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Fourier Analysis of TMS (TMS International Corp. Class A)


TMS (TMS International Corp. Class A) appears to have interesting cyclic behaviour every 36 weeks (11962.37*sine), 24 weeks (8631.411*sine), and 20 weeks (6191.454*cosine).

TMS (TMS International Corp. Class A) has an average price of 55,439.77 (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 2/22/2010 to 1/16/2017 for TMS (TMS International Corp. Class A), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
055,439.77   0 
1-18,389.29 -47,960.96 (1*2π)/360360 weeks
2-11,900.08 72,524.65 (2*2π)/360180 weeks
329,852.67 17,527.14 (3*2π)/360120 weeks
4-6,215.966 -3,660.842 (4*2π)/36090 weeks
5-18,374.54 -10,984.59 (5*2π)/36072 weeks
6-8,965.391 16,036.71 (6*2π)/36060 weeks
723,182.09 -1,206.703 (7*2π)/36051 weeks
82,492.031 -4,973.463 (8*2π)/36045 weeks
9-1,221.406 5,875.333 (9*2π)/36040 weeks
10-4,608.867 11,962.37 (10*2π)/36036 weeks
113,948.178 4,482.092 (11*2π)/36033 weeks
12-1,131.721 -1,279.127 (12*2π)/36030 weeks
131,202.031 -3,212.384 (13*2π)/36028 weeks
14-6,186.048 4,405.472 (14*2π)/36026 weeks
156,005.049 8,631.411 (15*2π)/36024 weeks
16667.0778 -1,917.079 (16*2π)/36023 weeks
17-2,394.524 -1,781.925 (17*2π)/36021 weeks
18-6,191.454 570.874 (18*2π)/36020 weeks
195,719.157 5,433.468 (19*2π)/36019 weeks
204,052.355 -3,794.103 (20*2π)/36018 weeks
2153.06713 2,021.909 (21*2π)/36017 weeks
22-3,007.481 1,529.963 (22*2π)/36016 weeks
23-18.508 6,997.347 (23*2π)/36016 weeks
243,070.367 -2,277.732 (24*2π)/36015 weeks
25-1,161.228 -834.1833 (25*2π)/36014 weeks
26-1,610.399 -702.1212 (26*2π)/36014 weeks
27-848.8117 6,707.293 (27*2π)/36013 weeks
285,367.29 -330.0575 (28*2π)/36013 weeks
29-3,164.809 -2,480.456 (29*2π)/36012 weeks
30-1,996.636 606.3647 (30*2π)/36012 weeks
31121.1714 3,253.759 (31*2π)/36012 weeks
325,388.854 -292.4164 (32*2π)/36011 weeks
33-1,159.758 -1,291.762 (33*2π)/36011 weeks
34-818.1213 2,113.621 (34*2π)/36011 weeks
35-1,753.098 3,068.814 (35*2π)/36010 weeks
363,313.572 1,046.404 (36*2π)/36010 weeks
37-1,343.305 -3,072.03 (37*2π)/36010 weeks
38-358.1898 1,267.425 (38*2π)/3609 weeks
39-686.5331 909.8491 (39*2π)/3609 weeks
402,689.934 3,041.345 (40*2π)/3609 weeks
41980.212 -2,800.189 (41*2π)/3609 weeks
42-2,051.608 851.0614 (42*2π)/3609 weeks
43-329.9081 1,388.786 (43*2π)/3608 weeks
442,314.176 2,658.813 (44*2π)/3608 weeks
451,603.592 -2,574.237 (45*2π)/3608 weeks
46-2,859.903 1,221.347 (46*2π)/3608 weeks
47391.6492 1,506.891 (47*2π)/3608 weeks
48507.9677 1,111.719 (48*2π)/3608 weeks
491,932.21 -1,559.917 (49*2π)/3607 weeks
50-1,351.679 -385.6358 (50*2π)/3607 weeks
51685.1044 1,493.395 (51*2π)/3607 weeks
52681.6016 1,804.982 (52*2π)/3607 weeks
532,147.428 82.28458 (53*2π)/3607 weeks
54-1,376.838 -562.7045 (54*2π)/3607 weeks
55-595.2618 1,386.929 (55*2π)/3607 weeks
56-127.5089 1,849.418 (56*2π)/3606 weeks
572,639.028 -71.2871 (57*2π)/3606 weeks
58-1,804.354 -1,950.89 (58*2π)/3606 weeks
59-457.7712 2,265.575 (59*2π)/3606 weeks
60876.6734 373.3752 (60*2π)/3606 weeks
611,434.337 786.2042 (61*2π)/3606 weeks
6221.79939 -1,324.777 (62*2π)/3606 weeks
63-1,137.498 1,460.043 (63*2π)/3606 weeks
64246.2038 1,036.2 (64*2π)/3606 weeks
651,152.171 1,185.232 (65*2π)/3606 weeks
66712.5069 -1,856.094 (66*2π)/3605 weeks
67-2,188.397 613.021 (67*2π)/3605 weeks
68374.7084 1,969.378 (68*2π)/3605 weeks
691,658.034 418.6324 (69*2π)/3605 weeks
7042.76986 -2,429.887 (70*2π)/3605 weeks
71-2,186.35 1,038.792 (71*2π)/3605 weeks
722,034.715 1,189.52 (72*2π)/3605 weeks
73592.6085 -418.6676 (73*2π)/3605 weeks
74816.0467 127.5515 (74*2π)/3605 weeks
75-803.0283 -189.0539 (75*2π)/3605 weeks
76-252.8213 1,269.627 (76*2π)/3605 weeks
77928.6138 839.0617 (77*2π)/3605 weeks
781,506.538 -949.0438 (78*2π)/3605 weeks
79-1,545.6 -596.6151 (79*2π)/3605 weeks
80-20.62723 2,098.522 (80*2π)/3605 weeks
81992.2737 353.6784 (81*2π)/3604 weeks
821,021.973 -840.6754 (82*2π)/3604 weeks
83-1,145.714 -1,315.547 (83*2π)/3604 weeks
84112.2587 2,094.277 (84*2π)/3604 weeks
852,090.179 435.9812 (85*2π)/3604 weeks
86608.1605 -189.6167 (86*2π)/3604 weeks
87-1,133.415 -264.9846 (87*2π)/3604 weeks
88-594.4758 1,726.314 (88*2π)/3604 weeks
891,467.667 -209.0805 (89*2π)/3604 weeks
90467.5571 -540.7623 (90*2π)/3604 weeks
9186.85541 -11.04566 (91*2π)/3604 weeks
92-149.8969 1,585.862 (92*2π)/3604 weeks
93403.2891 401.0467 (93*2π)/3604 weeks
94-443.9439 417.6914 (94*2π)/3604 weeks
95675.6376 -1,228.97 (95*2π)/3604 weeks
96-1,099.225 -305.0349 (96*2π)/3604 weeks
971,421.104 1,357.52 (97*2π)/3604 weeks
981,184.556 258.7842 (98*2π)/3604 weeks
99180.004 -286.778 (99*2π)/3604 weeks
100-1,855.046 491.1382 (100*2π)/3604 weeks
101776.0473 1,036.045 (101*2π)/3604 weeks
102580.7994 -1,030.973 (102*2π)/3604 weeks
103899.6239 -169.0001 (103*2π)/3603 weeks
104-604.0239 -225.5139 (104*2π)/3603 weeks
105219.212 2,093.709 (105*2π)/3603 weeks
106720.2861 -585.9507 (106*2π)/3603 weeks
107-144.0937 -311.8033 (107*2π)/3603 weeks
108192.1143 -1,052.385 (108*2π)/3603 weeks
109-20.41168 1,271.921 (109*2π)/3603 weeks
1101,835.463 944.6765 (110*2π)/3603 weeks
111264.3608 -17.58652 (111*2π)/3603 weeks
112-1,250.578 -480.4485 (112*2π)/3603 weeks
113-1,162.083 1,189.17 (113*2π)/3603 weeks
1142,000.617 -299.8532 (114*2π)/3603 weeks
115621.0982 -1,292.043 (115*2π)/3603 weeks
11633.01517 233.2239 (116*2π)/3603 weeks
117-404.1747 1,749.374 (117*2π)/3603 weeks
118998.731 653.188 (118*2π)/3603 weeks
119-449.8101 -1,064.18 (119*2π)/3603 weeks
12035.80162 -793.9351 (120*2π)/3603 weeks
121-230.3325 247.4236 (121*2π)/3603 weeks
1222,044.943 1,525.902 (122*2π)/3603 weeks
123649.6833 -469.3428 (123*2π)/3603 weeks
124-1,102.588 420.9734 (124*2π)/3603 weeks
125-1,266.065 389.1881 (125*2π)/3603 weeks
1261,034.623 455.7639 (126*2π)/3603 weeks
1271,052.06 -1,960.22 (127*2π)/3603 weeks
128-211.3702 403.5149 (128*2π)/3603 weeks
129519.8159 891.8493 (129*2π)/3603 weeks
13030.16174 929.7244 (130*2π)/3603 weeks
131141.3456 -597.4624 (131*2π)/3603 weeks
132-164.2618 -678.1898 (132*2π)/3603 weeks
133422.0992 -659.4104 (133*2π)/3603 weeks
134660.9916 1,311.914 (134*2π)/3603 weeks
1351,675.866 470.9436 (135*2π)/3603 weeks
136-833.6666 46.7694 (136*2π)/3603 weeks
137-875.3517 -17.43741 (137*2π)/3603 weeks
138-585.6093 232.409 (138*2π)/3603 weeks
1392,146.282 -577.61 (139*2π)/3603 weeks
140435.8029 -1,159.839 (140*2π)/3603 weeks
141208.2264 1,294.132 (141*2π)/3603 weeks
142-138.1715 1,281.006 (142*2π)/3603 weeks
143378.1074 491.2515 (143*2π)/3603 weeks
144-449.0146 -1,463.693 (144*2π)/3603 weeks
145-122.3314 -425.8121 (145*2π)/3602 weeks
146530.7805 311.8494 (146*2π)/3602 weeks
1471,681.904 1,282.186 (147*2π)/3602 weeks
148224.8521 -672.9393 (148*2π)/3602 weeks
149-1,596.438 556.4332 (149*2π)/3602 weeks
150-191.5647 34.19154 (150*2π)/3602 weeks
151936.3658 -331.905 (151*2π)/3602 weeks
1521,340.868 -1,155.727 (152*2π)/3602 weeks
153-34.08601 500.811 (153*2π)/3602 weeks
15435.37577 1,261.324 (154*2π)/3602 weeks
155-59.00528 1,021.39 (155*2π)/3602 weeks
156331.5255 -1,272.683 (156*2π)/3602 weeks
157-916.5104 -1,040.325 (157*2π)/3602 weeks
158746.1951 345.9896 (158*2π)/3602 weeks
1591,247.858 808.796 (159*2π)/3602 weeks
1601,040.2 -117.7847 (160*2π)/3602 weeks
161-1,579.809 -107.5419 (161*2π)/3602 weeks
162-159.134 523.826 (162*2π)/3602 weeks
163582.4789 -855.8993 (163*2π)/3602 weeks
1641,436.849 -445.8258 (164*2π)/3602 weeks
165636.454 -122.8489 (165*2π)/3602 weeks
16662.72609 1,330.924 (166*2π)/3602 weeks
167-471.2073 1,014.128 (167*2π)/3602 weeks
168369.4131 -49.41285 (168*2π)/3602 weeks
169-486.4573 -1,959.062 (169*2π)/3602 weeks
17064.76 345.4735 (170*2π)/3602 weeks
1711,505.569 346.2956 (171*2π)/3602 weeks
172816.7581 855.9886 (172*2π)/3602 weeks
173-234.5232 -187.3904 (173*2π)/3602 weeks
174-1,299.863 219.8164 (174*2π)/3602 weeks
175100.9131 -302.7467 (175*2π)/3602 weeks
1761,267.775 -189.7984 (176*2π)/3602 weeks
1771,335.292 -1,018.711 (177*2π)/3602 weeks
178-785.6902 1,183.399 (178*2π)/3602 weeks
179314.3868 1,358.588 (179*2π)/3602 weeks
180-595.7778   (180*2π)/3602 weeks
181314.3868 -1,358.588 (181*2π)/3602 weeks
182-785.6902 -1,183.399 (182*2π)/3602 weeks
1831,335.292 1,018.711 (183*2π)/3602 weeks
1841,267.775 189.7984 (184*2π)/3602 weeks
185100.9131 302.7467 (185*2π)/3602 weeks
186-1,299.863 -219.8164 (186*2π)/3602 weeks
187-234.5232 187.3904 (187*2π)/3602 weeks
188816.7581 -855.9886 (188*2π)/3602 weeks
1891,505.569 -346.2956 (189*2π)/3602 weeks
19064.76 -345.4735 (190*2π)/3602 weeks
191-486.4573 1,959.062 (191*2π)/3602 weeks
192369.4131 49.41285 (192*2π)/3602 weeks
193-471.2073 -1,014.128 (193*2π)/3602 weeks
19462.72609 -1,330.924 (194*2π)/3602 weeks
195636.454 122.8489 (195*2π)/3602 weeks
1961,436.849 445.8258 (196*2π)/3602 weeks
197582.4789 855.8993 (197*2π)/3602 weeks
198-159.134 -523.826 (198*2π)/3602 weeks
199-1,579.809 107.5419 (199*2π)/3602 weeks
2001,040.2 117.7847 (200*2π)/3602 weeks
2011,247.858 -808.796 (201*2π)/3602 weeks
202746.1951 -345.9896 (202*2π)/3602 weeks
203-916.5104 1,040.325 (203*2π)/3602 weeks
204331.5255 1,272.683 (204*2π)/3602 weeks
205-59.00528 -1,021.39 (205*2π)/3602 weeks
20635.37577 -1,261.324 (206*2π)/3602 weeks
207-34.08601 -500.811 (207*2π)/3602 weeks
2081,340.868 1,155.727 (208*2π)/3602 weeks
209936.3658 331.905 (209*2π)/3602 weeks
210-191.5647 -34.19154 (210*2π)/3602 weeks
211-1,596.438 -556.4332 (211*2π)/3602 weeks
212224.8521 672.9393 (212*2π)/3602 weeks
2131,681.904 -1,282.186 (213*2π)/3602 weeks
214530.7805 -311.8494 (214*2π)/3602 weeks
215-122.3314 425.8121 (215*2π)/3602 weeks
216-449.0146 1,463.693 (216*2π)/3602 weeks
217378.1074 -491.2515 (217*2π)/3602 weeks
218-138.1715 -1,281.006 (218*2π)/3602 weeks
219208.2264 -1,294.132 (219*2π)/3602 weeks
220435.8029 1,159.839 (220*2π)/3602 weeks
2212,146.282 577.61 (221*2π)/3602 weeks
222-585.6093 -232.409 (222*2π)/3602 weeks
223-875.3517 17.43741 (223*2π)/3602 weeks
224-833.6666 -46.7694 (224*2π)/3602 weeks
2251,675.866 -470.9436 (225*2π)/3602 weeks
226660.9916 -1,311.914 (226*2π)/3602 weeks
227422.0992 659.4104 (227*2π)/3602 weeks
228-164.2618 678.1898 (228*2π)/3602 weeks
229141.3456 597.4624 (229*2π)/3602 weeks
23030.16174 -929.7244 (230*2π)/3602 weeks
231519.8159 -891.8493 (231*2π)/3602 weeks
232-211.3702 -403.5149 (232*2π)/3602 weeks
2331,052.06 1,960.22 (233*2π)/3602 weeks
2341,034.623 -455.7639 (234*2π)/3602 weeks
235-1,266.065 -389.1881 (235*2π)/3602 weeks
236-1,102.588 -420.9734 (236*2π)/3602 weeks
237649.6833 469.3428 (237*2π)/3602 weeks
2382,044.943 -1,525.902 (238*2π)/3602 weeks
239-230.3325 -247.4236 (239*2π)/3602 weeks
24035.80162 793.9351 (240*2π)/3602 weeks
241-449.8101 1,064.18 (241*2π)/3601 weeks
242998.731 -653.188 (242*2π)/3601 weeks
243-404.1747 -1,749.374 (243*2π)/3601 weeks
24433.01517 -233.2239 (244*2π)/3601 weeks
245621.0982 1,292.043 (245*2π)/3601 weeks
2462,000.617 299.8532 (246*2π)/3601 weeks
247-1,162.083 -1,189.17 (247*2π)/3601 weeks
248-1,250.578 480.4485 (248*2π)/3601 weeks
249264.3608 17.58652 (249*2π)/3601 weeks
2501,835.463 -944.6765 (250*2π)/3601 weeks
251-20.41168 -1,271.921 (251*2π)/3601 weeks
252192.1143 1,052.385 (252*2π)/3601 weeks
253-144.0937 311.8033 (253*2π)/3601 weeks
254720.2861 585.9507 (254*2π)/3601 weeks
255219.212 -2,093.709 (255*2π)/3601 weeks
256-604.0239 225.5139 (256*2π)/3601 weeks
257899.6239 169.0001 (257*2π)/3601 weeks
258580.7994 1,030.973 (258*2π)/3601 weeks
259776.0473 -1,036.045 (259*2π)/3601 weeks
260-1,855.046 -491.1382 (260*2π)/3601 weeks
261180.004 286.778 (261*2π)/3601 weeks
2621,184.556 -258.7842 (262*2π)/3601 weeks
2631,421.104 -1,357.52 (263*2π)/3601 weeks
264-1,099.225 305.0349 (264*2π)/3601 weeks
265675.6376 1,228.97 (265*2π)/3601 weeks
266-443.9439 -417.6914 (266*2π)/3601 weeks
267403.2891 -401.0467 (267*2π)/3601 weeks
268-149.8969 -1,585.862 (268*2π)/3601 weeks
26986.85541 11.04566 (269*2π)/3601 weeks
270467.5571 540.7623 (270*2π)/3601 weeks
2711,467.667 209.0805 (271*2π)/3601 weeks
272-594.4758 -1,726.314 (272*2π)/3601 weeks
273-1,133.415 264.9846 (273*2π)/3601 weeks
274608.1605 189.6167 (274*2π)/3601 weeks
2752,090.179 -435.9812 (275*2π)/3601 weeks
276112.2587 -2,094.277 (276*2π)/3601 weeks
277-1,145.714 1,315.547 (277*2π)/3601 weeks
2781,021.973 840.6754 (278*2π)/3601 weeks
279992.2737 -353.6784 (279*2π)/3601 weeks
280-20.62723 -2,098.522 (280*2π)/3601 weeks
281-1,545.6 596.6151 (281*2π)/3601 weeks
2821,506.538 949.0438 (282*2π)/3601 weeks
283928.6138 -839.0617 (283*2π)/3601 weeks
284-252.8213 -1,269.627 (284*2π)/3601 weeks
285-803.0283 189.0539 (285*2π)/3601 weeks
286816.0467 -127.5515 (286*2π)/3601 weeks
287592.6085 418.6676 (287*2π)/3601 weeks
2882,034.715 -1,189.52 (288*2π)/3601 weeks
289-2,186.35 -1,038.792 (289*2π)/3601 weeks
29042.76986 2,429.887 (290*2π)/3601 weeks
2911,658.034 -418.6324 (291*2π)/3601 weeks
292374.7084 -1,969.378 (292*2π)/3601 weeks
293-2,188.397 -613.021 (293*2π)/3601 weeks
294712.5069 1,856.094 (294*2π)/3601 weeks
2951,152.171 -1,185.232 (295*2π)/3601 weeks
296246.2038 -1,036.2 (296*2π)/3601 weeks
297-1,137.498 -1,460.043 (297*2π)/3601 weeks
29821.79939 1,324.777 (298*2π)/3601 weeks
2991,434.337 -786.2042 (299*2π)/3601 weeks
300876.6734 -373.3752 (300*2π)/3601 weeks
301-457.7712 -2,265.575 (301*2π)/3601 weeks
302-1,804.354 1,950.89 (302*2π)/3601 weeks
3032,639.028 71.2871 (303*2π)/3601 weeks
304-127.5089 -1,849.418 (304*2π)/3601 weeks
305-595.2618 -1,386.929 (305*2π)/3601 weeks
306-1,376.838 562.7045 (306*2π)/3601 weeks
3072,147.428 -82.28458 (307*2π)/3601 weeks
308681.6016 -1,804.982 (308*2π)/3601 weeks
309685.1044 -1,493.395 (309*2π)/3601 weeks
310-1,351.679 385.6358 (310*2π)/3601 weeks
3111,932.21 1,559.917 (311*2π)/3601 weeks
312507.9677 -1,111.719 (312*2π)/3601 weeks
313391.6492 -1,506.891 (313*2π)/3601 weeks
314-2,859.903 -1,221.347 (314*2π)/3601 weeks
3151,603.592 2,574.237 (315*2π)/3601 weeks
3162,314.176 -2,658.813 (316*2π)/3601 weeks
317-329.9081 -1,388.786 (317*2π)/3601 weeks
318-2,051.608 -851.0614 (318*2π)/3601 weeks
319980.212 2,800.189 (319*2π)/3601 weeks
3202,689.934 -3,041.345 (320*2π)/3601 weeks
321-686.5331 -909.8491 (321*2π)/3601 weeks
322-358.1898 -1,267.425 (322*2π)/3601 weeks
323-1,343.305 3,072.03 (323*2π)/3601 weeks
3243,313.572 -1,046.404 (324*2π)/3601 weeks
325-1,753.098 -3,068.814 (325*2π)/3601 weeks
326-818.1213 -2,113.621 (326*2π)/3601 weeks
327-1,159.758 1,291.762 (327*2π)/3601 weeks
3285,388.854 292.4164 (328*2π)/3601 weeks
329121.1714 -3,253.759 (329*2π)/3601 weeks
330-1,996.636 -606.3647 (330*2π)/3601 weeks
331-3,164.809 2,480.456 (331*2π)/3601 weeks
3325,367.29 330.0575 (332*2π)/3601 weeks
333-848.8117 -6,707.293 (333*2π)/3601 weeks
334-1,610.399 702.1212 (334*2π)/3601 weeks
335-1,161.228 834.1833 (335*2π)/3601 weeks
3363,070.367 2,277.732 (336*2π)/3601 weeks
337-18.508 -6,997.347 (337*2π)/3601 weeks
338-3,007.481 -1,529.963 (338*2π)/3601 weeks
33953.06713 -2,021.909 (339*2π)/3601 weeks
3404,052.355 3,794.103 (340*2π)/3601 weeks
3415,719.157 -5,433.468 (341*2π)/3601 weeks
342-6,191.454 -570.874 (342*2π)/3601 weeks
343-2,394.524 1,781.925 (343*2π)/3601 weeks
344667.0778 1,917.079 (344*2π)/3601 weeks
3456,005.049 -8,631.411 (345*2π)/3601 weeks
346-6,186.048 -4,405.472 (346*2π)/3601 weeks
3471,202.031 3,212.384 (347*2π)/3601 weeks
348-1,131.721 1,279.127 (348*2π)/3601 weeks
3493,948.178 -4,482.092 (349*2π)/3601 weeks
350-4,608.867 -11,962.37 (350*2π)/3601 weeks
351-1,221.406 -5,875.333 (351*2π)/3601 weeks
3522,492.031 4,973.463 (352*2π)/3601 weeks
35323,182.09 1,206.703 (353*2π)/3601 weeks
354-8,965.391 -16,036.71 (354*2π)/3601 weeks
355-18,374.54 10,984.59 (355*2π)/3601 weeks
356-6,215.966 3,660.842 (356*2π)/3601 weeks
35729,852.67 -17,527.14 (357*2π)/3601 weeks
358-11,900.08 -72,524.65 (358*2π)/3601 weeks

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