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Fourier Analysis of SOXS (Direxion Daily Semiconductor Be)


SOXS (Direxion Daily Semiconductor Be) appears to have interesting cyclic behaviour every 23 weeks (84.7731*sine), 22 weeks (78.2049*sine), and 37 weeks (64.4074*sine).

SOXS (Direxion Daily Semiconductor Be) has an average price of 560.34 (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 3/11/2010 to 3/20/2017 for SOXS (Direxion Daily Semiconductor Be), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0560.3434   0 
1440.0138 556.9191 (1*2π)/368368 weeks
2180.0575 329.0851 (2*2π)/368184 weeks
3144.5307 283.6725 (3*2π)/368123 weeks
4101.6346 248.4592 (4*2π)/36892 weeks
586.8438 250.5366 (5*2π)/36874 weeks
6-7.32063 259.6634 (6*2π)/36861 weeks
7-84.54847 157.1754 (7*2π)/36853 weeks
8-48.32711 71.35661 (8*2π)/36846 weeks
9.51624 48.77764 (9*2π)/36841 weeks
1018.55065 64.40736 (10*2π)/36837 weeks
114.03969 63.60359 (11*2π)/36833 weeks
1217.55951 38.92756 (12*2π)/36831 weeks
1338.65142 51.35634 (13*2π)/36828 weeks
1427.98467 57.76165 (14*2π)/36826 weeks
1537.37996 49.74624 (15*2π)/36825 weeks
1636.99419 84.77308 (16*2π)/36823 weeks
17-6.43589 78.20485 (17*2π)/36822 weeks
181.7871 36.78582 (18*2π)/36820 weeks
1919.39359 49.38762 (19*2π)/36819 weeks
206.98947 54.98639 (20*2π)/36818 weeks
21-7.11205 51.8169 (21*2π)/36818 weeks
22-13.63139 31.46614 (22*2π)/36817 weeks
23-.11516 14.36986 (23*2π)/36816 weeks
2415.11579 15.3871 (24*2π)/36815 weeks
2515.30332 24.20903 (25*2π)/36815 weeks
2611.04593 16.9852 (26*2π)/36814 weeks
2722.92429 8.3769 (27*2π)/36814 weeks
2835.06909 20.60069 (28*2π)/36813 weeks
2934.09449 34.53616 (29*2π)/36813 weeks
3019.8871 37.15659 (30*2π)/36812 weeks
3112.85056 28.64337 (31*2π)/36812 weeks
3223.73958 19.89414 (32*2π)/36812 weeks
3324.94799 29.66062 (33*2π)/36811 weeks
3423.40953 30.02879 (34*2π)/36811 weeks
3524.6785 36.91533 (35*2π)/36811 weeks
3612.90588 42.24072 (36*2π)/36810 weeks
37.39224 33.15049 (37*2π)/36810 weeks
384.30658 13.9002 (38*2π)/36810 weeks
3918.13435 16.61857 (39*2π)/3689 weeks
4019.08369 21.26145 (40*2π)/3689 weeks
4118.13842 23.83836 (41*2π)/3689 weeks
4213.12347 22.34525 (42*2π)/3689 weeks
4318.30452 15.25346 (43*2π)/3689 weeks
4425.429 17.29504 (44*2π)/3688 weeks
4532.45741 28.9694 (45*2π)/3688 weeks
4619.81694 39.12772 (46*2π)/3688 weeks
4711.97081 29.81664 (47*2π)/3688 weeks
4816.80439 27.6282 (48*2π)/3688 weeks
4918.82109 29.91182 (49*2π)/3688 weeks
5017.43703 36.81199 (50*2π)/3687 weeks
517.61547 43.80474 (51*2π)/3687 weeks
52-6.43449 34.40263 (52*2π)/3687 weeks
53-3.36904 19.11647 (53*2π)/3687 weeks
549.2176 20.53347 (54*2π)/3687 weeks
553.82199 31.78675 (55*2π)/3687 weeks
56-7.30377 22.51342 (56*2π)/3687 weeks
57.72003 13.42123 (57*2π)/3686 weeks
583.28799 17.71488 (58*2π)/3686 weeks
59-.13328 15.30938 (59*2π)/3686 weeks
602.91998 13.79412 (60*2π)/3686 weeks
612.17106 12.77456 (61*2π)/3686 weeks
626.03163 8.34997 (62*2π)/3686 weeks
6313.05404 13.64122 (63*2π)/3686 weeks
645.32006 20.50687 (64*2π)/3686 weeks
65.14381 12.62588 (65*2π)/3686 weeks
665.30494 8.85204 (66*2π)/3686 weeks
677.09119 8.88371 (67*2π)/3685 weeks
688.84957 11.05469 (68*2π)/3685 weeks
698.79408 11.76679 (69*2π)/3685 weeks
709.43383 9.71219 (70*2π)/3685 weeks
7113.92386 14.01828 (71*2π)/3685 weeks
729.83094 17.43312 (72*2π)/3685 weeks
735.92735 19.61013 (73*2π)/3685 weeks
74.9578 19.81478 (74*2π)/3685 weeks
75-3.37178 14.20421 (75*2π)/3685 weeks
76-5.44573 8.38048 (76*2π)/3685 weeks
77-1.14743 1.25345 (77*2π)/3685 weeks
784.60549 1.79471 (78*2π)/3685 weeks
794.33003 4.41991 (79*2π)/3685 weeks
803.15768 1.15734 (80*2π)/3685 weeks
818.71716 -2.59334 (81*2π)/3685 weeks
8211.25855 .83913 (82*2π)/3684 weeks
8314.21282 .41992 (83*2π)/3684 weeks
8414.50501 5.86445 (84*2π)/3684 weeks
8511.01683 5.88262 (85*2π)/3684 weeks
8613.19076 4.6617 (86*2π)/3684 weeks
8712.5041 5.86094 (87*2π)/3684 weeks
8812.3209 4.63804 (88*2π)/3684 weeks
8913.94316 2.2167 (89*2π)/3684 weeks
9018.6039 3.64009 (90*2π)/3684 weeks
9119.40366 11.00484 (91*2π)/3684 weeks
9214.24054 13.88944 (92*2π)/3684 weeks
938.75787 9.52372 (93*2π)/3684 weeks
9412.54093 3.62085 (94*2π)/3684 weeks
9519.63841 6.1342 (95*2π)/3684 weeks
9618.55773 14.34452 (96*2π)/3684 weeks
9711.89503 16.81694 (97*2π)/3684 weeks
988.36984 10.86881 (98*2π)/3684 weeks
9914.62066 7.42812 (99*2π)/3684 weeks
10017.71239 16.74811 (100*2π)/3684 weeks
1017.37609 20.91411 (101*2π)/3684 weeks
1021.25592 13.37276 (102*2π)/3684 weeks
1035.27351 7.66219 (103*2π)/3684 weeks
1048.77986 9.19189 (104*2π)/3684 weeks
1059.12796 13.04571 (105*2π)/3684 weeks
1061.7657 13.86265 (106*2π)/3683 weeks
107-1.03914 5.89866 (107*2π)/3683 weeks
1083.90524 2.92653 (108*2π)/3683 weeks
1094.6766 3.73716 (109*2π)/3683 weeks
1105.18808 -1.28504 (110*2π)/3683 weeks
11112.34239 -1.29704 (111*2π)/3683 weeks
11214.55838 2.44026 (112*2π)/3683 weeks
11315.07874 5.35511 (113*2π)/3683 weeks
11414.73872 7.96742 (114*2π)/3683 weeks
11512.66468 9.5234 (115*2π)/3683 weeks
11611.81014 10.1702 (116*2π)/3683 weeks
11710.75899 11.3529 (117*2π)/3683 weeks
1187.98249 11.68931 (118*2π)/3683 weeks
1195.35125 9.39298 (119*2π)/3683 weeks
1206.62848 7.25854 (120*2π)/3683 weeks
1217.49784 7.25625 (121*2π)/3683 weeks
1227.02407 7.31116 (122*2π)/3683 weeks
1239.1684 7.12476 (123*2π)/3683 weeks
1246.53388 11.3862 (124*2π)/3683 weeks
125.75746 7.08957 (125*2π)/3683 weeks
1265.18009 1.33661 (126*2π)/3683 weeks
12710.18972 4.01586 (127*2π)/3683 weeks
1288.99045 9.74272 (128*2π)/3683 weeks
1291.79515 10.54635 (129*2π)/3683 weeks
130-2.14357 3.4291 (130*2π)/3683 weeks
1314.00263 -3.52342 (131*2π)/3683 weeks
13210.26159 1.00527 (132*2π)/3683 weeks
1336.61896 6.53235 (133*2π)/3683 weeks
134-.94947 3.72557 (134*2π)/3683 weeks
1351.49267 -8.49271 (135*2π)/3683 weeks
13614.69942 -7.78579 (136*2π)/3683 weeks
13715.7216 2.13583 (137*2π)/3683 weeks
13811.44349 3.46803 (138*2π)/3683 weeks
1399.45787 2.49758 (139*2π)/3683 weeks
14011.24934 -.54962 (140*2π)/3683 weeks
14115.27577 1.6913 (141*2π)/3683 weeks
14214.26712 6.78479 (142*2π)/3683 weeks
1438.68624 8.26218 (143*2π)/3683 weeks
1447.73604 2.97381 (144*2π)/3683 weeks
14510.49975 2.09107 (145*2π)/3683 weeks
14611.81253 2.64818 (146*2π)/3683 weeks
14713.53249 5.3319 (147*2π)/3683 weeks
14812.5163 8.68942 (148*2π)/3682 weeks
1498.33086 9.78363 (149*2π)/3682 weeks
1504.84365 7.99479 (150*2π)/3682 weeks
1514.34009 2.72238 (151*2π)/3682 weeks
1529.93329 2.90066 (152*2π)/3682 weeks
1538.88302 7.32544 (153*2π)/3682 weeks
1545.43524 6.89893 (154*2π)/3682 weeks
1553.73184 3.93292 (155*2π)/3682 weeks
1565.74355 2.22153 (156*2π)/3682 weeks
1577.23565 4.4073 (157*2π)/3682 weeks
1584.4572 5.7456 (158*2π)/3682 weeks
159.05527 3.84958 (159*2π)/3682 weeks
160.63555 -4.54994 (160*2π)/3682 weeks
1619.66849 -4.29916 (161*2π)/3682 weeks
1628.814 2.62009 (162*2π)/3682 weeks
1634.83517 .81837 (163*2π)/3682 weeks
1644.48701 -2.67633 (164*2π)/3682 weeks
1658.29804 -5.41229 (165*2π)/3682 weeks
16612.45473 -2.28857 (166*2π)/3682 weeks
16712.76884 -.87494 (167*2π)/3682 weeks
16813.61757 3.14323 (168*2π)/3682 weeks
1699.70112 5.09353 (169*2π)/3682 weeks
1707.42698 2.42536 (170*2π)/3682 weeks
17110.92455 3.37326 (171*2π)/3682 weeks
1727.39097 7.05362 (172*2π)/3682 weeks
1732.90055 5.54537 (173*2π)/3682 weeks
1741.78584 2.25854 (174*2π)/3682 weeks
175.45616 -.33074 (175*2π)/3682 weeks
1762.27454 -5.73565 (176*2π)/3682 weeks
1776.50553 -4.5472 (177*2π)/3682 weeks
1783.6338 -3.74208 (178*2π)/3682 weeks
1795.47719 -9.45775 (179*2π)/3682 weeks
18011.7678 -11.10202 (180*2π)/3682 weeks
18116.78865 -6.71369 (181*2π)/3682 weeks
18214.33552 -1.84844 (182*2π)/3682 weeks
18315.17952 -4.46687 (183*2π)/3682 weeks
18419.48643   (184*2π)/3682 weeks
18515.17952 4.46687 (185*2π)/3682 weeks
18614.33552 1.84844 (186*2π)/3682 weeks
18716.78865 6.71369 (187*2π)/3682 weeks
18811.7678 11.10202 (188*2π)/3682 weeks
1895.47719 9.45775 (189*2π)/3682 weeks
1903.6338 3.74208 (190*2π)/3682 weeks
1916.50553 4.5472 (191*2π)/3682 weeks
1922.27454 5.73565 (192*2π)/3682 weeks
193.45616 .33074 (193*2π)/3682 weeks
1941.78584 -2.25854 (194*2π)/3682 weeks
1952.90055 -5.54537 (195*2π)/3682 weeks
1967.39097 -7.05362 (196*2π)/3682 weeks
19710.92455 -3.37326 (197*2π)/3682 weeks
1987.42698 -2.42536 (198*2π)/3682 weeks
1999.70112 -5.09353 (199*2π)/3682 weeks
20013.61757 -3.14323 (200*2π)/3682 weeks
20112.76884 .87494 (201*2π)/3682 weeks
20212.45473 2.28857 (202*2π)/3682 weeks
2038.29804 5.41229 (203*2π)/3682 weeks
2044.48701 2.67633 (204*2π)/3682 weeks
2054.83517 -.81837 (205*2π)/3682 weeks
2068.814 -2.62009 (206*2π)/3682 weeks
2079.66849 4.29916 (207*2π)/3682 weeks
208.63555 4.54994 (208*2π)/3682 weeks
209.05527 -3.84958 (209*2π)/3682 weeks
2104.4572 -5.7456 (210*2π)/3682 weeks
2117.23565 -4.4073 (211*2π)/3682 weeks
2125.74355 -2.22153 (212*2π)/3682 weeks
2133.73184 -3.93292 (213*2π)/3682 weeks
2145.43524 -6.89893 (214*2π)/3682 weeks
2158.88302 -7.32544 (215*2π)/3682 weeks
2169.93329 -2.90066 (216*2π)/3682 weeks
2174.34009 -2.72238 (217*2π)/3682 weeks
2184.84365 -7.99479 (218*2π)/3682 weeks
2198.33086 -9.78363 (219*2π)/3682 weeks
22012.5163 -8.68942 (220*2π)/3682 weeks
22113.53249 -5.3319 (221*2π)/3682 weeks
22211.81253 -2.64818 (222*2π)/3682 weeks
22310.49975 -2.09107 (223*2π)/3682 weeks
2247.73604 -2.97381 (224*2π)/3682 weeks
2258.68624 -8.26218 (225*2π)/3682 weeks
22614.26712 -6.78479 (226*2π)/3682 weeks
22715.27577 -1.6913 (227*2π)/3682 weeks
22811.24934 .54962 (228*2π)/3682 weeks
2299.45787 -2.49758 (229*2π)/3682 weeks
23011.44349 -3.46803 (230*2π)/3682 weeks
23115.7216 -2.13583 (231*2π)/3682 weeks
23214.69942 7.78579 (232*2π)/3682 weeks
2331.49267 8.49271 (233*2π)/3682 weeks
234-.94947 -3.72557 (234*2π)/3682 weeks
2356.61896 -6.53235 (235*2π)/3682 weeks
23610.26159 -1.00527 (236*2π)/3682 weeks
2374.00263 3.52342 (237*2π)/3682 weeks
238-2.14357 -3.4291 (238*2π)/3682 weeks
2391.79515 -10.54635 (239*2π)/3682 weeks
2408.99045 -9.74272 (240*2π)/3682 weeks
24110.18972 -4.01586 (241*2π)/3682 weeks
2425.18009 -1.33661 (242*2π)/3682 weeks
243.75746 -7.08957 (243*2π)/3682 weeks
2446.53388 -11.3862 (244*2π)/3682 weeks
2459.1684 -7.12476 (245*2π)/3682 weeks
2467.02407 -7.31116 (246*2π)/3681 weeks
2477.49784 -7.25625 (247*2π)/3681 weeks
2486.62848 -7.25854 (248*2π)/3681 weeks
2495.35125 -9.39298 (249*2π)/3681 weeks
2507.98249 -11.68931 (250*2π)/3681 weeks
25110.75899 -11.3529 (251*2π)/3681 weeks
25211.81014 -10.1702 (252*2π)/3681 weeks
25312.66468 -9.5234 (253*2π)/3681 weeks
25414.73872 -7.96742 (254*2π)/3681 weeks
25515.07874 -5.35511 (255*2π)/3681 weeks
25614.55838 -2.44026 (256*2π)/3681 weeks
25712.34239 1.29704 (257*2π)/3681 weeks
2585.18808 1.28504 (258*2π)/3681 weeks
2594.6766 -3.73716 (259*2π)/3681 weeks
2603.90524 -2.92653 (260*2π)/3681 weeks
261-1.03914 -5.89866 (261*2π)/3681 weeks
2621.7657 -13.86265 (262*2π)/3681 weeks
2639.12796 -13.04571 (263*2π)/3681 weeks
2648.77986 -9.19189 (264*2π)/3681 weeks
2655.27351 -7.66219 (265*2π)/3681 weeks
2661.25592 -13.37276 (266*2π)/3681 weeks
2677.37609 -20.91411 (267*2π)/3681 weeks
26817.71239 -16.74811 (268*2π)/3681 weeks
26914.62066 -7.42812 (269*2π)/3681 weeks
2708.36984 -10.86881 (270*2π)/3681 weeks
27111.89503 -16.81694 (271*2π)/3681 weeks
27218.55773 -14.34452 (272*2π)/3681 weeks
27319.63841 -6.1342 (273*2π)/3681 weeks
27412.54093 -3.62085 (274*2π)/3681 weeks
2758.75787 -9.52372 (275*2π)/3681 weeks
27614.24054 -13.88944 (276*2π)/3681 weeks
27719.40366 -11.00484 (277*2π)/3681 weeks
27818.6039 -3.64009 (278*2π)/3681 weeks
27913.94316 -2.2167 (279*2π)/3681 weeks
28012.3209 -4.63804 (280*2π)/3681 weeks
28112.5041 -5.86094 (281*2π)/3681 weeks
28213.19076 -4.6617 (282*2π)/3681 weeks
28311.01683 -5.88262 (283*2π)/3681 weeks
28414.50501 -5.86445 (284*2π)/3681 weeks
28514.21282 -.41992 (285*2π)/3681 weeks
28611.25855 -.83913 (286*2π)/3681 weeks
2878.71716 2.59334 (287*2π)/3681 weeks
2883.15768 -1.15734 (288*2π)/3681 weeks
2894.33003 -4.41991 (289*2π)/3681 weeks
2904.60549 -1.79471 (290*2π)/3681 weeks
291-1.14743 -1.25345 (291*2π)/3681 weeks
292-5.44573 -8.38048 (292*2π)/3681 weeks
293-3.37178 -14.20421 (293*2π)/3681 weeks
294.9578 -19.81478 (294*2π)/3681 weeks
2955.92735 -19.61013 (295*2π)/3681 weeks
2969.83094 -17.43312 (296*2π)/3681 weeks
29713.92386 -14.01828 (297*2π)/3681 weeks
2989.43383 -9.71219 (298*2π)/3681 weeks
2998.79408 -11.76679 (299*2π)/3681 weeks
3008.84957 -11.05469 (300*2π)/3681 weeks
3017.09119 -8.88371 (301*2π)/3681 weeks
3025.30494 -8.85204 (302*2π)/3681 weeks
303.14381 -12.62588 (303*2π)/3681 weeks
3045.32006 -20.50687 (304*2π)/3681 weeks
30513.05404 -13.64122 (305*2π)/3681 weeks
3066.03163 -8.34997 (306*2π)/3681 weeks
3072.17106 -12.77456 (307*2π)/3681 weeks
3082.91998 -13.79412 (308*2π)/3681 weeks
309-.13328 -15.30938 (309*2π)/3681 weeks
3103.28799 -17.71488 (310*2π)/3681 weeks
311.72003 -13.42123 (311*2π)/3681 weeks
312-7.30377 -22.51342 (312*2π)/3681 weeks
3133.82199 -31.78675 (313*2π)/3681 weeks
3149.2176 -20.53347 (314*2π)/3681 weeks
315-3.36904 -19.11647 (315*2π)/3681 weeks
316-6.43449 -34.40263 (316*2π)/3681 weeks
3177.61547 -43.80474 (317*2π)/3681 weeks
31817.43703 -36.81199 (318*2π)/3681 weeks
31918.82109 -29.91182 (319*2π)/3681 weeks
32016.80439 -27.6282 (320*2π)/3681 weeks
32111.97081 -29.81664 (321*2π)/3681 weeks
32219.81694 -39.12772 (322*2π)/3681 weeks
32332.45741 -28.9694 (323*2π)/3681 weeks
32425.429 -17.29504 (324*2π)/3681 weeks
32518.30452 -15.25346 (325*2π)/3681 weeks
32613.12347 -22.34525 (326*2π)/3681 weeks
32718.13842 -23.83836 (327*2π)/3681 weeks
32819.08369 -21.26145 (328*2π)/3681 weeks
32918.13435 -16.61857 (329*2π)/3681 weeks
3304.30658 -13.9002 (330*2π)/3681 weeks
331.39224 -33.15049 (331*2π)/3681 weeks
33212.90588 -42.24072 (332*2π)/3681 weeks
33324.6785 -36.91533 (333*2π)/3681 weeks
33423.40953 -30.02879 (334*2π)/3681 weeks
33524.94799 -29.66062 (335*2π)/3681 weeks
33623.73958 -19.89414 (336*2π)/3681 weeks
33712.85056 -28.64337 (337*2π)/3681 weeks
33819.8871 -37.15659 (338*2π)/3681 weeks
33934.09449 -34.53616 (339*2π)/3681 weeks
34035.06909 -20.60069 (340*2π)/3681 weeks
34122.92429 -8.3769 (341*2π)/3681 weeks
34211.04593 -16.9852 (342*2π)/3681 weeks
34315.30332 -24.20903 (343*2π)/3681 weeks
34415.11579 -15.3871 (344*2π)/3681 weeks
345-.11516 -14.36986 (345*2π)/3681 weeks
346-13.63139 -31.46614 (346*2π)/3681 weeks
347-7.11205 -51.8169 (347*2π)/3681 weeks
3486.98947 -54.98639 (348*2π)/3681 weeks
34919.39359 -49.38762 (349*2π)/3681 weeks
3501.7871 -36.78582 (350*2π)/3681 weeks
351-6.43589 -78.20485 (351*2π)/3681 weeks
35236.99419 -84.77308 (352*2π)/3681 weeks
35337.37996 -49.74624 (353*2π)/3681 weeks
35427.98467 -57.76165 (354*2π)/3681 weeks
35538.65142 -51.35634 (355*2π)/3681 weeks
35617.55951 -38.92756 (356*2π)/3681 weeks
3574.03969 -63.60359 (357*2π)/3681 weeks
35818.55065 -64.40736 (358*2π)/3681 weeks
359.51624 -48.77764 (359*2π)/3681 weeks
360-48.32711 -71.35661 (360*2π)/3681 weeks
361-84.54847 -157.1754 (361*2π)/3681 weeks
362-7.32063 -259.6634 (362*2π)/3681 weeks
36386.8438 -250.5366 (363*2π)/3681 weeks
364101.6346 -248.4592 (364*2π)/3681 weeks
365144.5307 -283.6725 (365*2π)/3681 weeks
366180.0575 -329.0851 (366*2π)/3681 weeks

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