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Fourier Analysis of SDOW (UltraPro Short Dow30)


SDOW (UltraPro Short Dow30) appears to have interesting cyclic behaviour every 37 weeks (36.9567*sine), 34 weeks (25.9167*sine), and 21 weeks (15.3968*cosine).

SDOW (UltraPro Short Dow30) has an average price of 300.58 (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 3/13/2017 for SDOW (UltraPro Short Dow30), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0300.5783   0 
1179.3738 251.8444 (1*2π)/371371 weeks
256.7513 158.9348 (2*2π)/371186 weeks
334.77557 119.8257 (3*2π)/371124 weeks
421.87946 100.048 (4*2π)/37193 weeks
516.74133 92.41253 (5*2π)/37174 weeks
6-11.14251 80.52165 (6*2π)/37162 weeks
7-20.92139 45.28048 (7*2π)/37153 weeks
8-3.34317 30.81777 (8*2π)/37146 weeks
95.18115 31.28383 (9*2π)/37141 weeks
101.42275 36.9567 (10*2π)/37137 weeks
11-9.93957 25.9167 (11*2π)/37134 weeks
123.16633 13.51104 (12*2π)/37131 weeks
139.09811 19.04383 (13*2π)/37129 weeks
148.74384 17.72762 (14*2π)/37127 weeks
158.7466 16.81816 (15*2π)/37125 weeks
165.10244 20.39368 (16*2π)/37123 weeks
177.09525 12.99574 (17*2π)/37122 weeks
1815.39678 16.28669 (18*2π)/37121 weeks
1910.67131 19.86151 (19*2π)/37120 weeks
205.66252 16.72976 (20*2π)/37119 weeks
215.21466 12.87377 (21*2π)/37118 weeks
228.91119 13.5697 (22*2π)/37117 weeks
2311.44428 16.4882 (23*2π)/37116 weeks
247.72309 17.59641 (24*2π)/37115 weeks
256.8669 13.97626 (25*2π)/37115 weeks
268.95415 14.36167 (26*2π)/37114 weeks
2710.81624 15.88864 (27*2π)/37114 weeks
288.02533 21.39114 (28*2π)/37113 weeks
29.54026 20.24511 (29*2π)/37113 weeks
30-.57524 12.1028 (30*2π)/37112 weeks
313.76213 11.16009 (31*2π)/37112 weeks
325.7694 14.08475 (32*2π)/37112 weeks
332.25845 12.39474 (33*2π)/37111 weeks
341.93675 12.40422 (34*2π)/37111 weeks
35.44345 10.33464 (35*2π)/37111 weeks
363.44956 7.77031 (36*2π)/37110 weeks
375.18051 8.16042 (37*2π)/37110 weeks
386.98106 9.5658 (38*2π)/37110 weeks
395.23329 11.45669 (39*2π)/37110 weeks
403.1323 12.86897 (40*2π)/3719 weeks
41.3224 10.43303 (41*2π)/3719 weeks
421.26118 6.75497 (42*2π)/3719 weeks
434.01118 8.2758 (43*2π)/3719 weeks
443.60252 8.99124 (44*2π)/3718 weeks
45-1.47703 10.36209 (45*2π)/3718 weeks
46-.43081 2.72038 (46*2π)/3718 weeks
474.97927 3.84319 (47*2π)/3718 weeks
484.76762 5.81641 (48*2π)/3718 weeks
493.4369 7.30422 (49*2π)/3718 weeks
501.82689 4.18609 (50*2π)/3717 weeks
513.4418 .98329 (51*2π)/3717 weeks
5210.23053 2.38956 (52*2π)/3717 weeks
539.97019 8.24716 (53*2π)/3717 weeks
545.79982 9.80246 (54*2π)/3717 weeks
554.17774 7.20167 (55*2π)/3717 weeks
566.97599 7.24358 (56*2π)/3717 weeks
575.33336 10.24796 (57*2π)/3717 weeks
582.20275 9.2764 (58*2π)/3716 weeks
592.96236 7.60185 (59*2π)/3716 weeks
601.50704 7.15934 (60*2π)/3716 weeks
611.59831 6.07333 (61*2π)/3716 weeks
622.03515 6.30638 (62*2π)/3716 weeks
63.57658 5.42223 (63*2π)/3716 weeks
641.81395 3.05747 (64*2π)/3716 weeks
653.71363 4.00221 (65*2π)/3716 weeks
663.77228 3.98244 (66*2π)/3716 weeks
673.93214 4.29331 (67*2π)/3716 weeks
684.09605 3.42842 (68*2π)/3715 weeks
693.74309 4.24301 (69*2π)/3715 weeks
704.22401 4.22171 (70*2π)/3715 weeks
714.07618 3.59767 (71*2π)/3715 weeks
726.10248 4.46018 (72*2π)/3715 weeks
735.21494 5.72171 (73*2π)/3715 weeks
743.94355 5.2867 (74*2π)/3715 weeks
754.13275 6.16939 (75*2π)/3715 weeks
763.19819 6.62864 (76*2π)/3715 weeks
771.44382 5.46301 (77*2π)/3715 weeks
782.34942 3.99158 (78*2π)/3715 weeks
792.62052 3.2185 (79*2π)/3715 weeks
803.31213 4.092 (80*2π)/3715 weeks
811.85539 4.80444 (81*2π)/3715 weeks
822.44089 3.66074 (82*2π)/3715 weeks
832.03892 3.25734 (83*2π)/3714 weeks
843.23655 2.76769 (84*2π)/3714 weeks
852.39671 3.16396 (85*2π)/3714 weeks
862.03072 2.48431 (86*2π)/3714 weeks
872.62721 1.98706 (87*2π)/3714 weeks
882.76862 1.47994 (88*2π)/3714 weeks
893.5703 1.32205 (89*2π)/3714 weeks
904.60716 .68871 (90*2π)/3714 weeks
915.92389 .53825 (91*2π)/3714 weeks
926.246 2.78332 (92*2π)/3714 weeks
935.09889 4.12912 (93*2π)/3714 weeks
944.41822 2.99144 (94*2π)/3714 weeks
956.13561 2.16794 (95*2π)/3714 weeks
966.81664 4.38035 (96*2π)/3714 weeks
975.11679 5.59025 (97*2π)/3714 weeks
983.05196 5.36534 (98*2π)/3714 weeks
993.12254 4.49215 (99*2π)/3714 weeks
1003.90297 4.59946 (100*2π)/3714 weeks
1012.38387 5.44901 (101*2π)/3714 weeks
102.90065 4.2884 (102*2π)/3714 weeks
1031.46119 2.3961 (103*2π)/3714 weeks
1042.54348 2.89413 (104*2π)/3714 weeks
1051.56001 3.42083 (105*2π)/3714 weeks
106.87282 2.7775 (106*2π)/3714 weeks
107.54822 .16627 (107*2π)/3713 weeks
1083.23059 -.42657 (108*2π)/3713 weeks
1094.09263 .63328 (109*2π)/3713 weeks
1103.67354 1.16083 (110*2π)/3713 weeks
1115.13105 .79104 (111*2π)/3713 weeks
1124.52888 3.08327 (112*2π)/3713 weeks
1133.20137 2.11425 (113*2π)/3713 weeks
1143.56387 1.82756 (114*2π)/3713 weeks
1153.68349 2.07289 (115*2π)/3713 weeks
1163.8091 1.65921 (116*2π)/3713 weeks
1173.11385 2.47719 (117*2π)/3713 weeks
1182.85385 1.65929 (118*2π)/3713 weeks
1193.33772 1.38675 (119*2π)/3713 weeks
1203.83142 1.41305 (120*2π)/3713 weeks
1213.35244 1.93556 (121*2π)/3713 weeks
1222.82923 1.35566 (122*2π)/3713 weeks
1233.67699 .55194 (123*2π)/3713 weeks
1244.0804 2.03172 (124*2π)/3713 weeks
1252.6814 1.43524 (125*2π)/3713 weeks
1263.47585 -.1505 (126*2π)/3713 weeks
1274.57663 .68783 (127*2π)/3713 weeks
1284.20239 1.92092 (128*2π)/3713 weeks
1293.31093 1.09606 (129*2π)/3713 weeks
1303.79078 -.53691 (130*2π)/3713 weeks
1316.33417 .10172 (131*2π)/3713 weeks
1326.41989 3.5211 (132*2π)/3713 weeks
1333.37819 3.51178 (133*2π)/3713 weeks
1342.91979 1.6678 (134*2π)/3713 weeks
1354.64278 .484 (135*2π)/3713 weeks
1365.82024 3.27501 (136*2π)/3713 weeks
1372.6488 4.75985 (137*2π)/3713 weeks
138.8319 2.46853 (138*2π)/3713 weeks
1391.63189 1.24761 (139*2π)/3713 weeks
1402.69945 .81826 (140*2π)/3713 weeks
1412.72641 1.50066 (141*2π)/3713 weeks
1421.67042 1.53115 (142*2π)/3713 weeks
1431.43513 -.23354 (143*2π)/3713 weeks
1442.88466 -1.54135 (144*2π)/3713 weeks
1454.04568 .10608 (145*2π)/3713 weeks
1463.34498 .67268 (146*2π)/3713 weeks
1473.02349 .06817 (147*2π)/3713 weeks
1482.98274 -.65801 (148*2π)/3713 weeks
1493.58635 -1.0466 (149*2π)/3712 weeks
1504.97661 -1.12193 (150*2π)/3712 weeks
1515.61571 .2278 (151*2π)/3712 weeks
1524.5443 1.5988 (152*2π)/3712 weeks
1533.11174 .04135 (153*2π)/3712 weeks
1544.57618 -1.09734 (154*2π)/3712 weeks
1555.58799 .67293 (155*2π)/3712 weeks
1564.65783 1.96393 (156*2π)/3712 weeks
1573.71111 1.02862 (157*2π)/3712 weeks
1583.95247 .50698 (158*2π)/3712 weeks
1594.31961 .52488 (159*2π)/3712 weeks
1604.66068 1.12585 (160*2π)/3712 weeks
1613.35192 1.91024 (161*2π)/3712 weeks
1623.11397 -.45823 (162*2π)/3712 weeks
1635.21341 -.15137 (163*2π)/3712 weeks
1644.63646 2.01691 (164*2π)/3712 weeks
1652.93888 1.6724 (165*2π)/3712 weeks
1662.77079 .18308 (166*2π)/3712 weeks
1673.56678 -1.30941 (167*2π)/3712 weeks
1685.06498 .3032 (168*2π)/3712 weeks
1694.78026 1.00792 (169*2π)/3712 weeks
1704.01639 .92757 (170*2π)/3712 weeks
1714.14396 1.19244 (171*2π)/3712 weeks
1724.35223 .88598 (172*2π)/3712 weeks
1733.91881 2.50644 (173*2π)/3712 weeks
1741.80931 2.3693 (174*2π)/3712 weeks
175.8157 .44201 (175*2π)/3712 weeks
1761.47122 -.55008 (176*2π)/3712 weeks
1771.57758 -1.1969 (177*2π)/3712 weeks
1783.07832 -1.64526 (178*2π)/3712 weeks
1793.04922 -1.62701 (179*2π)/3712 weeks
1803.16016 -2.82391 (180*2π)/3712 weeks
1814.81288 -2.71407 (181*2π)/3712 weeks
1825.86969 -1.12076 (182*2π)/3712 weeks
1835.7056 -.59758 (183*2π)/3712 weeks
1845.18245 -1.16108 (184*2π)/3712 weeks
1856.44442 -1.15943 (185*2π)/3712 weeks
1866.44442 1.15943 (186*2π)/3712 weeks
1875.18245 1.16108 (187*2π)/3712 weeks
1885.7056 .59758 (188*2π)/3712 weeks
1895.86969 1.12076 (189*2π)/3712 weeks
1904.81288 2.71407 (190*2π)/3712 weeks
1913.16016 2.82391 (191*2π)/3712 weeks
1923.04922 1.62701 (192*2π)/3712 weeks
1933.07832 1.64526 (193*2π)/3712 weeks
1941.57758 1.1969 (194*2π)/3712 weeks
1951.47122 .55008 (195*2π)/3712 weeks
196.8157 -.44201 (196*2π)/3712 weeks
1971.80931 -2.3693 (197*2π)/3712 weeks
1983.91881 -2.50644 (198*2π)/3712 weeks
1994.35223 -.88598 (199*2π)/3712 weeks
2004.14396 -1.19244 (200*2π)/3712 weeks
2014.01639 -.92757 (201*2π)/3712 weeks
2024.78026 -1.00792 (202*2π)/3712 weeks
2035.06498 -.3032 (203*2π)/3712 weeks
2043.56678 1.30941 (204*2π)/3712 weeks
2052.77079 -.18308 (205*2π)/3712 weeks
2062.93888 -1.6724 (206*2π)/3712 weeks
2074.63646 -2.01691 (207*2π)/3712 weeks
2085.21341 .15137 (208*2π)/3712 weeks
2093.11397 .45823 (209*2π)/3712 weeks
2103.35192 -1.91024 (210*2π)/3712 weeks
2114.66068 -1.12585 (211*2π)/3712 weeks
2124.31961 -.52488 (212*2π)/3712 weeks
2133.95247 -.50698 (213*2π)/3712 weeks
2143.71111 -1.02862 (214*2π)/3712 weeks
2154.65783 -1.96393 (215*2π)/3712 weeks
2165.58799 -.67293 (216*2π)/3712 weeks
2174.57618 1.09734 (217*2π)/3712 weeks
2183.11174 -.04135 (218*2π)/3712 weeks
2194.5443 -1.5988 (219*2π)/3712 weeks
2205.61571 -.2278 (220*2π)/3712 weeks
2214.97661 1.12193 (221*2π)/3712 weeks
2223.58635 1.0466 (222*2π)/3712 weeks
2232.98274 .65801 (223*2π)/3712 weeks
2243.02349 -.06817 (224*2π)/3712 weeks
2253.34498 -.67268 (225*2π)/3712 weeks
2264.04568 -.10608 (226*2π)/3712 weeks
2272.88466 1.54135 (227*2π)/3712 weeks
2281.43513 .23354 (228*2π)/3712 weeks
2291.67042 -1.53115 (229*2π)/3712 weeks
2302.72641 -1.50066 (230*2π)/3712 weeks
2312.69945 -.81826 (231*2π)/3712 weeks
2321.63189 -1.24761 (232*2π)/3712 weeks
233.8319 -2.46853 (233*2π)/3712 weeks
2342.6488 -4.75985 (234*2π)/3712 weeks
2355.82024 -3.27501 (235*2π)/3712 weeks
2364.64278 -.484 (236*2π)/3712 weeks
2372.91979 -1.6678 (237*2π)/3712 weeks
2383.37819 -3.51178 (238*2π)/3712 weeks
2396.41989 -3.5211 (239*2π)/3712 weeks
2406.33417 -.10172 (240*2π)/3712 weeks
2413.79078 .53691 (241*2π)/3712 weeks
2423.31093 -1.09606 (242*2π)/3712 weeks
2434.20239 -1.92092 (243*2π)/3712 weeks
2444.57663 -.68783 (244*2π)/3712 weeks
2453.47585 .1505 (245*2π)/3712 weeks
2462.6814 -1.43524 (246*2π)/3712 weeks
2474.0804 -2.03172 (247*2π)/3712 weeks
2483.67699 -.55194 (248*2π)/3711 weeks
2492.82923 -1.35566 (249*2π)/3711 weeks
2503.35244 -1.93556 (250*2π)/3711 weeks
2513.83142 -1.41305 (251*2π)/3711 weeks
2523.33772 -1.38675 (252*2π)/3711 weeks
2532.85385 -1.65929 (253*2π)/3711 weeks
2543.11385 -2.47719 (254*2π)/3711 weeks
2553.8091 -1.65921 (255*2π)/3711 weeks
2563.68349 -2.07289 (256*2π)/3711 weeks
2573.56387 -1.82756 (257*2π)/3711 weeks
2583.20137 -2.11425 (258*2π)/3711 weeks
2594.52888 -3.08327 (259*2π)/3711 weeks
2605.13105 -.79104 (260*2π)/3711 weeks
2613.67354 -1.16083 (261*2π)/3711 weeks
2624.09263 -.63328 (262*2π)/3711 weeks
2633.23059 .42657 (263*2π)/3711 weeks
264.54822 -.16627 (264*2π)/3711 weeks
265.87282 -2.7775 (265*2π)/3711 weeks
2661.56001 -3.42083 (266*2π)/3711 weeks
2672.54348 -2.89413 (267*2π)/3711 weeks
2681.46119 -2.3961 (268*2π)/3711 weeks
269.90065 -4.2884 (269*2π)/3711 weeks
2702.38387 -5.44901 (270*2π)/3711 weeks
2713.90297 -4.59946 (271*2π)/3711 weeks
2723.12254 -4.49215 (272*2π)/3711 weeks
2733.05196 -5.36534 (273*2π)/3711 weeks
2745.11679 -5.59025 (274*2π)/3711 weeks
2756.81664 -4.38035 (275*2π)/3711 weeks
2766.13561 -2.16794 (276*2π)/3711 weeks
2774.41822 -2.99144 (277*2π)/3711 weeks
2785.09889 -4.12912 (278*2π)/3711 weeks
2796.246 -2.78332 (279*2π)/3711 weeks
2805.92389 -.53825 (280*2π)/3711 weeks
2814.60716 -.68871 (281*2π)/3711 weeks
2823.5703 -1.32205 (282*2π)/3711 weeks
2832.76862 -1.47994 (283*2π)/3711 weeks
2842.62721 -1.98706 (284*2π)/3711 weeks
2852.03072 -2.48431 (285*2π)/3711 weeks
2862.39671 -3.16396 (286*2π)/3711 weeks
2873.23655 -2.76769 (287*2π)/3711 weeks
2882.03892 -3.25734 (288*2π)/3711 weeks
2892.44089 -3.66074 (289*2π)/3711 weeks
2901.85539 -4.80444 (290*2π)/3711 weeks
2913.31213 -4.092 (291*2π)/3711 weeks
2922.62052 -3.2185 (292*2π)/3711 weeks
2932.34942 -3.99158 (293*2π)/3711 weeks
2941.44382 -5.46301 (294*2π)/3711 weeks
2953.19819 -6.62864 (295*2π)/3711 weeks
2964.13275 -6.16939 (296*2π)/3711 weeks
2973.94355 -5.2867 (297*2π)/3711 weeks
2985.21494 -5.72171 (298*2π)/3711 weeks
2996.10248 -4.46018 (299*2π)/3711 weeks
3004.07618 -3.59767 (300*2π)/3711 weeks
3014.22401 -4.22171 (301*2π)/3711 weeks
3023.74309 -4.24301 (302*2π)/3711 weeks
3034.09605 -3.42842 (303*2π)/3711 weeks
3043.93214 -4.29331 (304*2π)/3711 weeks
3053.77228 -3.98244 (305*2π)/3711 weeks
3063.71363 -4.00221 (306*2π)/3711 weeks
3071.81395 -3.05747 (307*2π)/3711 weeks
308.57658 -5.42223 (308*2π)/3711 weeks
3092.03515 -6.30638 (309*2π)/3711 weeks
3101.59831 -6.07333 (310*2π)/3711 weeks
3111.50704 -7.15934 (311*2π)/3711 weeks
3122.96236 -7.60185 (312*2π)/3711 weeks
3132.20275 -9.2764 (313*2π)/3711 weeks
3145.33336 -10.24796 (314*2π)/3711 weeks
3156.97599 -7.24358 (315*2π)/3711 weeks
3164.17774 -7.20167 (316*2π)/3711 weeks
3175.79982 -9.80246 (317*2π)/3711 weeks
3189.97019 -8.24716 (318*2π)/3711 weeks
31910.23053 -2.38956 (319*2π)/3711 weeks
3203.4418 -.98329 (320*2π)/3711 weeks
3211.82689 -4.18609 (321*2π)/3711 weeks
3223.4369 -7.30422 (322*2π)/3711 weeks
3234.76762 -5.81641 (323*2π)/3711 weeks
3244.97927 -3.84319 (324*2π)/3711 weeks
325-.43081 -2.72038 (325*2π)/3711 weeks
326-1.47703 -10.36209 (326*2π)/3711 weeks
3273.60252 -8.99124 (327*2π)/3711 weeks
3284.01118 -8.2758 (328*2π)/3711 weeks
3291.26118 -6.75497 (329*2π)/3711 weeks
330.3224 -10.43303 (330*2π)/3711 weeks
3313.1323 -12.86897 (331*2π)/3711 weeks
3325.23329 -11.45669 (332*2π)/3711 weeks
3336.98106 -9.5658 (333*2π)/3711 weeks
3345.18051 -8.16042 (334*2π)/3711 weeks
3353.44956 -7.77031 (335*2π)/3711 weeks
336.44345 -10.33464 (336*2π)/3711 weeks
3371.93675 -12.40422 (337*2π)/3711 weeks
3382.25845 -12.39474 (338*2π)/3711 weeks
3395.7694 -14.08475 (339*2π)/3711 weeks
3403.76213 -11.16009 (340*2π)/3711 weeks
341-.57524 -12.1028 (341*2π)/3711 weeks
342.54026 -20.24511 (342*2π)/3711 weeks
3438.02533 -21.39114 (343*2π)/3711 weeks
34410.81624 -15.88864 (344*2π)/3711 weeks
3458.95415 -14.36167 (345*2π)/3711 weeks
3466.8669 -13.97626 (346*2π)/3711 weeks
3477.72309 -17.59641 (347*2π)/3711 weeks
34811.44428 -16.4882 (348*2π)/3711 weeks
3498.91119 -13.5697 (349*2π)/3711 weeks
3505.21466 -12.87377 (350*2π)/3711 weeks
3515.66252 -16.72976 (351*2π)/3711 weeks
35210.67131 -19.86151 (352*2π)/3711 weeks
35315.39678 -16.28669 (353*2π)/3711 weeks
3547.09525 -12.99574 (354*2π)/3711 weeks
3555.10244 -20.39368 (355*2π)/3711 weeks
3568.7466 -16.81816 (356*2π)/3711 weeks
3578.74384 -17.72762 (357*2π)/3711 weeks
3589.09811 -19.04383 (358*2π)/3711 weeks
3593.16633 -13.51104 (359*2π)/3711 weeks
360-9.93957 -25.9167 (360*2π)/3711 weeks
3611.42275 -36.9567 (361*2π)/3711 weeks
3625.18115 -31.28383 (362*2π)/3711 weeks
363-3.34317 -30.81777 (363*2π)/3711 weeks
364-20.92139 -45.28048 (364*2π)/3711 weeks
365-11.14251 -80.52165 (365*2π)/3711 weeks
36616.74133 -92.41253 (366*2π)/3711 weeks
36721.87946 -100.048 (367*2π)/3711 weeks
36834.77557 -119.8257 (368*2π)/3711 weeks
36956.7513 -158.9348 (369*2π)/3711 weeks

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