24011 weeks
22-2.18684 2.20108 (22*2π)/24011 weeks
23.51693 5.86398 (23*2π)/24010 weeks
24-3.1899 5.41385 (24*2π)/24010 weeks
25-1.54656 2.07362 (25*2π)/24010 weeks
261.1369 .90153 (26*2π)/2409 weeks
271.90742 3.24485 (27*2π)/2409 weeks
28-1.09126 2.18348 (28*2π)/2409 weeks
291.86395 .9746 (29*2π)/2408 weeks
302.02108 2.67237 (30*2π)/2408 weeks
311.4059 1.64066 (31*2π)/2408 weeks
321.58705 2.25472 (32*2π)/2408 weeks
333.3073 2.80702 (33*2π)/2407 weeks
341.33361 5.0402 (34*2π)/2407 weeks
35-.85497 2.23213 (35*2π)/2407 weeks
361.7166 -.16158 (36*2π)/2407 weeks
373.0925 3.48496 (37*2π)/2406 weeks
38-.29841 3.467 (38*2π)/2406 weeks
391.60637 .50847 (39*2π)/2406 weeks
401.31124 3.75977 (40*2π)/2406 weeks
41-1.78556 1.56449 (41*2π)/2406 weeks
422.47085 -1.65468 (42*2π)/2406 weeks
435.08868 2.26686 (43*2π)/2406 weeks
442.73974 3.64452 (44*2π)/2405 weeks
45.07111 1.62976 (45*2π)/2405 weeks
462.60485 .6433 (46*2π)/2405 weeks
472.63938 3.36088 (47*2π)/2405 weeks
48-.04879 2.97881 (48*2π)/2405 weeks
49.07022 .70649 (49*2π)/2405 weeks
501.82703 -.0948 (50*2π)/2405 weeks
513.55635 1.51897 (51*2π)/2405 weeks
522.08125 2.02822 (52*2π)/2405 weeks
532.35307 .63437 (53*2π)/2405 weeks
543.15357 2.0567 (54*2π)/2404 weeks
551.221 2.59746 (55*2π)/2404 weeks
56.98724 1.16284 (56*2π)/2404 weeks
572.18402 1.62579 (57*2π)/2404 weeks
58.43805 1.37032 (58*2π)/2404 weeks
591.83634 .17711 (59*2π)/2404 weeks
602.29419 1.85136 (60*2π)/2404 weeks
611.2454 .9838 (61*2π)/2404 weeks
622.10116 .47285 (62*2π)/2404 weeks
631.9358 1.18818 (63*2π)/2404 weeks
641.31076 1.14462 (64*2π)/2404 weeks
651.41886 .53005 (65*2π)/2404 weeks
662.13188 .56078 (66*2π)/2404 weeks
672.01296 1.17588 (67*2π)/2404 weeks
681.91416 1.76139 (68*2π)/2404 weeks
691.10294 1.30945 (69*2π)/2403 weeks
701.9004 .60932 (70*2π)/2403 weeks
711.33831 1.11232 (71*2π)/2403 weeks
721.25345 .26694 (72*2π)/2403 weeks
732.4161 .72888 (73*2π)/2403 weeks
741.23354 1.46903 (74*2π)/2403 weeks
75.53875 -.22135 (75*2π)/2403 weeks
762.76948 .0095 (76*2π)/2403 weeks
772.13626 1.52724 (77*2π)/2403 weeks
781.07855 .57857 (78*2π)/2403 weeks
793.06362 .13808 (79*2π)/2403 weeks
802.10458 1.88336 (80*2π)/2403 weeks
81.44697 -.2985 (81*2π)/2403 weeks
822.44192 -1.4331 (82*2π)/2403 weeks
834.12513 .87992 (83*2π)/2403 weeks
841.47485 1.78969 (84*2π)/2403 weeks
852.01197 -.55128 (85*2π)/2403 weeks
863.3156 1.62507 (86*2π)/2403 weeks
871.10455 1.63116 (87*2π)/2403 weeks
882.10721 -.06801 (88*2π)/2403 weeks
892.5707 1.06276 (89*2π)/2403 weeks
901.84787 .87189 (90*2π)/2403 weeks
911.96648 .64431 (91*2π)/2403 weeks
922.6574 1.13333 (92*2π)/2403 weeks
931.5014 2.03394 (93*2π)/2403 weeks
94.36466 .96659 (94*2π)/2403 weeks
951.69147 .65645 (95*2π)/2403 weeks
961.13398 1.05051 (96*2π)/2403 weeks
971.53366 .32581 (97*2π)/2402 weeks
981.3349 .6389 (98*2π)/2402 weeks
991.00006 -.52673 (99*2π)/2402 weeks
1002.17561 -.30795 (100*2π)/2402 weeks
1011.15866 .56372 (101*2π)/2402 weeks
1021.35125 .15986 (102*2π)/2402 weeks
1031.68782 .49211 (103*2π)/2402 weeks
1041.5195 .46351 (104*2π)/2402 weeks
1051.09338 -.18125 (105*2π)/2402 weeks
1061.87087 .35254 (106*2π)/2402 weeks
1071.44924 .17605 (107*2π)/2402 weeks
1081.72817 -.81914 (108*2π)/2402 weeks
1092.05374 -.20587 (109*2π)/2402 weeks
1101.68689 .15112 (110*2π)/2402 weeks
1111.73281 -.42651 (111*2π)/2402 weeks
1121.76212 .01534 (112*2π)/2402 weeks
1131.90498 -.23051 (113*2π)/2402 weeks
1142.46748 -.16689 (114*2π)/2402 weeks
1152.33796 .74263 (115*2π)/2402 weeks
1162.3988 .54302 (116*2π)/2402 weeks
1171.85734 .58747 (117*2π)/2402 weeks
1181.90331 .9329 (118*2π)/2402 weeks
119.51151 .78882 (119*2π)/2402 weeks
120.3429   (120*2π)/2402 weeks
121.51151 -.78882 (121*2π)/2402 weeks
1221.90331 -.9329 (122*2π)/2402 weeks
1231.85734 -.58747 (123*2π)/2402 weeks
1242.3988 -.54302 (124*2π)/2402 weeks
1252.33796 -.74263 (125*2π)/2402 weeks
1262.46748 .16689 (126*2π)/2402 weeks
1271.90498 .23051 (127*2π)/2402 weeks
1281.76212 -.01534 (128*2π)/2402 weeks
1291.73281 .42651 (129*2π)/2402 weeks
1301.68689 -.15112 (130*2π)/2402 weeks
1312.05374 .20587 (131*2π)/2402 weeks
1321.72817 .81914 (132*2π)/2402 weeks
1331.44924 -.17605 (133*2π)/2402 weeks
1341.87087 -.35254 (134*2π)/2402 weeks
1351.09338 .18125 (135*2π)/2402 weeks
1361.5195 -.46351 (136*2π)/2402 weeks
1371.68782 -.49211 (137*2π)/2402 weeks
1381.35125 -.15986 (138*2π)/2402 weeks
1391.15866 -.56372 (139*2π)/2402 weeks
1402.17561 .30795 (140*2π)/2402 weeks
1411.00006 .52673 (141*2π)/2402 weeks
1421.3349 -.6389 (142*2π)/2402 weeks
1431.53366 -.32581 (143*2π)/2402 weeks
1441.13398 -1.05051 (144*2π)/2402 weeks
1451.69147 -.65645 (145*2π)/2402 weeks
146.36466 -.96659 (146*2π)/2402 weeks
1471.5014 -2.03394 (147*2π)/2402 weeks
1482.6574 -1.13333 (148*2π)/2402 weeks
1491.96648 -.64431 (149*2π)/2402 weeks
1501.84787 -.87189 (150*2π)/2402 weeks
1512.5707 -1.06276 (151*2π)/2402 weeks
1522.10721 .06801 (152*2π)/2402 weeks
1531.10455 -1.63116 (153*2π)/2402 weeks
1543.3156 -1.62507 (154*2π)/2402 weeks
1552.01197 .55128 (155*2π)/2402 weeks
1561.47485 -1.78969 (156*2π)/2402 weeks
1574.12513 -.87992 (157*2π)/2402 weeks
1582.44192 1.4331 (158*2π)/2402 weeks
159.44697 .2985 (159*2π)/2402 weeks
1602.10458 -1.88336 (160*2π)/2402 weeks
1613.06362 -.13808 (161*2π)/2401 weeks
1621.07855 -.57857 (162*2π)/2401 weeks
1632.13626 -1.52724 (163*2π)/2401 weeks
1642.76948 -.0095 (164*2π)/2401 weeks
165.53875 .22135 (165*2π)/2401 weeks
1661.23354 -1.46903 (166*2π)/2401 weeks
1672.4161 -.72888 (167*2π)/2401 weeks
1681.25345 -.26694 (168*2π)/2401 weeks
1691.33831 -1.11232 (169*2π)/2401 weeks
1701.9004 -.60932 (170*2π)/2401 weeks
1711.10294 -1.30945 (171*2π)/2401 weeks
1721.91416 -1.76139 (172*2π)/2401 weeks
1732.01296 -1.17588 (173*2π)/2401 weeks
1742.13188 -.56078 (174*2π)/2401 weeks
1751.41886 -.53005 (175*2π)/2401 weeks
1761.31076 -1.14462 (176*2π)/2401 weeks
1771.9358 -1.18818 (177*2π)/2401 weeks
1782.10116 -.47285 (178*2π)/2401 weeks
1791.2454 -.9838 (179*2π)/2401 weeks
1802.29419 -1.85136 (180*2π)/2401 weeks
1811.83634 -.17711 (181*2π)/2401 weeks
182.43805 -1.37032 (182*2π)/2401 weeks
1832.18402 -1.62579 (183*2π)/2401 weeks
184.98724 -1.16284 (184*2π)/2401 weeks
1851.221 -2.59746 (185*2π)/2401 weeks
1863.15357 -2.0567 (186*2π)/2401 weeks
1872.35307 -.63437 (187*2π)/2401 weeks
1882.08125 -2.02822 (188*2π)/2401 weeks
1893.55635 -1.51897 (189*2π)/2401 weeks
1901.82703 .0948 (190*2π)/2401 weeks
191.07022 -.70649 (191*2π)/2401 weeks
192-.04879 -2.97881 (192*2π)/2401 weeks
1932.63938 -3.36088 (193*2π)/2401 weeks
1942.60485 -.6433 (194*2π)/2401 weeks
195.07111 -1.62976 (195*2π)/2401 weeks
1962.73974 -3.64452 (196*2π)/2401 weeks
1975.08868 -2.26686 (197*2π)/2401 weeks
1982.47085 1.65468 (198*2π)/2401 weeks
199-1.78556 -1.56449 (199*2π)/2401 weeks
2001.31124 -3.75977 (200*2π)/2401 weeks
2011.60637 -.50847 (201*2π)/2401 weeks
202-.29841 -3.467 (202*2π)/2401 weeks
2033.0925 -3.48496 (203*2π)/2401 weeks
2041.7166 .16158 (204*2π)/2401 weeks
205-.85497 -2.23213 (205*2π)/2401 weeks
2061.33361 -5.0402 (206*2π)/2401 weeks
2073.3073 -2.80702 (207*2π)/2401 weeks
2081.58705 -2.25472 (208*2π)/2401 weeks
2091.4059 -1.64066 (209*2π)/2401 weeks
2102.02108 -2.67237 (210*2π)/2401 weeks
2111.86395 -.9746 (211*2π)/2401 weeks
212-1.09126 -2.18348 (212*2π)/2401 weeks
2131.90742 -3.24485 (213*2π)/2401 weeks
2141.1369 -.90153 (214*2π)/2401 weeks
215-1.54656 -2.07362 (215*2π)/2401 weeks
216-3.1899 -5.41385 (216*2π)/2401 weeks
217.51693 -5.86398 (217*2π)/2401 weeks
218-2.18684 -2.20108 (218*2π)/2401 weeks
219-3.79216 -9.10661 (219*2π)/2401 weeks
220.24566 -8.22837 (220*2π)/2401 weeks
221-1.34447 -7.53482 (221*2π)/2401 weeks
2222.93775 -8.8396 (222*2π)/2401 weeks
2233.41994 -7.77375 (223*2π)/2401 weeks
224-.01473 -7.61016 (224*2π)/2401 weeks
225-3.09958 -9.73669 (225*2π)/2401 weeks
2262.18667 -13.56628 (226*2π)/2401 weeks
2274.21036 -9.66449 (227*2π)/2401 weeks
228-1.7123 -9.85169 (228*2π)/2401 weeks
2292.12739 -20.74638 (229*2π)/2401 weeks
2307.45891 -17.15329 (230*2π)/2401 weeks
23112.29427 -13.40978 (231*2π)/2401 weeks
23214.24588 -10.90768 (232*2π)/2401 weeks
23319.98204 -7.44599 (233*2π)/2401 weeks
2344.99713 3.82363 (234*2π)/2401 weeks
235-8.67895 -22.65617 (235*2π)/2401 weeks
23620.87567 -31.1651 (236*2π)/2401 weeks
23720.12287 -12.84848 (237*2π)/2401 weeks
238-14.04285 -23.97326 (238*2π)/2401 weeks



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