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# Fourier Analysis of BTI (British American Tobacco Indus)

BTI (British American Tobacco Indus) appears to have interesting cyclic behaviour every 192 weeks (3.933*sine), 147 weeks (3.455*sine), and 160 weeks (2.8997*sine).

BTI (British American Tobacco Indus) has an average price of 25.66 (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 4/14/1980 to 1/9/2017 for BTI (British American Tobacco Indus), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
025.66046   0
123.84444 -26.74269 (1*2π)/19171,917 weeks
25.48607 -21.58595 (2*2π)/1917959 weeks
32.16222 -12.91387 (3*2π)/1917639 weeks
41.39658 -11.55909 (4*2π)/1917479 weeks
5-1.55314 -8.47252 (5*2π)/1917383 weeks
6-.94572 -4.99768 (6*2π)/1917320 weeks
7.95686 -3.80086 (7*2π)/1917274 weeks
81.5783 -5.21456 (8*2π)/1917240 weeks
9-.10039 -5.14192 (9*2π)/1917213 weeks
10-.54696 -3.93302 (10*2π)/1917192 weeks
11-.14136 -2.76869 (11*2π)/1917174 weeks
12.87499 -2.89974 (12*2π)/1917160 weeks
13.04054 -3.45496 (13*2π)/1917147 weeks
14-.1793 -2.79661 (14*2π)/1917137 weeks
15.16626 -2.22862 (15*2π)/1917128 weeks
16.65058 -2.36509 (16*2π)/1917120 weeks
17.45321 -2.8908 (17*2π)/1917113 weeks
18-.36851 -2.85033 (18*2π)/1917107 weeks
19-.40584 -2.08944 (19*2π)/1917101 weeks
20.1309 -1.8374 (20*2π)/191796 weeks
21.12802 -2.46211 (21*2π)/191791 weeks
22-.61609 -2.20871 (22*2π)/191787 weeks
23-.62349 -1.85121 (23*2π)/191783 weeks
24-.511 -1.23519 (24*2π)/191780 weeks
25.09142 -1.24561 (25*2π)/191777 weeks
26-.02217 -1.78462 (26*2π)/191774 weeks
27-.36828 -1.4656 (27*2π)/191771 weeks
28-.3228 -1.21258 (28*2π)/191768 weeks
29-.01545 -1.10444 (29*2π)/191766 weeks
30.22063 -1.36415 (30*2π)/191764 weeks
31.05686 -1.51823 (31*2π)/191762 weeks
32-.28039 -1.67423 (32*2π)/191760 weeks
33-.40156 -1.32402 (33*2π)/191758 weeks
34-.39946 -1.38342 (34*2π)/191756 weeks
35-.47739 -1.29369 (35*2π)/191755 weeks
36-.71388 -1.16953 (36*2π)/191753 weeks
37-.67943 -.69877 (37*2π)/191752 weeks
38-.40449 -.63925 (38*2π)/191750 weeks
39-.316 -.54567 (39*2π)/191749 weeks
40-.03039 -.64845 (40*2π)/191748 weeks
41-.12834 -.80516 (41*2π)/191747 weeks
42-.20008 -.73819 (42*2π)/191746 weeks
43-.14449 -.76366 (43*2π)/191745 weeks
44-.23838 -.70309 (44*2π)/191744 weeks
45-.16257 -.64249 (45*2π)/191743 weeks
46-.08723 -.66033 (46*2π)/191742 weeks
47-.17867 -.70645 (47*2π)/191741 weeks
48-.13934 -.66557 (48*2π)/191740 weeks
49-.24021 -.70718 (49*2π)/191739 weeks
50-.33468 -.51541 (50*2π)/191738 weeks
51-.13741 -.38205 (51*2π)/191738 weeks
52-.03673 -.39522 (52*2π)/191737 weeks
53.01047 -.55659 (53*2π)/191736 weeks
54-.10619 -.58115 (54*2π)/191736 weeks
55-.07183 -.43369 (55*2π)/191735 weeks
56-.03537 -.41576 (56*2π)/191734 weeks
57.0592 -.36619 (57*2π)/191734 weeks
58.14413 -.48252 (58*2π)/191733 weeks
59.23916 -.54166 (59*2π)/191732 weeks
60.15805 -.81355 (60*2π)/191732 weeks
61-.12229 -.80824 (61*2π)/191731 weeks
62-.29438 -.63474 (62*2π)/191731 weeks
63-.23373 -.40563 (63*2π)/191730 weeks
64-.00631 -.34467 (64*2π)/191730 weeks
65.03283 -.52016 (65*2π)/191729 weeks
66-.13227 -.53251 (66*2π)/191729 weeks
67-.06938 -.32357 (67*2π)/191729 weeks
68.10565 -.40824 (68*2π)/191728 weeks
69.12428 -.50171 (69*2π)/191728 weeks
70.09291 -.67012 (70*2π)/191727 weeks
71-.06583 -.68331 (71*2π)/191727 weeks
72-.23391 -.64866 (72*2π)/191727 weeks
73-.27876 -.47146 (73*2π)/191726 weeks
74-.24519 -.38681 (74*2π)/191726 weeks
75-.10533 -.30276 (75*2π)/191726 weeks
76-.11752 -.35907 (76*2π)/191725 weeks
77-.14415 -.31841 (77*2π)/191725 weeks
78-.09612 -.2828 (78*2π)/191725 weeks
79.02357 -.27305 (79*2π)/191724 weeks
80-.02663 -.35002 (80*2π)/191724 weeks
81-.03293 -.29306 (81*2π)/191724 weeks
82.01465 -.34441 (82*2π)/191723 weeks
83-.00044 -.29628 (83*2π)/191723 weeks
84.08305 -.36129 (84*2π)/191723 weeks
85-.02505 -.41735 (85*2π)/191723 weeks
86-.09772 -.37308 (86*2π)/191722 weeks
87-.08344 -.20053 (87*2π)/191722 weeks
88.0888 -.24124 (88*2π)/191722 weeks
89.01649 -.30852 (89*2π)/191722 weeks
90.01299 -.25228 (90*2π)/191721 weeks
91.21225 -.13629 (91*2π)/191721 weeks
92.32226 -.44347 (92*2π)/191721 weeks
93.06485 -.59017 (93*2π)/191721 weeks
94-.10074 -.46858 (94*2π)/191720 weeks
95-.02875 -.23043 (95*2π)/191720 weeks
96.11823 -.31011 (96*2π)/191720 weeks
97.13715 -.40512 (97*2π)/191720 weeks
98.03574 -.48648 (98*2π)/191720 weeks
99-.0013 -.32538 (99*2π)/191719 weeks
100.15209 -.37814 (100*2π)/191719 weeks
101.09932 -.52635 (101*2π)/191719 weeks
102-.03433 -.55525 (102*2π)/191719 weeks
103-.13145 -.46456 (103*2π)/191719 weeks
104-.13921 -.34151 (104*2π)/191718 weeks
105.0181 -.24893 (105*2π)/191718 weeks
106.04184 -.41914 (106*2π)/191718 weeks
107.00198 -.44204 (107*2π)/191718 weeks
108-.05199 -.43523 (108*2π)/191718 weeks
109-.06923 -.44981 (109*2π)/191718 weeks
110-.15052 -.45302 (110*2π)/191717 weeks
111-.24352 -.35609 (111*2π)/191717 weeks
112-.20401 -.19361 (112*2π)/191717 weeks
113-.04274 -.16624 (113*2π)/191717 weeks
114-.00313 -.23308 (114*2π)/191717 weeks
115.02471 -.30992 (115*2π)/191717 weeks
116-.06331 -.28829 (116*2π)/191717 weeks
117-.02418 -.24949 (117*2π)/191716 weeks
118.03062 -.27454 (118*2π)/191716 weeks
119.04367 -.30086 (119*2π)/191716 weeks
120-.02044 -.33005 (120*2π)/191716 weeks
121-.03875 -.31992 (121*2π)/191716 weeks
122-.03097 -.2506 (122*2π)/191716 weeks
123.06942 -.30654 (123*2π)/191716 weeks
124-.02626 -.37784 (124*2π)/191715 weeks
125-.03578 -.3075 (125*2π)/191715 weeks
126-.07513 -.31097 (126*2π)/191715 weeks
127-.02621 -.24639 (127*2π)/191715 weeks
128-.00023 -.28265 (128*2π)/191715 weeks
129.0668 -.2522 (129*2π)/191715 weeks
130.06614 -.41705 (130*2π)/191715 weeks
131-.06652 -.40506 (131*2π)/191715 weeks
132-.11547 -.35726 (132*2π)/191715 weeks
133-.08455 -.29545 (133*2π)/191714 weeks
134-.0695 -.30001 (134*2π)/191714 weeks
135-.04898 -.28327 (135*2π)/191714 weeks
136-.10225 -.34643 (136*2π)/191714 weeks
137-.12449 -.23828 (137*2π)/191714 weeks
138-.05375 -.22857 (138*2π)/191714 weeks
139-.03208 -.2563 (139*2π)/191714 weeks
140-.04803 -.24312 (140*2π)/191714 weeks
141-.01251 -.28436 (141*2π)/191714 weeks
142-.05343 -.32057 (142*2π)/191714 weeks
143-.10957 -.31492 (143*2π)/191713 weeks
144-.15778 -.2233 (144*2π)/191713 weeks
145-.0825 -.14636 (145*2π)/191713 weeks
146-.02827 -.21235 (146*2π)/191713 weeks
147-.03281 -.17226 (147*2π)/191713 weeks
148.05105 -.19905 (148*2π)/191713 weeks
149.02135 -.28425 (149*2π)/191713 weeks
150-.03926 -.25054 (150*2π)/191713 weeks
151.002 -.23477 (151*2π)/191713 weeks
152.01838 -.25922 (152*2π)/191713 weeks
153.03194 -.28134 (153*2π)/191713 weeks
154.01468 -.31836 (154*2π)/191712 weeks
155-.00159 -.32518 (155*2π)/191712 weeks
156-.04346 -.35129 (156*2π)/191712 weeks
157-.04247 -.3227 (157*2π)/191712 weeks
158-.06111 -.38592 (158*2π)/191712 weeks
159-.13882 -.36402 (159*2π)/191712 weeks
160-.19289 -.27454 (160*2π)/191712 weeks
161-.13436 -.23471 (161*2π)/191712 weeks
162-.1064 -.28101 (162*2π)/191712 weeks
163-.14817 -.27777 (163*2π)/191712 weeks
164-.2275 -.24591 (164*2π)/191712 weeks
165-.2118 -.13593 (165*2π)/191712 weeks
166-.15671 -.09357 (166*2π)/191712 weeks
167-.06736 -.04679 (167*2π)/191711 weeks
168.01345 -.07596 (168*2π)/191711 weeks
169.07324 -.14711 (169*2π)/191711 weeks
170.05445 -.24699 (170*2π)/191711 weeks
171-.00759 -.26954 (171*2π)/191711 weeks
172-.00977 -.23101 (172*2π)/191711 weeks
173.03144 -.26981 (173*2π)/191711 weeks
174-.04343 -.36394 (174*2π)/191711 weeks
175-.13034 -.30049 (175*2π)/191711 weeks
176-.13795 -.27167 (176*2π)/191711 weeks
177-.13299 -.20165 (177*2π)/191711 weeks
178-.07627 -.21028 (178*2π)/191711 weeks
179-.08857 -.23884 (179*2π)/191711 weeks
180-.11859 -.21778 (180*2π)/191711 weeks
181-.0873 -.21971 (181*2π)/191711 weeks
182-.11659 -.26961 (182*2π)/191711 weeks
183-.16469 -.2272 (183*2π)/191710 weeks
184-.20575 -.16906 (184*2π)/191710 weeks
185-.14066 -.09114 (185*2π)/191710 weeks
186-.07723 -.11158 (186*2π)/191710 weeks
187-.0624 -.13314 (187*2π)/191710 weeks
188-.05584 -.14464 (188*2π)/191710 weeks
189-.0673 -.17264 (189*2π)/191710 weeks
190-.04951 -.17024 (190*2π)/191710 weeks
191-.07958 -.19601 (191*2π)/191710 weeks
192-.12093 -.16668 (192*2π)/191710 weeks
193-.08319 -.11427 (193*2π)/191710 weeks
194-.03214 -.13371 (194*2π)/191710 weeks
195-.04569 -.1903 (195*2π)/191710 weeks
196-.08757 -.18259 (196*2π)/191710 weeks
197-.10103 -.15639 (197*2π)/191710 weeks
198-.10425 -.10879 (198*2π)/191710 weeks
199-.02176 -.10789 (199*2π)/191710 weeks
200-.07809 -.16085 (200*2π)/191710 weeks
201-.07437 -.09416 (201*2π)/191710 weeks
202.00504 -.0738 (202*2π)/19179 weeks
203.05302 -.13947 (203*2π)/19179 weeks
204.02975 -.21257 (204*2π)/19179 weeks
205-.04196 -.215 (205*2π)/19179 weeks
206-.01156 -.19342 (206*2π)/19179 weeks
207-.02188 -.2522 (207*2π)/19179 weeks
208-.10514 -.2325 (208*2π)/19179 weeks
209-.12277 -.18889 (209*2π)/19179 weeks
210-.08869 -.13466 (210*2π)/19179 weeks
211-.06128 -.18079 (211*2π)/19179 weeks
212-.08314 -.16912 (212*2π)/19179 weeks
213-.0917 -.19237 (213*2π)/19179 weeks
214-.13164 -.1454 (214*2π)/19179 weeks
215-.11934 -.08553 (215*2π)/19179 weeks
216-.04524 -.07581 (216*2π)/19179 weeks
217-.00779 -.13029 (217*2π)/19179 weeks
218-.03446 -.15768 (218*2π)/19179 weeks
219-.03139 -.12933 (219*2π)/19179 weeks
220-.01898 -.18389 (220*2π)/19179 weeks
221-.07395 -.20016 (221*2π)/19179 weeks
222-.08643 -.14447 (222*2π)/19179 weeks
223-.08528 -.13393 (223*2π)/19179 weeks
224-.05036 -.1137 (224*2π)/19179 weeks
225-.02699 -.16804 (225*2π)/19179 weeks
226-.08071 -.16603 (226*2π)/19178 weeks
227-.1032 -.13972 (227*2π)/19178 weeks
228-.08605 -.08589 (228*2π)/19178 weeks
229-.03571 -.06987 (229*2π)/19178 weeks
230.01602 -.0991 (230*2π)/19178 weeks
231.02439 -.13757 (231*2π)/19178 weeks
232.00803 -.17224 (232*2π)/19178 weeks
233.01538 -.19803 (233*2π)/19178 weeks
234-.03248 -.25233 (234*2π)/19178 weeks
235-.10885 -.22171 (235*2π)/19178 weeks
236-.13666 -.17428 (236*2π)/19178 weeks
237-.1204 -.11479 (237*2π)/19178 weeks
238-.05541 -.08195 (238*2π)/19178 weeks
239-.01231 -.10798 (239*2π)/19178 weeks
240-.0018 -.17818 (240*2π)/19178 weeks
241-.05646 -.21193 (241*2π)/19178 weeks
242-.08435 -.17192 (242*2π)/19178 weeks
243-.07097 -.18133 (243*2π)/19178 weeks
244-.12233 -.20594 (244*2π)/19178 weeks
245-.17985 -.13185 (245*2π)/19178 weeks
246-.11656 -.05387 (246*2π)/19178 weeks
247-.06574 -.07894 (247*2π)/19178 weeks
248-.07647 -.10219 (248*2π)/19178 weeks
249-.07986 -.07404 (249*2π)/19178 weeks
250-.04224 -.06967 (250*2π)/19178 weeks
251-.01449 -.08981 (251*2π)/19178 weeks
252-.043 -.12172 (252*2π)/19178 weeks
253-.03307 -.07819 (253*2π)/19178 weeks
254-.0034 -.10536 (254*2π)/19178 weeks
255.02988 -.11345 (255*2π)/19178 weeks
256.00397 -.20502 (256*2π)/19177 weeks
257-.07555 -.19623 (257*2π)/19177 weeks
258-.11258 -.13496 (258*2π)/19177 weeks
259-.05711 -.0646 (259*2π)/19177 weeks
260.00385 -.12086 (260*2π)/19177 weeks
261-.02013 -.17532 (261*2π)/19177 weeks
262-.0755 -.18652 (262*2π)/19177 weeks
263-.13297 -.1109 (263*2π)/19177 weeks
264-.05652 -.06081 (264*2π)/19177 weeks
265-.00167 -.07389 (265*2π)/19177 weeks
266.03245 -.14607 (266*2π)/19177 weeks
267-.01463 -.19473 (267*2π)/19177 weeks
268-.07491 -.19571 (268*2π)/19177 weeks
269-.09669 -.16998 (269*2π)/19177 weeks
270-.13781 -.15375 (270*2π)/19177 weeks
271-.14376 -.058 (271*2π)/19177 weeks
272-.06876 -.00899 (272*2π)/19177 weeks
273.03291 -.05675 (273*2π)/19177 weeks
274.0157 -.1367 (274*2π)/19177 weeks
275-.03441 -.15516 (275*2π)/19177 weeks
276-.05421 -.12068 (276*2π)/19177 weeks
277-.03512 -.09906 (277*2π)/19177 weeks
278.00028 -.12449 (278*2π)/19177 weeks
279-.02754 -.15821 (279*2π)/19177 weeks
280-.03237 -.14859 (280*2π)/19177 weeks
281-.02619 -.14743 (281*2π)/19177 weeks
282-.03528 -.18211 (282*2π)/19177 weeks
283-.10095 -.18506 (283*2π)/19177 weeks
284-.09656 -.1213 (284*2π)/19177 weeks
285-.07795 -.12324 (285*2π)/19177 weeks
286-.06978 -.10402 (286*2π)/19177 weeks
287-.06067 -.11256 (287*2π)/19177 weeks
288-.03942 -.11812 (288*2π)/19177 weeks
289-.05144 -.14218 (289*2π)/19177 weeks
290-.06459 -.1337 (290*2π)/19177 weeks
291-.06533 -.12324 (291*2π)/19177 weeks
292-.05831 -.13802 (292*2π)/19177 weeks
293-.09806 -.1271 (293*2π)/19177 weeks
294-.06646 -.0922 (294*2π)/19177 weeks
295-.03257 -.11183 (295*2π)/19176 weeks
296-.0577 -.14759 (296*2π)/19176 weeks
297-.07946 -.12368 (297*2π)/19176 weeks
298-.0711 -.13381 (298*2π)/19176 weeks
299-.09613 -.10905 (299*2π)/19176 weeks
300-.06751 -.09518 (300*2π)/19176 weeks
301-.06841 -.11568 (301*2π)/19176 weeks
302-.07064 -.1121 (302*2π)/19176 weeks
303-.10593 -.08012 (303*2π)/19176 weeks
304-.03185 -.05158 (304*2π)/19176 weeks
305-.00099 -.1237 (305*2π)/19176 weeks
306-.05006 -.14533 (306*2π)/19176 weeks
307-.07252 -.11357 (307*2π)/19176 weeks
308-.05315 -.10825 (308*2π)/19176 weeks
309-.0455 -.1305 (309*2π)/19176 weeks
310-.05704 -.13094 (310*2π)/19176 weeks
311-.06599 -.13545 (311*2π)/19176 weeks
312-.08027 -.14572 (312*2π)/19176 weeks
313-.114 -.13186 (313*2π)/19176 weeks
314-.09503 -.09611 (314*2π)/19176 weeks
315-.08441 -.11175 (315*2π)/19176 weeks
316-.11129 -.1081 (316*2π)/19176 weeks
317-.10901 -.0673 (317*2π)/19176 weeks
318-.06071 -.06767 (318*2π)/19176 weeks
319-.06694 -.0862 (319*2π)/19176 weeks
320-.05074 -.10836 (320*2π)/19176 weeks
321-.10465 -.11413 (321*2π)/19176 weeks
322-.09767 -.08056 (322*2π)/19176 weeks
323-.10174 -.06984 (323*2π)/19176 weeks
324-.09447 -.06077 (324*2π)/19176 weeks
325-.08294 -.03441 (325*2π)/19176 weeks
326-.06071 -.02605 (326*2π)/19176 weeks
327-.03101 -.03556 (327*2π)/19176 weeks
328-.02451 -.06739 (328*2π)/19176 weeks
329-.03934 -.08033 (329*2π)/19176 weeks
330-.0214 -.06129 (330*2π)/19176 weeks
331-.01885 -.07501 (331*2π)/19176 weeks
332-.0294 -.11104 (332*2π)/19176 weeks
333-.05105 -.09307 (333*2π)/19176 weeks
334-.02737 -.09358 (334*2π)/19176 weeks
335-.05081 -.11143 (335*2π)/19176 weeks
336-.0708 -.10527 (336*2π)/19176 weeks
337-.08548 -.08366 (337*2π)/19176 weeks
338-.06358 -.05801 (338*2π)/19176 weeks
339-.05533 -.05162 (339*2π)/19176 weeks
340-.03547 -.0618 (340*2π)/19176 weeks
341-.0317 -.06745 (341*2π)/19176 weeks
342-.04247 -.08411 (342*2π)/19176 weeks
343-.04943 -.05201 (343*2π)/19176 weeks
344-.02307 -.05392 (344*2π)/19176 weeks
345.00199 -.06079 (345*2π)/19176 weeks
346-.01966 -.09354 (346*2π)/19176 weeks
347-.03096 -.06867 (347*2π)/19176 weeks
348-.01185 -.06737 (348*2π)/19176 weeks
349.02311 -.06805 (349*2π)/19175 weeks
350.02092 -.1094 (350*2π)/19175 weeks
351-.00444 -.11152 (351*2π)/19175 weeks
352-.00031 -.11461 (352*2π)/19175 weeks
353.00253 -.13453 (353*2π)/19175 weeks
354.00163 -.13703 (354*2π)/19175 weeks
355-.01466 -.15435 (355*2π)/19175 weeks
356-.03797 -.15648 (356*2π)/19175 weeks
357-.04226 -.14323 (357*2π)/19175 weeks
358-.0249 -.1679 (358*2π)/19175 weeks
359-.07512 -.1898 (359*2π)/19175 weeks
360-.12331 -.15672 (360*2π)/19175 weeks
361-.103 -.09983 (361*2π)/19175 weeks
362-.0795 -.10948 (362*2π)/19175 weeks
363-.08599 -.12644 (363*2π)/19175 weeks
364-.11794 -.1095 (364*2π)/19175 weeks
365-.09144 -.06485 (365*2π)/19175 weeks
366-.05575 -.09607 (366*2π)/19175 weeks
367-.10189 -.12325 (367*2π)/19175 weeks
368-.12446 -.08337 (368*2π)/19175 weeks
369-.09656 -.0419 (369*2π)/19175 weeks
370-.06838 -.05554 (370*2π)/19175 weeks
371-.08363 -.04663 (371*2π)/19175 weeks
372-.05578 -.04604 (372*2π)/19175 weeks
373-.04017 -.038 (373*2π)/19175 weeks
374-.01911 -.0686