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# Fourier Analysis of ABT (Abbott Laboratories Common Stoc)

ABT (Abbott Laboratories Common Stoc) appears to have interesting cyclic behaviour every 193 weeks (1.4706*sine), 161 weeks (.9764*sine), and 176 weeks (.7957*sine).

ABT (Abbott Laboratories Common Stoc) has an average price of 12.33 (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 3/17/1980 to 3/20/2017 for ABT (Abbott Laboratories Common Stoc), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
012.33132   0
15.00103 -11.50938 (1*2π)/19311,931 weeks
23.0391 -6.00937 (2*2π)/1931966 weeks
31.06169 -5.41676 (3*2π)/1931644 weeks
41.08002 -4.17622 (4*2π)/1931483 weeks
5-.57821 -4.02901 (5*2π)/1931386 weeks
6-.61174 -2.46356 (6*2π)/1931322 weeks
7-.41819 -1.63831 (7*2π)/1931276 weeks
8-.26617 -1.68071 (8*2π)/1931241 weeks
9-.19745 -1.40291 (9*2π)/1931215 weeks
10-.12958 -1.47065 (10*2π)/1931193 weeks
11-.49008 -.7957 (11*2π)/1931176 weeks
12.29466 -.97635 (12*2π)/1931161 weeks
13-.49555 -.95478 (13*2π)/1931149 weeks
14-.06032 -.3982 (14*2π)/1931138 weeks
15.10957 -.63292 (15*2π)/1931129 weeks
16.31167 -.48522 (16*2π)/1931121 weeks
17.1726 -.82085 (17*2π)/1931114 weeks
18.17058 -.59303 (18*2π)/1931107 weeks
19.16998 -.82618 (19*2π)/1931102 weeks
20.076 -.59308 (20*2π)/193197 weeks
21.16584 -.64058 (21*2π)/193192 weeks
22.30161 -.70879 (22*2π)/193188 weeks
23-.13888 -.90771 (23*2π)/193184 weeks
24-.03097 -.43736 (24*2π)/193180 weeks
25.11517 -.64348 (25*2π)/193177 weeks
26-.01691 -.57144 (26*2π)/193174 weeks
27.06018 -.68015 (27*2π)/193172 weeks
28-.24221 -.59105 (28*2π)/193169 weeks
29-.04944 -.40161 (29*2π)/193167 weeks
30-.07831 -.46175 (30*2π)/193164 weeks
31.04445 -.39859 (31*2π)/193162 weeks
32-.08233 -.58498 (32*2π)/193160 weeks
33-.23944 -.32096 (33*2π)/193159 weeks
34-.06183 -.31172 (34*2π)/193157 weeks
35-.0591 -.2883 (35*2π)/193155 weeks
36.01872 -.25603 (36*2π)/193154 weeks
37.00321 -.31499 (37*2π)/193152 weeks
38-.02242 -.26187 (38*2π)/193151 weeks
39.02424 -.26756 (39*2π)/193150 weeks
40.07178 -.28894 (40*2π)/193148 weeks
41.08467 -.36719 (41*2π)/193147 weeks
42-.07935 -.37136 (42*2π)/193146 weeks
43-.07771 -.20486 (43*2π)/193145 weeks
44.07141 -.16305 (44*2π)/193144 weeks
45.05484 -.29451 (45*2π)/193143 weeks
46.05336 -.24961 (46*2π)/193142 weeks
47.09295 -.32167 (47*2π)/193141 weeks
48-.018 -.28093 (48*2π)/193140 weeks
49.03929 -.33096 (49*2π)/193139 weeks
50-.08007 -.2609 (50*2π)/193139 weeks
51.02367 -.19545 (51*2π)/193138 weeks
52.02778 -.28843 (52*2π)/193137 weeks
53-.07963 -.24807 (53*2π)/193136 weeks
54-.01092 -.14172 (54*2π)/193136 weeks
55-.01871 -.10669 (55*2π)/193135 weeks
56.21069 -.10122 (56*2π)/193134 weeks
57.14228 -.35057 (57*2π)/193134 weeks
58.00545 -.24976 (58*2π)/193133 weeks
59.10482 -.24725 (59*2π)/193133 weeks
60.007 -.30843 (60*2π)/193132 weeks
61.00386 -.19555 (61*2π)/193132 weeks
62.01061 -.22392 (62*2π)/193131 weeks
63.0531 -.12874 (63*2π)/193131 weeks
64.16795 -.30703 (64*2π)/193130 weeks
65-.0314 -.27934 (65*2π)/193130 weeks
66.0472 -.16581 (66*2π)/193129 weeks
67.09967 -.24638 (67*2π)/193129 weeks
68.05062 -.29209 (68*2π)/193128 weeks
69.05397 -.27503 (69*2π)/193128 weeks
70.03434 -.3435 (70*2π)/193128 weeks
71-.1021 -.26164 (71*2π)/193127 weeks
72.00235 -.19613 (72*2π)/193127 weeks
73-.02463 -.28021 (73*2π)/193126 weeks
74-.04877 -.17219 (74*2π)/193126 weeks
75.00047 -.25952 (75*2π)/193126 weeks
76-.06085 -.15369 (76*2π)/193125 weeks
77.02192 -.18181 (77*2π)/193125 weeks
78-.04621 -.21932 (78*2π)/193125 weeks
79-.00702 -.13869 (79*2π)/193124 weeks
80.0144 -.1406 (80*2π)/193124 weeks
81.08228 -.18696 (81*2π)/193124 weeks
82.01957 -.22642 (82*2π)/193124 weeks
83.02292 -.20923 (83*2π)/193123 weeks
84.03101 -.21988 (84*2π)/193123 weeks
85.00305 -.21709 (85*2π)/193123 weeks
86.0181 -.21333 (86*2π)/193122 weeks
87.02092 -.24368 (87*2π)/193122 weeks
88-.03255 -.24452 (88*2π)/193122 weeks
89-.02022 -.20964 (89*2π)/193122 weeks
90.00937 -.22801 (90*2π)/193121 weeks
91-.01197 -.28571 (91*2π)/193121 weeks
92-.11697 -.2662 (92*2π)/193121 weeks
93-.12216 -.21895 (93*2π)/193121 weeks
94-.11996 -.13579 (94*2π)/193121 weeks
95-.05159 -.17265 (95*2π)/193120 weeks
96-.10906 -.13993 (96*2π)/193120 weeks
97-.03467 -.17416 (97*2π)/193120 weeks
98-.1475 -.15102 (98*2π)/193120 weeks
99-.05178 -.091 (99*2π)/193120 weeks
100-.09209 -.12327 (100*2π)/193119 weeks
101-.02541 -.11517 (101*2π)/193119 weeks
102-.14249 -.1256 (102*2π)/193119 weeks
103-.07314 -.00965 (103*2π)/193119 weeks
104-.006 -.05589 (104*2π)/193119 weeks
105.00653 -.05379 (105*2π)/193118 weeks
106-.02087 -.06626 (106*2π)/193118 weeks
107.04703 -.06881 (107*2π)/193118 weeks
108.01255 -.03606 (108*2π)/193118 weeks
109.11063 -.10366 (109*2π)/193118 weeks
110.05626 -.14534 (110*2π)/193118 weeks
111.04196 -.12457 (111*2π)/193117 weeks
112.07641 -.1271 (112*2π)/193117 weeks
113.07066 -.19537 (113*2π)/193117 weeks
114.01636 -.17527 (114*2π)/193117 weeks
115.03973 -.19416 (115*2π)/193117 weeks
116-.00304 -.20933 (116*2π)/193117 weeks
117-.01333 -.17904 (117*2π)/193117 weeks
118-.02335 -.18712 (118*2π)/193116 weeks
119-.02284 -.16002 (119*2π)/193116 weeks
120-.02585 -.1821 (120*2π)/193116 weeks
121-.0515 -.17441 (121*2π)/193116 weeks
122-.0376 -.16532 (122*2π)/193116 weeks
123-.04703 -.12894 (123*2π)/193116 weeks
124-.00947 -.17179 (124*2π)/193116 weeks
125-.08526 -.19318 (125*2π)/193115 weeks
126-.07204 -.10303 (126*2π)/193115 weeks
127-.05168 -.16596 (127*2π)/193115 weeks
128-.09706 -.10987 (128*2π)/193115 weeks
129-.04122 -.10476 (129*2π)/193115 weeks
130-.08254 -.09436 (130*2π)/193115 weeks
131-.01551 -.08504 (131*2π)/193115 weeks
132-.02839 -.11205 (132*2π)/193115 weeks
133-.01647 -.13288 (133*2π)/193115 weeks
134-.03724 -.13804 (134*2π)/193114 weeks
135-.07704 -.12702 (135*2π)/193114 weeks
136-.05618 -.08563 (136*2π)/193114 weeks
137-.0568 -.11893 (137*2π)/193114 weeks
138-.06578 -.07656 (138*2π)/193114 weeks
139-.04942 -.07697 (139*2π)/193114 weeks
140-.04103 -.07975 (140*2π)/193114 weeks
141-.02845 -.04437 (141*2π)/193114 weeks
142.02768 -.09372 (142*2π)/193114 weeks
143-.02035 -.14113 (143*2π)/193114 weeks
144-.02874 -.09898 (144*2π)/193113 weeks
145-.05689 -.12978 (145*2π)/193113 weeks
146-.06319 -.08809 (146*2π)/193113 weeks
147-.04967 -.07658 (147*2π)/193113 weeks
148-.06163 -.0655 (148*2π)/193113 weeks
149-.00589 -.03738 (149*2π)/193113 weeks
150-.00382 -.10677 (150*2π)/193113 weeks
151-.049 -.08371 (151*2π)/193113 weeks
152-.02932 -.07847 (152*2π)/193113 weeks
153-.03701 -.05288 (153*2π)/193113 weeks
154.00983 -.06013 (154*2π)/193113 weeks
155-.01775 -.08284 (155*2π)/193112 weeks
156.01727 -.0579 (156*2π)/193112 weeks
157-.00605 -.1283 (157*2π)/193112 weeks
158-.02884 -.05765 (158*2π)/193112 weeks
159.02359 -.09066 (159*2π)/193112 weeks
160-.01687 -.10232 (160*2π)/193112 weeks
161.0038 -.08529 (161*2π)/193112 weeks
162-.00452 -.12685 (162*2π)/193112 weeks
163-.02528 -.08352 (163*2π)/193112 weeks
164.01038 -.13094 (164*2π)/193112 weeks
165-.05493 -.13565 (165*2π)/193112 weeks
166-.05074 -.09334 (166*2π)/193112 weeks
167-.04041 -.08999 (167*2π)/193112 weeks
168-.0495 -.0959 (168*2π)/193111 weeks
169-.05799 -.08104 (169*2π)/193111 weeks
170-.04181 -.05138 (170*2π)/193111 weeks
171-.03931 -.06973 (171*2π)/193111 weeks
172-.00725 -.0461 (172*2π)/193111 weeks
173-.01347 -.09229 (173*2π)/193111 weeks
174-.0293 -.05733 (174*2π)/193111 weeks
175.00342 -.08056 (175*2π)/193111 weeks
176-.03547 -.07853 (176*2π)/193111 weeks
177.01121 -.06309 (177*2π)/193111 weeks
178-.02229 -.10444 (178*2π)/193111 weeks
179-.02506 -.06299 (179*2π)/193111 weeks
180-.00387 -.07623 (180*2π)/193111 weeks
181-.00908 -.07213 (181*2π)/193111 weeks
182.0216 -.09606 (182*2π)/193111 weeks
183-.01438 -.12 (183*2π)/193111 weeks
184-.01928 -.10736 (184*2π)/193110 weeks
185-.04514 -.10626 (185*2π)/193110 weeks
186-.02895 -.10244 (186*2π)/193110 weeks
187-.06476 -.08841 (187*2π)/193110 weeks
188-.03761 -.07744 (188*2π)/193110 weeks
189-.03667 -.07608 (189*2π)/193110 weeks
190-.02843 -.08401 (190*2π)/193110 weeks
191-.04116 -.07715 (191*2π)/193110 weeks
192-.03677 -.08792 (192*2π)/193110 weeks
193-.06354 -.06372 (193*2π)/193110 weeks
194-.01965 -.05054 (194*2π)/193110 weeks
195-.01816 -.07884 (195*2π)/193110 weeks
196-.03197 -.07869 (196*2π)/193110 weeks
197-.03665 -.08821 (197*2π)/193110 weeks
198-.04522 -.0748 (198*2π)/193110 weeks
199-.05118 -.06521 (199*2π)/193110 weeks
200-.04703 -.06441 (200*2π)/193110 weeks
201-.02929 -.05348 (201*2π)/193110 weeks
202-.05687 -.06511 (202*2π)/193110 weeks
203-.04318 -.03198 (203*2π)/193110 weeks
204-.01372 -.03242 (204*2π)/19319 weeks
205-.00503 -.04895 (205*2π)/19319 weeks
206.00509 -.07018 (206*2π)/19319 weeks
207-.02172 -.0929 (207*2π)/19319 weeks
208-.02571 -.06671 (208*2π)/19319 weeks
209-.03873 -.09833 (209*2π)/19319 weeks
210-.06512 -.05415 (210*2π)/19319 weeks
211-.03822 -.04753 (211*2π)/19319 weeks
212-.04691 -.02904 (212*2π)/19319 weeks
213-.0057 -.03193 (213*2π)/19319 weeks
214.00455 -.05983 (214*2π)/19319 weeks
215-.01664 -.07808 (215*2π)/19319 weeks
216-.0589 -.06174 (216*2π)/19319 weeks
217-.00872 -.01566 (217*2π)/19319 weeks
218.00409 -.06935 (218*2π)/19319 weeks
219-.02742 -.06993 (219*2π)/19319 weeks
220-.01728 -.05643 (220*2π)/19319 weeks
221-.02132 -.06533 (221*2π)/19319 weeks
222-.03063 -.05742 (222*2π)/19319 weeks
223-.02061 -.05883 (223*2π)/19319 weeks
224-.03205 -.06268 (224*2π)/19319 weeks
225-.02906 -.03698 (225*2π)/19319 weeks
226-.00774 -.05051 (226*2π)/19319 weeks
227-.01148 -.04178 (227*2π)/19319 weeks
228-.02663 -.07069 (228*2π)/19318 weeks
229-.01338 -.00592 (229*2π)/19318 weeks
230.02955 -.07141 (230*2π)/19318 weeks
231-.00553 -.05575 (231*2π)/19318 weeks
232.01724 -.07434 (232*2π)/19318 weeks
233-.00025 -.09062 (233*2π)/19318 weeks
234-.01037 -.08938 (234*2π)/19318 weeks
235-.02401 -.0996 (235*2π)/19318 weeks
236-.04544 -.09082 (236*2π)/19318 weeks
237-.04378 -.05308 (237*2π)/19318 weeks
238-.01822 -.06116 (238*2π)/19318 weeks
239-.03447 -.05673 (239*2π)/19318 weeks
240-.01052 -.06836 (240*2π)/19318 weeks
241-.0328 -.06483 (241*2π)/19318 weeks
242.00001 -.0646 (242*2π)/19318 weeks
243-.0239 -.09383 (243*2π)/19318 weeks
244-.04445 -.08043 (244*2π)/19318 weeks
245-.03746 -.06504 (245*2π)/19318 weeks
246-.03326 -.0771 (246*2π)/19318 weeks
247-.0472 -.07131 (247*2π)/19318 weeks
248-.04919 -.0735 (248*2π)/19318 weeks
249-.05666 -.05321 (249*2π)/19318 weeks
250-.04296 -.03097 (250*2π)/19318 weeks
251-.00195 -.06732 (251*2π)/19318 weeks
252-.05487 -.07841 (252*2π)/19318 weeks
253-.03405 -.06135 (253*2π)/19318 weeks
254-.06522 -.07173 (254*2π)/19318 weeks
255-.04672 -.05787 (255*2π)/19318 weeks
256-.07921 -.05463 (256*2π)/19318 weeks
257-.06844 -.03101 (257*2π)/19318 weeks
258-.06413 -.02166 (258*2π)/19317 weeks
259-.04636 .01087 (259*2π)/19317 weeks
260-.00741 -.01637 (260*2π)/19317 weeks
261-.02961 -.0321 (261*2π)/19317 weeks
262-.00352 -.00625 (262*2π)/19317 weeks
263-.00029 -.04072 (263*2π)/19317 weeks
264-.00667 -.05968 (264*2π)/19317 weeks
265-.02185 -.05163 (265*2π)/19317 weeks
266-.01969 -.05187 (266*2π)/19317 weeks
267-.03783 -.05359 (267*2π)/19317 weeks
268-.0249 -.03354 (268*2π)/19317 weeks
269-.03767 -.05357 (269*2π)/19317 weeks
270-.0331 -.02918 (270*2π)/19317 weeks
271-.02226 -.01665 (271*2π)/19317 weeks
272.0064 -.02017 (272*2π)/19317 weeks
273.01579 -.05941 (273*2π)/19317 weeks
274-.01684 -.07756 (274*2π)/19317 weeks
275-.03983 -.05709 (275*2π)/19317 weeks
276-.03223 -.0429 (276*2π)/19317 weeks
277-.00865 -.03578 (277*2π)/19317 weeks
278-.02263 -.05857 (278*2π)/19317 weeks
279-.02457 -.06914 (279*2π)/19317 weeks
280-.0374 -.03453 (280*2π)/19317 weeks
281-.01597 -.05534 (281*2π)/19317 weeks
282-.0333 -.05684 (282*2π)/19317 weeks
283-.02996 -.06895 (283*2π)/19317 weeks
284-.06609 -.0454 (284*2π)/19317 weeks
285-.04308 -.03126 (285*2π)/19317 weeks
286-.04292 -.02219 (286*2π)/19317 weeks
287-.01085 -.01903 (287*2π)/19317 weeks
288-.02957 -.04892 (288*2π)/19317 weeks
289-.02626 -.03259 (289*2π)/19317 weeks
290-.03255 -.03217 (290*2π)/19317 weeks
291-.01852 -.02848 (291*2π)/19317 weeks
292-.0204 -.03732 (292*2π)/19317 weeks
293-.02817 -.05404 (293*2π)/19317 weeks
294-.04138 -.02613 (294*2π)/19317 weeks
295-.02141 -.02504 (295*2π)/19317 weeks
296-.02029 -.02853 (296*2π)/19317 weeks
297-.02629 -.03887 (297*2π)/19317 weeks
298-.028 -.0187 (298*2π)/19316 weeks
299-.00692 -.02021 (299*2π)/19316 weeks
300-.01261 -.03827 (300*2π)/19316 weeks
301-.00517 -.03683 (301*2π)/19316 weeks
302-.02877 -.05412 (302*2π)/19316 weeks
303-.03644 -.0158 (303*2π)/19316 weeks
304-.00162 -.02353 (304*2π)/19316 weeks
305-.00398 -.04506 (305*2π)/19316 weeks
306-.03043 -.04864 (306*2π)/19316 weeks
307-.03499 -.01331 (307*2π)/19316 weeks
308-.0021 -.01327 (308*2π)/19316 weeks
309.01024 -.03152 (309*2π)/19316 weeks
310-.01107 -.05006 (310*2π)/19316 weeks
311-.00229 -.02172 (311*2π)/19316 weeks
312.01154 -.04473 (312*2π)/19316 weeks
313-.00075 -.06045 (313*2π)/19316 weeks
314-.00768 -.04997 (314*2π)/19316 weeks
315-.01079 -.06037 (315*2π)/19316 weeks
316-.01234 -.05044 (316*2π)/19316 weeks
317-.02178 -.05628 (317*2π)/19316 weeks
318-.00677 -.04845 (318*2π)/19316 weeks
319-.01958 -.06934 (319*2π)/19316 weeks
320-.03836 -.05796 (320*2π)/19316 weeks
321-.03528 -.03423 (321*2π)/19316 weeks
322.00315 -.03608 (322*2π)/19316 weeks
323-.01658 -.07292 (323*2π)/19316 weeks
324-.03128 -.06278 (324*2π)/19316 weeks
325-.04458 -.05783 (325*2π)/19316 weeks
326-.03663 -.03972 (326*2π)/19316 weeks
327-.03106 -.04878 (327*2π)/19316 weeks
328-.04185 -.06072 (328*2π)/19316 weeks
329-.05498 -.02919 (329*2π)/19316 weeks
330-.0459 -.03046 (330*2π)/19316 weeks
331-.02949 -.01337 (331*2π)/19316 weeks
332-.03098 -.03107 (332*2π)/19316 weeks
333-.02148 -.01398 (333*2π)/19316 weeks
334-.00135 -.03493 (334*2π)/19316 weeks
335-.02515 -.04858 (335*2π)/19316 weeks
336-.02646 -.04458 (336*2π)/19316 weeks
337-.04133 -.03146 (337*2π)/19316 weeks
338-.02441 -.03646 (338*2π)/19316 weeks
339-.03766 -.03584 (339*2π)/19316 weeks
340-.03805 -.01618 (340*2π)/19316 weeks
341-.01501 -.01862 (341*2π)/19316 weeks
342-.02233 -.0299 (342*2π)/19316 weeks
343-.02264 -.02672 (343*2π)/19316 weeks
344-.0184 -.02759 (344*2π)/19316 weeks
345-.02053 -.02057 (345*2π)/19316 weeks
346-.00345 -.03184 (346*2π)/19316 weeks
347-.02162 -.04617 (347*2π)/19316 weeks
348-.02282 -.02881 (348*2π)/19316 weeks
349-.01941 -.03563 (349*2π)/19316 weeks
350-.02503 -.03326 (350*2π)/19316 weeks
351-.03819 -.02228 (351*2π)/19316 weeks
352-.00387 -.01203 (352*2π)/19315 weeks
353-.0122 -.03079 (353*2π)/19315 weeks
354-.00086 -.02465 (354*2π)/19315 weeks
355-.01283 -.03688 (355*2π)/19315 weeks
356-.00344 -.02632 (356*2π)/19315 weeks
357-.00064 -.05549 (357*2π)/19315 weeks
358-.02103 -.03744 (358*2π)/19315 weeks
359-.00398 -.0532 (359*2π)/19315 weeks
360-.03386 -.04175 (360*2π)/19315 weeks
361-.00932 -.03812 (361*2π)/19315 weeks
362-.01877 -.05512 (362*2π)/19315 weeks
363-.03573 -.03872 (363*2π)/19315 weeks
364-.02053 -.02788 (364*2π)/19315 weeks
365-.00451 -.03549 (365*2π)/19315 weeks
366-.01994 -.05158 (366*2π)/19315 weeks
367-.02045 -.04739 (367*2π)/19315 weeks
368-.03045 -.04923 (368*2π)/19315 weeks
369-.01942 -.02813 (369*2π)/19315 weeks
370-.02918 -.0702 (370*2π)/19315 weeks
371-.04134 -.03764 (371*2π)/19315 weeks
372-.04832