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Fourier Analysis of SDOW (UltraPro Short Dow30)


SDOW (UltraPro Short Dow30) appears to have interesting cyclic behaviour every 36 weeks (36.793*sine), 13 weeks (21.9126*sine), and 19 weeks (21.4161*sine).

SDOW (UltraPro Short Dow30) has an average price of 307.15 (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 2/11/2010 to 1/9/2017 for SDOW (UltraPro Short Dow30), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0307.1456   0 
1178.2785 255.7723 (1*2π)/362362 weeks
257.40605 158.6152 (2*2π)/362181 weeks
334.82303 119.6379 (3*2π)/362121 weeks
421.20285 99.67181 (4*2π)/36291 weeks
514.14747 95.08943 (5*2π)/36272 weeks
6-14.70357 78.27849 (6*2π)/36260 weeks
7-18.1092 40.57938 (7*2π)/36252 weeks
8-.95224 30.69926 (8*2π)/36245 weeks
96.35173 32.9519 (9*2π)/36240 weeks
10-1.65524 36.793 (10*2π)/36236 weeks
11-8.96833 19.33527 (11*2π)/36233 weeks
126.16444 14.35781 (12*2π)/36230 weeks
137.29653 19.76056 (13*2π)/36228 weeks
148.58239 19.26878 (14*2π)/36226 weeks
1510.77567 19.09955 (15*2π)/36224 weeks
164.11186 16.20089 (16*2π)/36223 weeks
1710.30426 11.36778 (17*2π)/36221 weeks
1812.17192 20.20053 (18*2π)/36220 weeks
197.0387 21.41607 (19*2π)/36219 weeks
205.856 17.09657 (20*2π)/36218 weeks
219.46741 13.1131 (21*2π)/36217 weeks
2211.68155 13.88746 (22*2π)/36216 weeks
239.54174 17.96935 (23*2π)/36216 weeks
246.28837 15.85321 (24*2π)/36215 weeks
258.86474 14.29156 (25*2π)/36214 weeks
2610.27709 15.15649 (26*2π)/36214 weeks
2710.43036 20.38499 (27*2π)/36213 weeks
282.98163 21.91261 (28*2π)/36213 weeks
29-1.60428 14.48602 (29*2π)/36212 weeks
303.39471 11.16279 (30*2π)/36212 weeks
316.27906 12.83929 (31*2π)/36212 weeks
322.02084 13.38748 (32*2π)/36211 weeks
332.35838 12.8536 (33*2π)/36211 weeks
34.74315 11.14853 (34*2π)/36211 weeks
353.18343 7.69953 (35*2π)/36210 weeks
365.12058 8.11472 (36*2π)/36210 weeks
376.98684 9.35879 (37*2π)/36210 weeks
385.33798 11.6475 (38*2π)/36210 weeks
393.2919 13.11925 (39*2π)/3629 weeks
40.29528 10.6441 (40*2π)/3629 weeks
411.33756 6.81105 (41*2π)/3629 weeks
424.02825 8.53358 (42*2π)/3629 weeks
433.71732 9.36309 (43*2π)/3628 weeks
44-2.15708 9.84581 (44*2π)/3628 weeks
45.3247 2.31209 (45*2π)/3628 weeks
465.18682 4.43998 (46*2π)/3628 weeks
474.84376 6.09652 (47*2π)/3628 weeks
482.68656 7.27794 (48*2π)/3628 weeks
492.16221 3.71757 (49*2π)/3627 weeks
505.03902 .06593 (50*2π)/3627 weeks
5111.05931 4.23176 (51*2π)/3627 weeks
529.04446 9.53505 (52*2π)/3627 weeks
534.87243 9.41637 (53*2π)/3627 weeks
544.99442 6.49883 (54*2π)/3627 weeks
557.11673 8.88189 (55*2π)/3627 weeks
563.99408 10.6216 (56*2π)/3626 weeks
571.9754 8.18728 (57*2π)/3626 weeks
582.41071 8.45281 (58*2π)/3626 weeks
591.77394 6.91697 (59*2π)/3626 weeks
602.34223 6.03817 (60*2π)/3626 weeks
611.50153 6.33849 (61*2π)/3626 weeks
62.96933 3.82321 (62*2π)/3626 weeks
633.51795 3.02152 (63*2π)/3626 weeks
643.48544 3.86858 (64*2π)/3626 weeks
653.82863 4.07053 (65*2π)/3626 weeks
663.3699 3.88808 (66*2π)/3625 weeks
674.22239 4.66411 (67*2π)/3625 weeks
684.36846 4.13966 (68*2π)/3625 weeks
694.07522 4.03882 (69*2π)/3625 weeks
705.96686 3.70482 (70*2π)/3625 weeks
715.39571 5.59685 (71*2π)/3625 weeks
723.92098 5.80821 (72*2π)/3625 weeks
734.48528 6.18912 (73*2π)/3625 weeks
743.55272 6.65442 (74*2π)/3625 weeks
751.59138 5.86807 (75*2π)/3625 weeks
762.24682 4.01165 (76*2π)/3625 weeks
772.45843 3.36488 (77*2π)/3625 weeks
783.35659 4.16681 (78*2π)/3625 weeks
791.97533 5.00301 (79*2π)/3625 weeks
802.48981 3.73237 (80*2π)/3625 weeks
812.06893 3.30919 (81*2π)/3624 weeks
823.33043 2.90019 (82*2π)/3624 weeks
832.43823 3.18178 (83*2π)/3624 weeks
842.09499 2.39037 (84*2π)/3624 weeks
852.67727 1.97385 (85*2π)/3624 weeks
862.87927 1.33614 (86*2π)/3624 weeks
873.52615 1.26672 (87*2π)/3624 weeks
884.80612 .90433 (88*2π)/3624 weeks
896.67387 1.07655 (89*2π)/3624 weeks
906.40089 3.06565 (90*2π)/3624 weeks
914.64771 3.87707 (91*2π)/3624 weeks
924.47363 2.60738 (92*2π)/3624 weeks
936.72263 2.97002 (93*2π)/3624 weeks
946.46882 5.4444 (94*2π)/3624 weeks
954.77015 6.15485 (95*2π)/3624 weeks
963.26196 4.81198 (96*2π)/3624 weeks
973.40994 4.1948 (97*2π)/3624 weeks
983.58344 5.45104 (98*2π)/3624 weeks
991.69718 5.23738 (99*2π)/3624 weeks
100.88353 3.29665 (100*2π)/3624 weeks
1012.39894 2.46039 (101*2π)/3624 weeks
1022.38902 3.45804 (102*2π)/3624 weeks
1031.32159 2.86914 (103*2π)/3624 weeks
104.09983 1.42465 (104*2π)/3623 weeks
1052.28326 -.80371 (105*2π)/3623 weeks
1063.94455 .24087 (106*2π)/3623 weeks
1074.01252 1.23133 (107*2π)/3623 weeks
1084.43977 .40989 (108*2π)/3623 weeks
1095.23377 2.68715 (109*2π)/3623 weeks
1103.21408 2.53521 (110*2π)/3623 weeks
1113.56296 1.88838 (111*2π)/3623 weeks
1123.80615 2.01145 (112*2π)/3623 weeks
1133.60994 1.68822 (113*2π)/3623 weeks
1143.41757 2.659 (114*2π)/3623 weeks
1152.90722 1.8201 (115*2π)/3623 weeks
1163.39215 1.40436 (116*2π)/3623 weeks
1173.85415 1.36665 (117*2π)/3623 weeks
1183.46361 1.98744 (118*2π)/3623 weeks
1192.88467 1.4301 (119*2π)/3623 weeks
1203.72051 .5594 (120*2π)/3623 weeks
1214.14531 2.08798 (121*2π)/3623 weeks
1222.7074 1.42217 (122*2π)/3623 weeks
1233.68229 -.16268 (123*2π)/3623 weeks
1244.71314 .76474 (124*2π)/3623 weeks
1254.07282 1.98203 (125*2π)/3623 weeks
1263.32979 1.01627 (126*2π)/3623 weeks
1274.30895 -.71802 (127*2π)/3623 weeks
1286.83948 .53753 (128*2π)/3623 weeks
1295.80854 4.0796 (129*2π)/3623 weeks
1303.07393 3.18593 (130*2π)/3623 weeks
1313.12311 1.35383 (131*2π)/3623 weeks
1325.60529 1.03917 (132*2π)/3623 weeks
1335.38184 4.38825 (133*2π)/3623 weeks
1341.8368 4.31688 (134*2π)/3623 weeks
1351.26963 1.659 (135*2π)/3623 weeks
1361.94726 .76547 (136*2π)/3623 weeks
1372.91853 1.08506 (137*2π)/3623 weeks
1382.4331 1.63933 (138*2π)/3623 weeks
1391.15874 .74295 (139*2π)/3623 weeks
1401.815 -.90919 (140*2π)/3623 weeks
1414.2018 -.87943 (141*2π)/3623 weeks
1423.84 .42706 (142*2π)/3623 weeks
1432.98549 .23579 (143*2π)/3623 weeks
1442.87138 -.24223 (144*2π)/3623 weeks
1453.47657 -.91825 (145*2π)/3622 weeks
1464.45207 -1.42821 (146*2π)/3622 weeks
1475.61286 -.33466 (147*2π)/3622 weeks
1485.19402 1.29244 (148*2π)/3622 weeks
1493.07902 .79346 (149*2π)/3622 weeks
1504.01959 -.89468 (150*2π)/3622 weeks
1515.87884 .33684 (151*2π)/3622 weeks
1525.27397 1.80893 (152*2π)/3622 weeks
1533.79735 1.19697 (153*2π)/3622 weeks
1543.95783 .55527 (154*2π)/3622 weeks
1554.36373 .51726 (155*2π)/3622 weeks
1564.77721 1.01209 (156*2π)/3622 weeks
1573.67427 1.98209 (157*2π)/3622 weeks
1583.00915 -.37069 (158*2π)/3622 weeks
1595.23647 -.25544 (159*2π)/3622 weeks
1604.77604 2.0404 (160*2π)/3622 weeks
1612.98273 1.70566 (161*2π)/3622 weeks
1622.82768 .16944 (162*2π)/3622 weeks
1633.81099 -1.38601 (163*2π)/3622 weeks
1645.10452 .38981 (164*2π)/3622 weeks
1654.79711 1.13351 (165*2π)/3622 weeks
1664.13596 .88936 (166*2π)/3622 weeks
1674.10674 1.24953 (167*2π)/3622 weeks
1684.6549 1.15305 (168*2π)/3622 weeks
1693.62164 2.75912 (169*2π)/3622 weeks
1701.49886 2.11907 (170*2π)/3622 weeks
1711.09943 -.03092 (171*2π)/3622 weeks
1721.68397 -.8073 (172*2π)/3622 weeks
1731.86044 -1.8994 (173*2π)/3622 weeks
1743.01442 -1.51675 (174*2π)/3622 weeks
1752.94021 -1.74001 (175*2π)/3622 weeks
1764.1472 -3.08923 (176*2π)/3622 weeks
1775.74685 -2.64233 (177*2π)/3622 weeks
1785.57176 -1.14715 (178*2π)/3622 weeks
1795.09257 -.51216 (179*2π)/3622 weeks
1805.71035 -1.24807 (180*2π)/3622 weeks
1817.26188   (181*2π)/3622 weeks
1825.71035 1.24807 (182*2π)/3622 weeks
1835.09257 .51216 (183*2π)/3622 weeks
1845.57176 1.14715 (184*2π)/3622 weeks
1855.74685 2.64233 (185*2π)/3622 weeks
1864.1472 3.08923 (186*2π)/3622 weeks
1872.94021 1.74001 (187*2π)/3622 weeks
1883.01442 1.51675 (188*2π)/3622 weeks
1891.86044 1.8994 (189*2π)/3622 weeks
1901.68397 .8073 (190*2π)/3622 weeks
1911.09943 .03092 (191*2π)/3622 weeks
1921.49886 -2.11907 (192*2π)/3622 weeks
1933.62164 -2.75912 (193*2π)/3622 weeks
1944.6549 -1.15305 (194*2π)/3622 weeks
1954.10674 -1.24953 (195*2π)/3622 weeks
1964.13596 -.88936 (196*2π)/3622 weeks
1974.79711 -1.13351 (197*2π)/3622 weeks
1985.10452 -.38981 (198*2π)/3622 weeks
1993.81099 1.38601 (199*2π)/3622 weeks
2002.82768 -.16944 (200*2π)/3622 weeks
2012.98273 -1.70566 (201*2π)/3622 weeks
2024.77604 -2.0404 (202*2π)/3622 weeks
2035.23647 .25544 (203*2π)/3622 weeks
2043.00915 .37069 (204*2π)/3622 weeks
2053.67427 -1.98209 (205*2π)/3622 weeks
2064.77721 -1.01209 (206*2π)/3622 weeks
2074.36373 -.51726 (207*2π)/3622 weeks
2083.95783 -.55527 (208*2π)/3622 weeks
2093.79735 -1.19697 (209*2π)/3622 weeks
2105.27397 -1.80893 (210*2π)/3622 weeks
2115.87884 -.33684 (211*2π)/3622 weeks
2124.01959 .89468 (212*2π)/3622 weeks
2133.07902 -.79346 (213*2π)/3622 weeks
2145.19402 -1.29244 (214*2π)/3622 weeks
2155.61286 .33466 (215*2π)/3622 weeks
2164.45207 1.42821 (216*2π)/3622 weeks
2173.47657 .91825 (217*2π)/3622 weeks
2182.87138 .24223 (218*2π)/3622 weeks
2192.98549 -.23579 (219*2π)/3622 weeks
2203.84 -.42706 (220*2π)/3622 weeks
2214.2018 .87943 (221*2π)/3622 weeks
2221.815 .90919 (222*2π)/3622 weeks
2231.15874 -.74295 (223*2π)/3622 weeks
2242.4331 -1.63933 (224*2π)/3622 weeks
2252.91853 -1.08506 (225*2π)/3622 weeks
2261.94726 -.76547 (226*2π)/3622 weeks
2271.26963 -1.659 (227*2π)/3622 weeks
2281.8368 -4.31688 (228*2π)/3622 weeks
2295.38184 -4.38825 (229*2π)/3622 weeks
2305.60529 -1.03917 (230*2π)/3622 weeks
2313.12311 -1.35383 (231*2π)/3622 weeks
2323.07393 -3.18593 (232*2π)/3622 weeks
2335.80854 -4.0796 (233*2π)/3622 weeks
2346.83948 -.53753 (234*2π)/3622 weeks
2354.30895 .71802 (235*2π)/3622 weeks
2363.32979 -1.01627 (236*2π)/3622 weeks
2374.07282 -1.98203 (237*2π)/3622 weeks
2384.71314 -.76474 (238*2π)/3622 weeks
2393.68229 .16268 (239*2π)/3622 weeks
2402.7074 -1.42217 (240*2π)/3622 weeks
2414.14531 -2.08798 (241*2π)/3622 weeks
2423.72051 -.5594 (242*2π)/3621 weeks
2432.88467 -1.4301 (243*2π)/3621 weeks
2443.46361 -1.98744 (244*2π)/3621 weeks
2453.85415 -1.36665 (245*2π)/3621 weeks
2463.39215 -1.40436 (246*2π)/3621 weeks
2472.90722 -1.8201 (247*2π)/3621 weeks
2483.41757 -2.659 (248*2π)/3621 weeks
2493.60994 -1.68822 (249*2π)/3621 weeks
2503.80615 -2.01145 (250*2π)/3621 weeks
2513.56296 -1.88838 (251*2π)/3621 weeks
2523.21408 -2.53521 (252*2π)/3621 weeks
2535.23377 -2.68715 (253*2π)/3621 weeks
2544.43977 -.40989 (254*2π)/3621 weeks
2554.01252 -1.23133 (255*2π)/3621 weeks
2563.94455 -.24087 (256*2π)/3621 weeks
2572.28326 .80371 (257*2π)/3621 weeks
258.09983 -1.42465 (258*2π)/3621 weeks
2591.32159 -2.86914 (259*2π)/3621 weeks
2602.38902 -3.45804 (260*2π)/3621 weeks
2612.39894 -2.46039 (261*2π)/3621 weeks
262.88353 -3.29665 (262*2π)/3621 weeks
2631.69718 -5.23738 (263*2π)/3621 weeks
2643.58344 -5.45104 (264*2π)/3621 weeks
2653.40994 -4.1948 (265*2π)/3621 weeks
2663.26196 -4.81198 (266*2π)/3621 weeks
2674.77015 -6.15485 (267*2π)/3621 weeks
2686.46882 -5.4444 (268*2π)/3621 weeks
2696.72263 -2.97002 (269*2π)/3621 weeks
2704.47363 -2.60738 (270*2π)/3621 weeks
2714.64771 -3.87707 (271*2π)/3621 weeks
2726.40089 -3.06565 (272*2π)/3621 weeks
2736.67387 -1.07655 (273*2π)/3621 weeks
2744.80612 -.90433 (274*2π)/3621 weeks
2753.52615 -1.26672 (275*2π)/3621 weeks
2762.87927 -1.33614 (276*2π)/3621 weeks
2772.67727 -1.97385 (277*2π)/3621 weeks
2782.09499 -2.39037 (278*2π)/3621 weeks
2792.43823 -3.18178 (279*2π)/3621 weeks
2803.33043 -2.90019 (280*2π)/3621 weeks
2812.06893 -3.30919 (281*2π)/3621 weeks
2822.48981 -3.73237 (282*2π)/3621 weeks
2831.97533 -5.00301 (283*2π)/3621 weeks
2843.35659 -4.16681 (284*2π)/3621 weeks
2852.45843 -3.36488 (285*2π)/3621 weeks
2862.24682 -4.01165 (286*2π)/3621 weeks
2871.59138 -5.86807 (287*2π)/3621 weeks
2883.55272 -6.65442 (288*2π)/3621 weeks
2894.48528 -6.18912 (289*2π)/3621 weeks
2903.92098 -5.80821 (290*2π)/3621 weeks
2915.39571 -5.59685 (291*2π)/3621 weeks
2925.96686 -3.70482 (292*2π)/3621 weeks
2934.07522 -4.03882 (293*2π)/3621 weeks
2944.36846 -4.13966 (294*2π)/3621 weeks
2954.22239 -4.66411 (295*2π)/3621 weeks
2963.3699 -3.88808 (296*2π)/3621 weeks
2973.82863 -4.07053 (297*2π)/3621 weeks
2983.48544 -3.86858 (298*2π)/3621 weeks
2993.51795 -3.02152 (299*2π)/3621 weeks
300.96933 -3.82321 (300*2π)/3621 weeks
3011.50153 -6.33849 (301*2π)/3621 weeks
3022.34223 -6.03817 (302*2π)/3621 weeks
3031.77394 -6.91697 (303*2π)/3621 weeks
3042.41071 -8.45281 (304*2π)/3621 weeks
3051.9754 -8.18728 (305*2π)/3621 weeks
3063.99408 -10.6216 (306*2π)/3621 weeks
3077.11673 -8.88189 (307*2π)/3621 weeks
3084.99442 -6.49883 (308*2π)/3621 weeks
3094.87243 -9.41637 (309*2π)/3621 weeks
3109.04446 -9.53505 (310*2π)/3621 weeks
31111.05931 -4.23176 (311*2π)/3621 weeks
3125.03902 -.06593 (312*2π)/3621 weeks
3132.16221 -3.71757 (313*2π)/3621 weeks
3142.68656 -7.27794 (314*2π)/3621 weeks
3154.84376 -6.09652 (315*2π)/3621 weeks
3165.18682 -4.43998 (316*2π)/3621 weeks
317.3247 -2.31209 (317*2π)/3621 weeks
318-2.15708 -9.84581 (318*2π)/3621 weeks
3193.71732 -9.36309 (319*2π)/3621 weeks
3204.02825 -8.53358 (320*2π)/3621 weeks
3211.33756 -6.81105 (321*2π)/3621 weeks
322.29528 -10.6441 (322*2π)/3621 weeks
3233.2919 -13.11925 (323*2π)/3621 weeks
3245.33798 -11.6475 (324*2π)/3621 weeks
3256.98684 -9.35879 (325*2π)/3621 weeks
3265.12058 -8.11472 (326*2π)/3621 weeks
3273.18343 -7.69953 (327*2π)/3621 weeks
328.74315 -11.14853 (328*2π)/3621 weeks
3292.35838 -12.8536 (329*2π)/3621 weeks
3302.02084 -13.38748 (330*2π)/3621 weeks
3316.27906 -12.83929 (331*2π)/3621 weeks
3323.39471 -11.16279 (332*2π)/3621 weeks
333-1.60428 -14.48602 (333*2π)/3621 weeks
3342.98163 -21.91261 (334*2π)/3621 weeks
33510.43036 -20.38499 (335*2π)/3621 weeks
33610.27709 -15.15649 (336*2π)/3621 weeks
3378.86474 -14.29156 (337*2π)/3621 weeks
3386.28837 -15.85321 (338*2π)/3621 weeks
3399.54174 -17.96935 (339*2π)/3621 weeks
34011.68155 -13.88746 (340*2π)/3621 weeks
3419.46741 -13.1131 (341*2π)/3621 weeks
3425.856 -17.09657 (342*2π)/3621 weeks
3437.0387 -21.41607 (343*2π)/3621 weeks
34412.17192 -20.20053 (344*2π)/3621 weeks
34510.30426 -11.36778 (345*2π)/3621 weeks
3464.11186 -16.20089 (346*2π)/3621 weeks
34710.77567 -19.09955 (347*2π)/3621 weeks
3488.58239 -19.26878 (348*2π)/3621 weeks
3497.29653 -19.76056 (349*2π)/3621 weeks
3506.16444 -14.35781 (350*2π)/3621 weeks
351-8.96833 -19.33527 (351*2π)/3621 weeks
352-1.65524 -36.793 (352*2π)/3621 weeks
3536.35173 -32.9519 (353*2π)/3621 weeks
354-.95224 -30.69926 (354*2π)/3621 weeks
355-18.1092 -40.57938 (355*2π)/3621 weeks
356-14.70357 -78.27849 (356*2π)/3621 weeks
35714.14747 -95.08943 (357*2π)/3621 weeks
35821.20285 -99.67181 (358*2π)/3621 weeks
35934.82303 -119.6379 (359*2π)/3621 weeks
36057.40605 -158.6152 (360*2π)/3621 weeks

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