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Fourier Analysis of SOXS (Direxion Daily Semiconductor Be)


SOXS (Direxion Daily Semiconductor Be) appears to have interesting cyclic behaviour every 22 weeks (91.5074*sine), 36 weeks (69.7546*sine), and 24 weeks (62.135*sine).

SOXS (Direxion Daily Semiconductor Be) has an average price of 575.76 (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 1/9/2017 for SOXS (Direxion Daily Semiconductor Be), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0575.7578   0 
1435.4182 567.7974 (1*2π)/358358 weeks
2184.7683 329.9973 (2*2π)/358179 weeks
3143.4478 287.5405 (3*2π)/358119 weeks
4101.4187 250.9612 (4*2π)/35890 weeks
580.89425 263.2893 (5*2π)/35872 weeks
6-27.82302 257.3384 (6*2π)/35860 weeks
7-85.41239 136.9304 (7*2π)/35851 weeks
8-38.80653 63.93363 (8*2π)/35845 weeks
910.13319 53.38947 (9*2π)/35840 weeks
1017.70923 69.75462 (10*2π)/35836 weeks
112.963 55.3331 (11*2π)/35833 weeks
1228.04083 39.62441 (12*2π)/35830 weeks
1336.48035 59.77209 (13*2π)/35828 weeks
1428.1716 55.35308 (14*2π)/35826 weeks
1548.7494 62.13504 (15*2π)/35824 weeks
1617.07214 91.5074 (16*2π)/35822 weeks
17-14.472 56.04966 (17*2π)/35821 weeks
1816.31029 41.47341 (18*2π)/35820 weeks
1913.22849 57.85939 (19*2π)/35819 weeks
201.49401 56.9641 (20*2π)/35818 weeks
21-13.06695 41.38877 (21*2π)/35817 weeks
22-7.36783 18.57672 (22*2π)/35816 weeks
2310.4105 13.56664 (23*2π)/35816 weeks
2417.81723 23.00761 (24*2π)/35815 weeks
2510.93198 21.0595 (25*2π)/35814 weeks
2618.29005 9.92409 (26*2π)/35814 weeks
2735.56037 17.60716 (27*2π)/35813 weeks
2836.89756 31.67429 (28*2π)/35813 weeks
2922.56867 39.02593 (29*2π)/35812 weeks
3013.78745 31.51452 (30*2π)/35812 weeks
3121.95872 19.72405 (31*2π)/35812 weeks
3226.16641 30.1855 (32*2π)/35811 weeks
3323.92023 30.8998 (33*2π)/35811 weeks
3425.67192 37.39264 (34*2π)/35811 weeks
3513.62674 43.43832 (35*2π)/35810 weeks
36.34372 33.97624 (36*2π)/35810 weeks
375.09081 13.92087 (37*2π)/35810 weeks
3818.8914 17.5608 (38*2π)/3589 weeks
3919.63517 22.12201 (39*2π)/3589 weeks
4018.35559 24.8053 (40*2π)/3589 weeks
4113.24003 21.58477 (41*2π)/3589 weeks
4220.55836 15.74691 (42*2π)/3589 weeks
4328.17226 18.3643 (43*2π)/3588 weeks
4431.81186 33.65581 (44*2π)/3588 weeks
4516.09 38.95136 (45*2π)/3588 weeks
4613.54944 28.58882 (46*2π)/3588 weeks
4717.71133 29.21122 (47*2π)/3588 weeks
4819.94107 33.11792 (48*2π)/3587 weeks
4916.06065 40.64734 (49*2π)/3587 weeks
50.57385 43.45758 (50*2π)/3587 weeks
51-7.77067 28.14818 (51*2π)/3587 weeks
523.09046 17.451 (52*2π)/3587 weeks
5310.14935 27.62864 (53*2π)/3587 weeks
54-4.10775 30.18297 (54*2π)/3587 weeks
55-4.83316 15.5933 (55*2π)/3587 weeks
563.79031 16.59656 (56*2π)/3586 weeks
57.77724 18.35948 (57*2π)/3586 weeks
582.48378 13.82637 (58*2π)/3586 weeks
592.8684 13.95154 (59*2π)/3586 weeks
603.91932 9.37591 (60*2π)/3586 weeks
6112.13455 10.73238 (61*2π)/3586 weeks
628.63127 20.8108 (62*2π)/3586 weeks
63-.08212 15.22633 (63*2π)/3586 weeks
644.23605 8.94029 (64*2π)/3586 weeks
656.66236 9.43493 (65*2π)/3586 weeks
669.28249 11.13955 (66*2π)/3585 weeks
679.20024 11.93358 (67*2π)/3585 weeks
689.22164 10.1559 (68*2π)/3585 weeks
6914.31148 13.72701 (69*2π)/3585 weeks
7010.14679 17.87755 (70*2π)/3585 weeks
716.16767 20.16807 (71*2π)/3585 weeks
72.87615 20.3365 (72*2π)/3585 weeks
73-3.53322 14.42701 (73*2π)/3585 weeks
74-5.5896 8.03531 (74*2π)/3585 weeks
75-.42417 1.01688 (75*2π)/3585 weeks
765.15642 2.1843 (76*2π)/3585 weeks
773.97839 4.27815 (77*2π)/3585 weeks
783.45621 .13396 (78*2π)/3585 weeks
7910.36234 -1.97469 (79*2π)/3585 weeks
8011.48356 .79836 (80*2π)/3584 weeks
8115.91562 1.88517 (81*2π)/3584 weeks
8213.98847 6.62087 (82*2π)/3584 weeks
8311.44274 4.58095 (83*2π)/3584 weeks
8413.50596 5.44603 (84*2π)/3584 weeks
8512.27169 5.55528 (85*2π)/3584 weeks
8612.48191 4.17281 (86*2π)/3584 weeks
8716.49212 2.59947 (87*2π)/3584 weeks
8821.25417 6.78756 (88*2π)/3584 weeks
8917.47306 12.99496 (89*2π)/3584 weeks
9010.69043 13.14421 (90*2π)/3584 weeks
919.85538 5.84842 (91*2π)/3584 weeks
9217.20398 4.1527 (92*2π)/3584 weeks
9321.03489 12.05533 (93*2π)/3584 weeks
9415.41918 17.1634 (94*2π)/3584 weeks
958.66538 13.57191 (95*2π)/3584 weeks
9612.03553 7.45916 (96*2π)/3584 weeks
9719.00073 13.80275 (97*2π)/3584 weeks
9810.68368 21.96515 (98*2π)/3584 weeks
991.75393 16.04577 (99*2π)/3584 weeks
1004.26455 8.3074 (100*2π)/3584 weeks
1018.77138 8.95849 (101*2π)/3584 weeks
1029.74261 12.44179 (102*2π)/3584 weeks
1032.71048 14.78237 (103*2π)/3583 weeks
104-1.37089 6.93646 (104*2π)/3583 weeks
1053.78362 2.997 (105*2π)/3583 weeks
1064.89992 3.8617 (106*2π)/3583 weeks
1075.25461 -1.26252 (107*2π)/3583 weeks
10812.76236 -1.25689 (108*2π)/3583 weeks
10915.01661 2.65 (109*2π)/3583 weeks
11015.49572 5.6985 (110*2π)/3583 weeks
11115.02883 8.48707 (111*2π)/3583 weeks
11212.86691 9.7706 (112*2π)/3583 weeks
11311.95748 10.54831 (113*2π)/3583 weeks
11410.57744 11.95203 (114*2π)/3583 weeks
1157.56576 11.87258 (115*2π)/3583 weeks
1165.58827 8.70122 (116*2π)/3583 weeks
1177.1048 7.34473 (117*2π)/3583 weeks
1187.73586 7.62271 (118*2π)/3583 weeks
1197.335 6.88193 (119*2π)/3583 weeks
1209.66027 9.10163 (120*2π)/3583 weeks
1213.87236 11.38767 (121*2π)/3583 weeks
1221.48423 3.78727 (122*2π)/3583 weeks
1238.0512 1.83512 (123*2π)/3583 weeks
12410.8655 6.96217 (124*2π)/3583 weeks
1255.97973 11.64425 (125*2π)/3583 weeks
126-1.16919 7.65039 (126*2π)/3583 weeks
127-.1982 -1.60728 (127*2π)/3583 weeks
1288.91811 -1.81919 (128*2π)/3583 weeks
1299.34048 5.37212 (129*2π)/3583 weeks
1302.0542 6.26892 (130*2π)/3583 weeks
131-1.62523 -4.78886 (131*2π)/3583 weeks
13211.35655 -10.35497 (132*2π)/3583 weeks
13317.39195 -.09776 (133*2π)/3583 weeks
13412.43547 3.70269 (134*2π)/3583 weeks
13510.19037 3.05841 (135*2π)/3583 weeks
13610.64775 -.27202 (136*2π)/3583 weeks
13715.15502 .92587 (137*2π)/3583 weeks
13815.13206 6.39282 (138*2π)/3583 weeks
1399.76329 8.82094 (139*2π)/3583 weeks
1407.67883 3.33797 (140*2π)/3583 weeks
14110.62366 2.09213 (141*2π)/3583 weeks
14212.04924 2.72037 (142*2π)/3583 weeks
14313.90402 5.46054 (143*2π)/3583 weeks
14412.78012 9.0147 (144*2π)/3582 weeks
1458.36299 10.01649 (145*2π)/3582 weeks
1464.72219 7.93625 (146*2π)/3582 weeks
1474.96018 2.24259 (147*2π)/3582 weeks
14810.50086 3.67481 (148*2π)/3582 weeks
1498.37049 7.83123 (149*2π)/3582 weeks
1505.07036 6.86807 (150*2π)/3582 weeks
1514.21542 3.37016 (151*2π)/3582 weeks
1526.63971 2.35731 (152*2π)/3582 weeks
1536.84307 5.26771 (153*2π)/3582 weeks
1543.45786 5.84985 (154*2π)/3582 weeks
155-1.14316 1.58914 (155*2π)/3582 weeks
1564.12321 -6.43419 (156*2π)/3582 weeks
15711.28868 -1.35652 (157*2π)/3582 weeks
1586.4858 2.64447 (158*2π)/3582 weeks
1594.47158 -.42005 (159*2π)/3582 weeks
1606.04205 -4.46221 (160*2π)/3582 weeks
16111.56955 -4.86059 (161*2π)/3582 weeks
16212.40113 -1.26082 (162*2π)/3582 weeks
16314.24359 .92425 (163*2π)/3582 weeks
16411.68278 5.14468 (164*2π)/3582 weeks
1657.87762 4.17958 (165*2π)/3582 weeks
16610.24886 1.76977 (166*2π)/3582 weeks
1679.39611 6.73156 (167*2π)/3582 weeks
1684.28359 6.59648 (168*2π)/3582 weeks
1691.92766 2.89565 (169*2π)/3582 weeks
170.84938 .5112 (170*2π)/3582 weeks
1711.03197 -4.91149 (171*2π)/3582 weeks
1726.30108 -5.28521 (172*2π)/3582 weeks
1734.49323 -3.17234 (173*2π)/3582 weeks
1744.9319 -9.2049 (174*2π)/3582 weeks
17511.21065 -11.57408 (175*2π)/3582 weeks
17616.97507 -7.43314 (176*2π)/3582 weeks
17715.00161 -1.85289 (177*2π)/3582 weeks
17815.45128 -4.5733 (178*2π)/3582 weeks
17920.02258   (179*2π)/3582 weeks
18015.45128 4.5733 (180*2π)/3582 weeks
18115.00161 1.85289 (181*2π)/3582 weeks
18216.97507 7.43314 (182*2π)/3582 weeks
18311.21065 11.57408 (183*2π)/3582 weeks
1844.9319 9.2049 (184*2π)/3582 weeks
1854.49323 3.17234 (185*2π)/3582 weeks
1866.30108 5.28521 (186*2π)/3582 weeks
1871.03197 4.91149 (187*2π)/3582 weeks
188.84938 -.5112 (188*2π)/3582 weeks
1891.92766 -2.89565 (189*2π)/3582 weeks
1904.28359 -6.59648 (190*2π)/3582 weeks
1919.39611 -6.73156 (191*2π)/3582 weeks
19210.24886 -1.76977 (192*2π)/3582 weeks
1937.87762 -4.17958 (193*2π)/3582 weeks
19411.68278 -5.14468 (194*2π)/3582 weeks
19514.24359 -.92425 (195*2π)/3582 weeks
19612.40113 1.26082 (196*2π)/3582 weeks
19711.56955 4.86059 (197*2π)/3582 weeks
1986.04205 4.46221 (198*2π)/3582 weeks
1994.47158 .42005 (199*2π)/3582 weeks
2006.4858 -2.64447 (200*2π)/3582 weeks
20111.28868 1.35652 (201*2π)/3582 weeks
2024.12321 6.43419 (202*2π)/3582 weeks
203-1.14316 -1.58914 (203*2π)/3582 weeks
2043.45786 -5.84985 (204*2π)/3582 weeks
2056.84307 -5.26771 (205*2π)/3582 weeks
2066.63971 -2.35731 (206*2π)/3582 weeks
2074.21542 -3.37016 (207*2π)/3582 weeks
2085.07036 -6.86807 (208*2π)/3582 weeks
2098.37049 -7.83123 (209*2π)/3582 weeks
21010.50086 -3.67481 (210*2π)/3582 weeks
2114.96018 -2.24259 (211*2π)/3582 weeks
2124.72219 -7.93625 (212*2π)/3582 weeks
2138.36299 -10.01649 (213*2π)/3582 weeks
21412.78012 -9.0147 (214*2π)/3582 weeks
21513.90402 -5.46054 (215*2π)/3582 weeks
21612.04924 -2.72037 (216*2π)/3582 weeks
21710.62366 -2.09213 (217*2π)/3582 weeks
2187.67883 -3.33797 (218*2π)/3582 weeks
2199.76329 -8.82094 (219*2π)/3582 weeks
22015.13206 -6.39282 (220*2π)/3582 weeks
22115.15502 -.92587 (221*2π)/3582 weeks
22210.64775 .27202 (222*2π)/3582 weeks
22310.19037 -3.05841 (223*2π)/3582 weeks
22412.43547 -3.70269 (224*2π)/3582 weeks
22517.39195 .09776 (225*2π)/3582 weeks
22611.35655 10.35497 (226*2π)/3582 weeks
227-1.62523 4.78886 (227*2π)/3582 weeks
2282.0542 -6.26892 (228*2π)/3582 weeks
2299.34048 -5.37212 (229*2π)/3582 weeks
2308.91811 1.81919 (230*2π)/3582 weeks
231-.1982 1.60728 (231*2π)/3582 weeks
232-1.16919 -7.65039 (232*2π)/3582 weeks
2335.97973 -11.64425 (233*2π)/3582 weeks
23410.8655 -6.96217 (234*2π)/3582 weeks
2358.0512 -1.83512 (235*2π)/3582 weeks
2361.48423 -3.78727 (236*2π)/3582 weeks
2373.87236 -11.38767 (237*2π)/3582 weeks
2389.66027 -9.10163 (238*2π)/3582 weeks
2397.335 -6.88193 (239*2π)/3581 weeks
2407.73586 -7.62271 (240*2π)/3581 weeks
2417.1048 -7.34473 (241*2π)/3581 weeks
2425.58827 -8.70122 (242*2π)/3581 weeks
2437.56576 -11.87258 (243*2π)/3581 weeks
24410.57744 -11.95203 (244*2π)/3581 weeks
24511.95748 -10.54831 (245*2π)/3581 weeks
24612.86691 -9.7706 (246*2π)/3581 weeks
24715.02883 -8.48707 (247*2π)/3581 weeks
24815.49572 -5.6985 (248*2π)/3581 weeks
24915.01661 -2.65 (249*2π)/3581 weeks
25012.76236 1.25689 (250*2π)/3581 weeks
2515.25461 1.26252 (251*2π)/3581 weeks
2524.89992 -3.8617 (252*2π)/3581 weeks
2533.78362 -2.997 (253*2π)/3581 weeks
254-1.37089 -6.93646 (254*2π)/3581 weeks
2552.71048 -14.78237 (255*2π)/3581 weeks
2569.74261 -12.44179 (256*2π)/3581 weeks
2578.77138 -8.95849 (257*2π)/3581 weeks
2584.26455 -8.3074 (258*2π)/3581 weeks
2591.75393 -16.04577 (259*2π)/3581 weeks
26010.68368 -21.96515 (260*2π)/3581 weeks
26119.00073 -13.80275 (261*2π)/3581 weeks
26212.03553 -7.45916 (262*2π)/3581 weeks
2638.66538 -13.57191 (263*2π)/3581 weeks
26415.41918 -17.1634 (264*2π)/3581 weeks
26521.03489 -12.05533 (265*2π)/3581 weeks
26617.20398 -4.1527 (266*2π)/3581 weeks
2679.85538 -5.84842 (267*2π)/3581 weeks
26810.69043 -13.14421 (268*2π)/3581 weeks
26917.47306 -12.99496 (269*2π)/3581 weeks
27021.25417 -6.78756 (270*2π)/3581 weeks
27116.49212 -2.59947 (271*2π)/3581 weeks
27212.48191 -4.17281 (272*2π)/3581 weeks
27312.27169 -5.55528 (273*2π)/3581 weeks
27413.50596 -5.44603 (274*2π)/3581 weeks
27511.44274 -4.58095 (275*2π)/3581 weeks
27613.98847 -6.62087 (276*2π)/3581 weeks
27715.91562 -1.88517 (277*2π)/3581 weeks
27811.48356 -.79836 (278*2π)/3581 weeks
27910.36234 1.97469 (279*2π)/3581 weeks
2803.45621 -.13396 (280*2π)/3581 weeks
2813.97839 -4.27815 (281*2π)/3581 weeks
2825.15642 -2.1843 (282*2π)/3581 weeks
283-.42417 -1.01688 (283*2π)/3581 weeks
284-5.5896 -8.03531 (284*2π)/3581 weeks
285-3.53322 -14.42701 (285*2π)/3581 weeks
286.87615 -20.3365 (286*2π)/3581 weeks
2876.16767 -20.16807 (287*2π)/3581 weeks
28810.14679 -17.87755 (288*2π)/3581 weeks
28914.31148 -13.72701 (289*2π)/3581 weeks
2909.22164 -10.1559 (290*2π)/3581 weeks
2919.20024 -11.93358 (291*2π)/3581 weeks
2929.28249 -11.13955 (292*2π)/3581 weeks
2936.66236 -9.43493 (293*2π)/3581 weeks
2944.23605 -8.94029 (294*2π)/3581 weeks
295-.08212 -15.22633 (295*2π)/3581 weeks
2968.63127 -20.8108 (296*2π)/3581 weeks
29712.13455 -10.73238 (297*2π)/3581 weeks
2983.91932 -9.37591 (298*2π)/3581 weeks
2992.8684 -13.95154 (299*2π)/3581 weeks
3002.48378 -13.82637 (300*2π)/3581 weeks
301.77724 -18.35948 (301*2π)/3581 weeks
3023.79031 -16.59656 (302*2π)/3581 weeks
303-4.83316 -15.5933 (303*2π)/3581 weeks
304-4.10775 -30.18297 (304*2π)/3581 weeks
30510.14935 -27.62864 (305*2π)/3581 weeks
3063.09046 -17.451 (306*2π)/3581 weeks
307-7.77067 -28.14818 (307*2π)/3581 weeks
308.57385 -43.45758 (308*2π)/3581 weeks
30916.06065 -40.64734 (309*2π)/3581 weeks
31019.94107 -33.11792 (310*2π)/3581 weeks
31117.71133 -29.21122 (311*2π)/3581 weeks
31213.54944 -28.58882 (312*2π)/3581 weeks
31316.09 -38.95136 (313*2π)/3581 weeks
31431.81186 -33.65581 (314*2π)/3581 weeks
31528.17226 -18.3643 (315*2π)/3581 weeks
31620.55836 -15.74691 (316*2π)/3581 weeks
31713.24003 -21.58477 (317*2π)/3581 weeks
31818.35559 -24.8053 (318*2π)/3581 weeks
31919.63517 -22.12201 (319*2π)/3581 weeks
32018.8914 -17.5608 (320*2π)/3581 weeks
3215.09081 -13.92087 (321*2π)/3581 weeks
322.34372 -33.97624 (322*2π)/3581 weeks
32313.62674 -43.43832 (323*2π)/3581 weeks
32425.67192 -37.39264 (324*2π)/3581 weeks
32523.92023 -30.8998 (325*2π)/3581 weeks
32626.16641 -30.1855 (326*2π)/3581 weeks
32721.95872 -19.72405 (327*2π)/3581 weeks
32813.78745 -31.51452 (328*2π)/3581 weeks
32922.56867 -39.02593 (329*2π)/3581 weeks
33036.89756 -31.67429 (330*2π)/3581 weeks
33135.56037 -17.60716 (331*2π)/3581 weeks
33218.29005 -9.92409 (332*2π)/3581 weeks
33310.93198 -21.0595 (333*2π)/3581 weeks
33417.81723 -23.00761 (334*2π)/3581 weeks
33510.4105 -13.56664 (335*2π)/3581 weeks
336-7.36783 -18.57672 (336*2π)/3581 weeks
337-13.06695 -41.38877 (337*2π)/3581 weeks
3381.49401 -56.9641 (338*2π)/3581 weeks
33913.22849 -57.85939 (339*2π)/3581 weeks
34016.31029 -41.47341 (340*2π)/3581 weeks
341-14.472 -56.04966 (341*2π)/3581 weeks
34217.07214 -91.5074 (342*2π)/3581 weeks
34348.7494 -62.13504 (343*2π)/3581 weeks
34428.1716 -55.35308 (344*2π)/3581 weeks
34536.48035 -59.77209 (345*2π)/3581 weeks
34628.04083 -39.62441 (346*2π)/3581 weeks
3472.963 -55.3331 (347*2π)/3581 weeks
34817.70923 -69.75462 (348*2π)/3581 weeks
34910.13319 -53.38947 (349*2π)/3581 weeks
350-38.80653 -63.93363 (350*2π)/3581 weeks
351-85.41239 -136.9304 (351*2π)/3581 weeks
352-27.82302 -257.3384 (352*2π)/3581 weeks
35380.89425 -263.2893 (353*2π)/3581 weeks
354101.4187 -250.9612 (354*2π)/3581 weeks
355143.4478 -287.5405 (355*2π)/3581 weeks
356184.7683 -329.9973 (356*2π)/3581 weeks

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