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# Fourier Analysis of CBT (Cabot Corporation Common Stock)

CBT (Cabot Corporation Common Stock) appears to have interesting cyclic behaviour every 158 weeks (2.701*sine), 158 weeks (2.0216*cosine), and 173 weeks (1.6644*cosine).

CBT (Cabot Corporation Common Stock) has an average price of 16.4 (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.

## Fourier Analysis

Using data from 11/5/1980 to 3/20/2017 for CBT (Cabot Corporation Common Stock), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
016.39681   0
14.42581 -15.32945 (1*2π)/18981,898 weeks
22.38313 -5.27636 (2*2π)/1898949 weeks
32.24563 -6.07367 (3*2π)/1898633 weeks
4-.77365 -5.54524 (4*2π)/1898475 weeks
5-.77399 -2.55541 (5*2π)/1898380 weeks
6-.59244 -1.01811 (6*2π)/1898316 weeks
71.82194 -1.75642 (7*2π)/1898271 weeks
8-.67868 -2.86079 (8*2π)/1898237 weeks
9-.31426 -.86758 (9*2π)/1898211 weeks
10-.14228 -.33995 (10*2π)/1898190 weeks
111.66436 .34576 (11*2π)/1898173 weeks
122.02155 -2.701 (12*2π)/1898158 weeks
13-.2785 -1.24054 (13*2π)/1898146 weeks
141.11996 -1.46102 (14*2π)/1898136 weeks
15.21497 -1.65036 (15*2π)/1898127 weeks
16.3323 -1.5934 (16*2π)/1898119 weeks
17.03829 -1.62843 (17*2π)/1898112 weeks
18-.32799 -1.2469 (18*2π)/1898105 weeks
19-.30568 -1.32657 (19*2π)/1898100 weeks
20-.73214 -.62911 (20*2π)/189895 weeks
21-.12997 -.54468 (21*2π)/189890 weeks
22-.10286 -.50754 (22*2π)/189886 weeks
23.12561 -.43803 (23*2π)/189883 weeks
24.07313 -.59329 (24*2π)/189879 weeks
25.55225 -.57637 (25*2π)/189876 weeks
26.24925 -1.28004 (26*2π)/189873 weeks
27-.65323 -1.12284 (27*2π)/189870 weeks
28-.46913 .06994 (28*2π)/189868 weeks
29.44757 -.15599 (29*2π)/189865 weeks
30.32356 -.84094 (30*2π)/189863 weeks
31-.13568 -.8543 (31*2π)/189861 weeks
32-.23556 -.46558 (32*2π)/189859 weeks
33-.20983 -.39812 (33*2π)/189858 weeks
34-.02427 -.08975 (34*2π)/189856 weeks
35.23652 -.1739 (35*2π)/189854 weeks
36.39761 -.24957 (36*2π)/189853 weeks
37.39925 -.76455 (37*2π)/189851 weeks
38.14805 -.59863 (38*2π)/189850 weeks
39.04876 -.78906 (39*2π)/189849 weeks
40-.15369 -.46466 (40*2π)/189847 weeks
41-.03088 -.3839 (41*2π)/189846 weeks
42.22582 -.39511 (42*2π)/189845 weeks
43.21411 -.6547 (43*2π)/189844 weeks
44-.07597 -.74895 (44*2π)/189843 weeks
45-.24785 -.5365 (45*2π)/189842 weeks
46-.17721 -.43587 (46*2π)/189841 weeks
47-.26384 -.37095 (47*2π)/189840 weeks
48-.12133 -.24811 (48*2π)/189840 weeks
49-.1921 -.15494 (49*2π)/189839 weeks
50.10169 -.15336 (50*2π)/189838 weeks
51.02228 -.17526 (51*2π)/189837 weeks
52.21359 -.42932 (52*2π)/189837 weeks
53-.02871 -.30064 (53*2π)/189836 weeks
54-.04471 -.43037 (54*2π)/189835 weeks
55-.04097 -.02782 (55*2π)/189835 weeks
56.23313 -.36646 (56*2π)/189834 weeks
57.07087 -.36376 (57*2π)/189833 weeks
58.01281 -.38901 (58*2π)/189833 weeks
59.03242 -.33853 (59*2π)/189832 weeks
60.00857 -.35058 (60*2π)/189832 weeks
61-.02911 -.35246 (61*2π)/189831 weeks
62-.09211 -.29487 (62*2π)/189831 weeks
63.04491 -.24356 (63*2π)/189830 weeks
64-.0443 -.45084 (64*2π)/189830 weeks
65-.12544 -.09864 (65*2π)/189829 weeks
66.04774 -.36392 (66*2π)/189829 weeks
67-.11326 -.19064 (67*2π)/189828 weeks
68.02465 -.18895 (68*2π)/189828 weeks
69.07801 -.2718 (69*2π)/189828 weeks
70-.07223 -.26827 (70*2π)/189827 weeks
71.01363 -.1713 (71*2π)/189827 weeks
72.04573 -.19616 (72*2π)/189826 weeks
73.03216 -.25863 (73*2π)/189826 weeks
74.1288 -.22505 (74*2π)/189826 weeks
75-.03651 -.34268 (75*2π)/189825 weeks
76-.06579 -.11855 (76*2π)/189825 weeks
77.20057 -.09287 (77*2π)/189825 weeks
78.21796 -.4009 (78*2π)/189824 weeks
79.06734 -.47582 (79*2π)/189824 weeks
80-.19261 -.35182 (80*2π)/189824 weeks
81-.00612 -.16071 (81*2π)/189823 weeks
82-.03991 -.34146 (82*2π)/189823 weeks
83-.07406 -.22549 (83*2π)/189823 weeks
84.03233 -.24663 (84*2π)/189823 weeks
85-.01642 -.24654 (85*2π)/189822 weeks
86.01848 -.25597 (86*2π)/189822 weeks
87.09198 -.29685 (87*2π)/189822 weeks
88-.10546 -.39164 (88*2π)/189822 weeks
89-.07012 -.26869 (89*2π)/189821 weeks
90-.08904 -.39513 (90*2π)/189821 weeks
91-.21725 -.27411 (91*2π)/189821 weeks
92-.19952 -.23055 (92*2π)/189821 weeks
93-.20846 -.02214 (93*2π)/189820 weeks
94.09474 -.07374 (94*2π)/189820 weeks
95-.05079 -.25021 (95*2π)/189820 weeks
96-.0914 -.09473 (96*2π)/189820 weeks
97.06129 -.15521 (97*2π)/189820 weeks
98-.10889 -.26212 (98*2π)/189819 weeks
99-.0913 -.08652 (99*2π)/189819 weeks
100-.08913 -.12657 (100*2π)/189819 weeks
101.0152 .02072 (101*2π)/189819 weeks
102.12295 -.12059 (102*2π)/189819 weeks
103.04339 -.20058 (103*2π)/189818 weeks
104-.03869 -.20094 (104*2π)/189818 weeks
105.00546 -.11757 (105*2π)/189818 weeks
106.03079 -.1434 (106*2π)/189818 weeks
107.06206 -.20049 (107*2π)/189818 weeks
108-.04557 -.21358 (108*2π)/189818 weeks
109.0072 -.14689 (109*2π)/189817 weeks
110.03888 -.14918 (110*2π)/189817 weeks
111.10952 -.25354 (111*2π)/189817 weeks
112-.05394 -.30868 (112*2π)/189817 weeks
113-.14515 -.17759 (113*2π)/189817 weeks
114-.02337 -.05207 (114*2π)/189817 weeks
115.12599 -.20158 (115*2π)/189817 weeks
116-.00742 -.34587 (116*2π)/189816 weeks
117-.18446 -.25548 (117*2π)/189816 weeks
118-.1446 -.06137 (118*2π)/189816 weeks
119-.01567 -.14203 (119*2π)/189816 weeks
120-.01976 -.13388 (120*2π)/189816 weeks
121-.0451 -.17512 (121*2π)/189816 weeks
122-.00427 -.16202 (122*2π)/189816 weeks
123-.05309 -.20727 (123*2π)/189815 weeks
124-.00609 -.19818 (124*2π)/189815 weeks
125-.19785 -.26612 (125*2π)/189815 weeks
126-.15166 -.06855 (126*2π)/189815 weeks
127-.10558 -.10435 (127*2π)/189815 weeks
128-.06215 -.01182 (128*2π)/189815 weeks
129.00689 -.13031 (129*2π)/189815 weeks
130-.05177 -.0451 (130*2π)/189815 weeks
131.04783 -.16716 (131*2π)/189814 weeks
132-.11699 -.14157 (132*2π)/189814 weeks
133.02617 -.03584 (133*2π)/189814 weeks
134.03213 -.16448 (134*2π)/189814 weeks
135-.0559 -.13488 (135*2π)/189814 weeks
136.00956 -.1799 (136*2π)/189814 weeks
137-.10909 -.10131 (137*2π)/189814 weeks
138.02545 -.10464 (138*2π)/189814 weeks
139-.05172 -.0885 (139*2π)/189814 weeks
140.07848 -.12334 (140*2π)/189814 weeks
141-.08278 -.18507 (141*2π)/189813 weeks
142.05282 -.06171 (142*2π)/189813 weeks
143.00864 -.26776 (143*2π)/189813 weeks
144-.11747 -.11358 (144*2π)/189813 weeks
145.03938 -.11455 (145*2π)/189813 weeks
146-.06941 -.19807 (146*2π)/189813 weeks
147-.00573 -.08579 (147*2π)/189813 weeks
148-.00773 -.2079 (148*2π)/189813 weeks
149-.06293 -.18366 (149*2π)/189813 weeks
150-.12731 -.14119 (150*2π)/189813 weeks
151-.09163 -.10901 (151*2π)/189813 weeks
152-.06055 -.0477 (152*2π)/189812 weeks
153.00497 -.08997 (153*2π)/189812 weeks
154-.02174 -.12055 (154*2π)/189812 weeks
155-.10407 -.10039 (155*2π)/189812 weeks
156.03124 -.04839 (156*2π)/189812 weeks
157-.00149 -.15838 (157*2π)/189812 weeks
158-.04128 -.1718 (158*2π)/189812 weeks
159-.10489 -.08961 (159*2π)/189812 weeks
160.00718 -.05739 (160*2π)/189812 weeks
161-.00758 -.1792 (161*2π)/189812 weeks
162-.04526 -.12665 (162*2π)/189812 weeks
163-.08114 -.18041 (163*2π)/189812 weeks
164-.06961 -.00195 (164*2π)/189812 weeks
165-.01358 -.16514 (165*2π)/189812 weeks
166-.12769 -.07412 (166*2π)/189811 weeks
167-.02055 -.0495 (167*2π)/189811 weeks
168-.05063 -.06081 (168*2π)/189811 weeks
169.0597 -.00483 (169*2π)/189811 weeks
170.05475 -.15118 (170*2π)/189811 weeks
171.03432 -.14388 (171*2π)/189811 weeks
172-.0027 -.2266 (172*2π)/189811 weeks
173-.12381 -.19799 (173*2π)/189811 weeks
174-.11778 -.08085 (174*2π)/189811 weeks
175-.06344 -.07628 (175*2π)/189811 weeks
176-.05303 -.06891 (176*2π)/189811 weeks
177-.01952 -.08774 (177*2π)/189811 weeks
178-.04497 -.1106 (178*2π)/189811 weeks
179-.0462 -.09359 (179*2π)/189811 weeks
180-.03721 -.10836 (180*2π)/189811 weeks
181-.10053 -.09957 (181*2π)/189810 weeks
182-.06468 -.01064 (182*2π)/189810 weeks
183.01152 -.0577 (183*2π)/189810 weeks
184-.02772 -.06839 (184*2π)/189810 weeks
185.00694 -.09868 (185*2π)/189810 weeks
186-.02171 -.08715 (186*2π)/189810 weeks
187-.032 -.15372 (187*2π)/189810 weeks
188-.101 -.07999 (188*2π)/189810 weeks
189-.00346 -.04671 (189*2π)/189810 weeks
190.00824 -.09053 (190*2π)/189810 weeks
191-.01456 -.13531 (191*2π)/189810 weeks
192-.06011 -.12091 (192*2π)/189810 weeks
193-.09602 -.12141 (193*2π)/189810 weeks
194-.07751 -.05018 (194*2π)/189810 weeks
195-.06163 -.07818 (195*2π)/189810 weeks
196-.04673 .00883 (196*2π)/189810 weeks
197.01697 -.07717 (197*2π)/189810 weeks
198-.07024 -.07515 (198*2π)/189810 weeks
199.01004 -.01524 (199*2π)/189810 weeks
200.01652 -.11017 (200*2π)/18989 weeks
201-.01767 -.08237 (201*2π)/18989 weeks
202-.03887 -.09773 (202*2π)/18989 weeks
203-.04769 -.07763 (203*2π)/18989 weeks
204-.03525 -.05368 (204*2π)/18989 weeks
205-.01782 -.09405 (205*2π)/18989 weeks
206-.058 -.05021 (206*2π)/18989 weeks
207-.03364 -.01854 (207*2π)/18989 weeks
208.01714 -.06147 (208*2π)/18989 weeks
209-.00392 -.0517 (209*2π)/18989 weeks
210.02404 -.13214 (210*2π)/18989 weeks
211-.0688 -.10503 (211*2π)/18989 weeks
212-.06545 -.08372 (212*2π)/18989 weeks
213-.05453 -.01117 (213*2π)/18989 weeks
214.04383 -.04542 (214*2π)/18989 weeks
215-.01764 -.13791 (215*2π)/18989 weeks
216-.03083 -.04884 (216*2π)/18989 weeks
217.00761 -.11912 (217*2π)/18989 weeks
218-.06082 -.09498 (218*2π)/18989 weeks
219-.04454 -.0928 (219*2π)/18989 weeks
220-.08868 -.07493 (220*2π)/18989 weeks
221-.07058 .00742 (221*2π)/18989 weeks
222-.00968 -.00569 (222*2π)/18989 weeks
223.03434 -.00539 (223*2π)/18989 weeks
224.04301 -.08885 (224*2π)/18988 weeks
225.0028 -.059 (225*2π)/18988 weeks
226.0451 -.11046 (226*2π)/18988 weeks
227-.02132 -.0867 (227*2π)/18988 weeks
228.03502 -.108 (228*2π)/18988 weeks
229-.04794 -.11462 (229*2π)/18988 weeks
230-.00097 -.05292 (230*2π)/18988 weeks
231.0216 -.16289 (231*2π)/18988 weeks
232-.11494 -.13051 (232*2π)/18988 weeks
233-.06959 -.04275 (233*2π)/18988 weeks
234-.05966 -.02014 (234*2π)/18988 weeks
235.04763 -.03126 (235*2π)/18988 weeks
236-.01059 -.13095 (236*2π)/18988 weeks
237-.02991 -.08992 (237*2π)/18988 weeks
238-.06903 -.10054 (238*2π)/18988 weeks
239-.03799 -.00703 (239*2π)/18988 weeks
240-.01552 -.08856 (240*2π)/18988 weeks
241-.04372 .00368 (241*2π)/18988 weeks
242.06583 -.05782 (242*2π)/18988 weeks
243.01341 -.09518 (243*2π)/18988 weeks
244.02364 -.14103 (244*2π)/18988 weeks
245-.09005 -.11291 (245*2π)/18988 weeks
246-.03059 -.02496 (246*2π)/18988 weeks
247.04151 -.10339 (247*2π)/18988 weeks
248-.02488 -.13299 (248*2π)/18988 weeks
249-.05927 -.11434 (249*2π)/18988 weeks
250-.05238 -.08291 (250*2π)/18988 weeks
251-.05305 -.08692 (251*2π)/18988 weeks
252-.06714 -.08791 (252*2π)/18988 weeks
253-.0903 -.04183 (253*2π)/18988 weeks
254-.03635 -.00095 (254*2π)/18987 weeks
255.00892 -.02573 (255*2π)/18987 weeks
256.02176 -.06969 (256*2π)/18987 weeks
257-.00976 -.11281 (257*2π)/18987 weeks
258-.06198 -.07141 (258*2π)/18987 weeks
259-.01849 -.02219 (259*2π)/18987 weeks
260.0202 -.05869 (260*2π)/18987 weeks
261.02402 -.09164 (261*2π)/18987 weeks
262.02391 -.12666 (262*2π)/18987 weeks
263-.03886 -.16353 (263*2π)/18987 weeks
264-.11816 -.12824 (264*2π)/18987 weeks
265-.10596 -.02578 (265*2π)/18987 weeks
266-.05154 -.01722 (266*2π)/18987 weeks
267-.03033 -.03021 (267*2π)/18987 weeks
268.00079 -.04071 (268*2π)/18987 weeks
269.00387 -.07838 (269*2π)/18987 weeks
270-.02833 -.10494 (270*2π)/18987 weeks
271-.07708 -.07069 (271*2π)/18987 weeks
272-.06289 .00275 (272*2π)/18987 weeks
273.05241 -.01526 (273*2π)/18987 weeks
274.03686 -.12181 (274*2π)/18987 weeks
275-.03175 -.09793 (275*2π)/18987 weeks
276-.01711 -.08741 (276*2π)/18987 weeks
277-.00517 -.09173 (277*2π)/18987 weeks
278-.04558 -.1536 (278*2π)/18987 weeks
279-.10162 -.06854 (279*2π)/18987 weeks
280-.01783 -.04349 (280*2π)/18987 weeks
281-.02779 -.08134 (281*2π)/18987 weeks
282-.01898 -.07815 (282*2π)/18987 weeks
283-.04889 -.11334 (283*2π)/18987 weeks
284-.07272 -.0708 (284*2π)/18987 weeks
285-.05303 -.06795 (285*2π)/18987 weeks
286-.06457 -.06222 (286*2π)/18987 weeks
287-.06567 -.03963 (287*2π)/18987 weeks
288-.03711 -.04189 (288*2π)/18987 weeks
289-.00977 -.04322 (289*2π)/18987 weeks
290-.04353 -.10137 (290*2π)/18987 weeks
291-.06843 -.04895 (291*2π)/18987 weeks
292-.05969 -.04869 (292*2π)/18987 weeks
293-.06101 -.01793 (293*2π)/18986 weeks
294-.00754 -.02316 (294*2π)/18986 weeks
295.01016 -.05855 (295*2π)/18986 weeks
296-.0271 -.10509 (296*2π)/18986 weeks
297-.09532 -.06738 (297*2π)/18986 weeks
298-.05119 -.01287 (298*2π)/18986 weeks
299-.04685 -.05636 (299*2π)/18986 weeks
300-.0537 -.02245 (300*2π)/18986 weeks
301-.02686 -.03525 (301*2π)/18986 weeks
302-.04411 -.0071 (302*2π)/18986 weeks
303.01938 -.01622 (303*2π)/18986 weeks
304-.03613 -.08057 (304*2π)/18986 weeks
305-.01885 -.01028 (305*2π)/18986 weeks
306.02686 -.07028 (306*2π)/18986 weeks
307-.05267 -.07048 (307*2π)/18986 weeks
308-.02373 -.0548 (308*2π)/18986 weeks
309-.05765 -.04208 (309*2π)/18986 weeks
310-.00865 -.02918 (310*2π)/18986 weeks
311.00871 -.03272 (311*2π)/18986 weeks
312-.00563 -.07238 (312*2π)/18986 weeks
313-.01831 -.07328 (313*2π)/18986 weeks
314-.02525 -.04822 (314*2π)/18986 weeks
315.00801 -.07426 (315*2π)/18986 weeks
316-.03364 -.09194 (316*2π)/18986 weeks
317-.05354 -.06161 (317*2π)/18986 weeks
318-.03593 -.05041 (318*2π)/18986 weeks
319-.0394 -.04337 (319*2π)/18986 weeks
320.00716 -.04457 (320*2π)/18986 weeks
321-.01993 -.0864 (321*2π)/18986 weeks
322-.03431 -.04899 (322*2π)/18986 weeks
323-.01587 -.071 (323*2π)/18986 weeks
324-.03375 -.06683 (324*2π)/18986 weeks
325-.04285 -.09383 (325*2π)/18986 weeks
326-.05985 -.03439 (326*2π)/18986 weeks
327.01024 -.05525 (327*2π)/18986 weeks
328-.04511 -.09112 (328*2π)/18986 weeks
329-.02291 -.07345 (329*2π)/18986 weeks
330-.0556 -.13512 (330*2π)/18986 weeks
331-.09801 -.03728 (331*2π)/18986 weeks
332-.04183 -.04847 (332*2π)/18986 weeks
333-.05509 -.06617 (333*2π)/18986 weeks
334-.08215 -.08014 (334*2π)/18986 weeks
335-.11429 -.02382 (335*2π)/18986 weeks
336-.03211 .00769 (336*2π)/18986 weeks
337-.04187 -.03096 (337*2π)/18986 weeks
338-.02113 -.02564 (338*2π)/18986 weeks
339-.05496 -.04121 (339*2π)/18986 weeks
340-.03686 -.01947 (340*2π)/18986 weeks
341-.01558 -.04495 (341*2π)/18986 weeks
342-.05026 -.0596 (342*2π)/18986 weeks
343-.06824 -.02967 (343*2π)/18986 weeks
344-.05133 .00055 (344*2π)/18986 weeks
345-.0206 -.00709 (345*2π)/18986 weeks
346-.0126 -.03126 (346*2π)/18985 weeks
347-.01814 -.01377 (347*2π)/18985 weeks
348.00319 -.03757 (348*2π)/18985 weeks
349-.03273 -.04727 (349*2π)/18985 weeks
350-.01182 -.03303 (350*2π)/18985 weeks
351-.02124 -.04028 (351*2π)/18985 weeks
352-.01837 -.02498 (352*2π)/18985 weeks
353.02526 -.03453 (353*2π)/18985 weeks
354-.01483 -.08189 (354*2π)/18985 weeks
355-.01604 -.03474 (355*2π)/18985 weeks
356.00598 -.10453 (356*2π)/18985 weeks
357-.08837 -.06839 (357*2π)/18985 weeks
358-.02996 -.03424 (358*2π)/18985 weeks
359-.02548 -.02388 (359*2π)/18985 weeks
360-.026 -.06253 (360*2π)/18985 weeks
361-.03928 -.03271 (361*2π)/18985 weeks
362-.00933 -.04111 (362*2π)/18985 weeks
363.00439 -.06608 (363*2π)/18985 weeks
364-.04071 -.09606 (364*2π)/18985 weeks
365-.06914 -.06511 (365*2π)/18985 weeks
366-.07522 -.01153 (366*2π)/18985 weeks
367-.01664 -.027 (367*2π)/18985 weeks
368-.02337 -.05156 (368*2π)/18985 weeks
369-.05629 -.04548 (369*2π)/18985 weeks
370-.04747 -.0133 (370*2π)/18985 weeks
371-.01915 -.00871 (371*2π)/18985 weeks
372.00126 -.0354 (372*2π)/18985 weeks
373-.00835 -.03757 (373*2π)/18985 weeks
374-.01135 -.06654 (374*2π)/18985 weeks
375-.02592 -.04365 (375*2π)/18985 weeks
376-.00471 -.05433 (376*2π)/18985 weeks
377-.00657 -.08984 (377*2π)/18985 weeks
378-.07521 -.08193 (378*2π)/18985 weeks
379-.0412 -.03673 (379*2π)/18985 weeks
380-.05723 -.06101 (380*2π)/18985 weeks
381-.01954 -.02537 (381*2π)/18985 weeks
382-.04807 -.09311 (382*2π)/18985 weeks
383-.07453 -.03422 (383*2π)/18985 weeks
384-.06192 -.0241 (384*2π)/18985 weeks
385-.03279