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# Fourier Analysis of AAPL (Apple Inc.)

AAPL (Apple Inc.) appears to have interesting cyclic behaviour every 189 weeks (3.3739*sine), 111 weeks (3.1001*sine), and 118 weeks (2.2816*cosine).

AAPL (Apple Inc.) has an average price of 17.95 (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 12/12/1980 to 3/20/2017 for AAPL (Apple Inc.), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
017.95284   0
124.65484 -17.07055 (1*2π)/18931,893 weeks
210.239 -19.71241 (2*2π)/1893947 weeks
33.11941 -14.7529 (3*2π)/1893631 weeks
41.17538 -10.66908 (4*2π)/1893473 weeks
5-.1993 -8.16041 (5*2π)/1893379 weeks
6.51809 -5.70494 (6*2π)/1893316 weeks
71.04634 -6.04618 (7*2π)/1893270 weeks
8-.03454 -6.16167 (8*2π)/1893237 weeks
9-1.48406 -5.50294 (9*2π)/1893210 weeks
10-1.95439 -3.37386 (10*2π)/1893189 weeks
11-1.35876 -2.05988 (11*2π)/1893172 weeks
12-.60525 -1.44175 (12*2π)/1893158 weeks
13-.15855 -1.08936 (13*2π)/1893146 weeks
14.5112 -.3885 (14*2π)/1893135 weeks
152.11493 -.82756 (15*2π)/1893126 weeks
162.28157 -2.26827 (16*2π)/1893118 weeks
171.36689 -3.10006 (17*2π)/1893111 weeks
18.31494 -2.65448 (18*2π)/1893105 weeks
19.36917 -2.02543 (19*2π)/1893100 weeks
20.39994 -1.99568 (20*2π)/189395 weeks
21.50975 -1.6833 (21*2π)/189390 weeks
22.68073 -1.66414 (22*2π)/189386 weeks
231.01549 -1.80542 (23*2π)/189382 weeks
24.91674 -2.49932 (24*2π)/189379 weeks
25.22161 -2.68027 (25*2π)/189376 weeks
26-.41897 -2.43729 (26*2π)/189373 weeks
27-.69661 -1.7039 (27*2π)/189370 weeks
28-.39926 -1.12069 (28*2π)/189368 weeks
29.09561 -.97031 (29*2π)/189365 weeks
30.32766 -1.21753 (30*2π)/189363 weeks
31.20009 -1.32109 (31*2π)/189361 weeks
32.31125 -1.35528 (32*2π)/189359 weeks
33.23199 -1.45851 (33*2π)/189357 weeks
34.01857 -1.47998 (34*2π)/189356 weeks
35-.14651 -1.3682 (35*2π)/189354 weeks
36-.20205 -1.09223 (36*2π)/189353 weeks
37-.0844 -.91194 (37*2π)/189351 weeks
38.17319 -.9591 (38*2π)/189350 weeks
39.18707 -1.13305 (39*2π)/189349 weeks
40-.07162 -.99466 (40*2π)/189347 weeks
41.21306 -.88123 (41*2π)/189346 weeks
42.37328 -1.18371 (42*2π)/189345 weeks
43.00735 -1.35268 (43*2π)/189344 weeks
44-.25196 -1.10288 (44*2π)/189343 weeks
45-.0863 -.86862 (45*2π)/189342 weeks
46.00151 -.98636 (46*2π)/189341 weeks
47-.19571 -.95444 (47*2π)/189340 weeks
48-.21716 -.76056 (48*2π)/189339 weeks
49-.11099 -.63595 (49*2π)/189339 weeks
50.09106 -.60128 (50*2π)/189338 weeks
51.07283 -.73447 (51*2π)/189337 weeks
52.04242 -.70191 (52*2π)/189336 weeks
53.13825 -.65415 (53*2π)/189336 weeks
54.19477 -.72483 (54*2π)/189335 weeks
55.12169 -.79368 (55*2π)/189334 weeks
56.05063 -.69626 (56*2π)/189334 weeks
57.25032 -.65055 (57*2π)/189333 weeks
58.34984 -.8539 (58*2π)/189333 weeks
59.15132 -1.11249 (59*2π)/189332 weeks
60-.23476 -1.03649 (60*2π)/189332 weeks
61-.2914 -.62598 (61*2π)/189331 weeks
62-.09122 -.45581 (62*2π)/189331 weeks
63.10858 -.51622 (63*2π)/189330 weeks
64.16457 -.61735 (64*2π)/189330 weeks
65.20054 -.63493 (65*2π)/189329 weeks
66.19649 -.83071 (66*2π)/189329 weeks
67-.02909 -.92335 (67*2π)/189328 weeks
68-.22954 -.75234 (68*2π)/189328 weeks
69-.21288 -.49531 (69*2π)/189327 weeks
70.01078 -.41154 (70*2π)/189327 weeks
71.07639 -.46586 (71*2π)/189327 weeks
72.13208 -.44702 (72*2π)/189326 weeks
73.2346 -.52666 (73*2π)/189326 weeks
74.23587 -.68824 (74*2π)/189326 weeks
75.02411 -.74929 (75*2π)/189325 weeks
76-.06913 -.49121 (76*2π)/189325 weeks
77.15971 -.36454 (77*2π)/189325 weeks
78.38616 -.49351 (78*2π)/189324 weeks
79.37785 -.75017 (79*2π)/189324 weeks
80.25013 -.85336 (80*2π)/189324 weeks
81.16979 -.927 (81*2π)/189323 weeks
82-.00432 -.93159 (82*2π)/189323 weeks
83-.15955 -.80871 (83*2π)/189323 weeks
84-.15593 -.7052 (84*2π)/189323 weeks
85-.02944 -.6128 (85*2π)/189322 weeks
86-.01352 -.71448 (86*2π)/189322 weeks
87-.07182 -.71283 (87*2π)/189322 weeks
88-.11359 -.69637 (88*2π)/189322 weeks
89-.11569 -.67729 (89*2π)/189321 weeks
90-.14372 -.76154 (90*2π)/189321 weeks
91-.31846 -.66781 (91*2π)/189321 weeks
92-.29646 -.48416 (92*2π)/189321 weeks
93-.17443 -.43739 (93*2π)/189320 weeks
94-.12231 -.53848 (94*2π)/189320 weeks
95-.23039 -.5311 (95*2π)/189320 weeks
96-.21124 -.43492 (96*2π)/189320 weeks
97-.20833 -.45489 (97*2π)/189320 weeks
98-.25779 -.39547 (98*2π)/189319 weeks
99-.25235 -.2527 (99*2π)/189319 weeks
100-.10416 -.14589 (100*2π)/189319 weeks
101.06275 -.22929 (101*2π)/189319 weeks
102.12441 -.33009 (102*2π)/189319 weeks
103.0662 -.42149 (103*2π)/189318 weeks
104-.00133 -.39442 (104*2π)/189318 weeks
105.07851 -.37598 (105*2π)/189318 weeks
106.07731 -.45521 (106*2π)/189318 weeks
107.03051 -.46922 (107*2π)/189318 weeks
108.00832 -.41612 (108*2π)/189318 weeks
109.10838 -.41641 (109*2π)/189317 weeks
110.09943 -.56267 (110*2π)/189317 weeks
111.00183 -.60289 (111*2π)/189317 weeks
112-.0764 -.56704 (112*2π)/189317 weeks
113-.04639 -.51786 (113*2π)/189317 weeks
114-.07235 -.58683 (114*2π)/189317 weeks
115-.19002 -.57642 (115*2π)/189316 weeks
116-.245 -.48072 (116*2π)/189316 weeks
117-.21335 -.35647 (117*2π)/189316 weeks
118-.12933 -.32414 (118*2π)/189316 weeks
119-.09322 -.34968 (119*2π)/189316 weeks
120-.08097 -.3709 (120*2π)/189316 weeks
121-.08418 -.33948 (121*2π)/189316 weeks
122-.01961 -.36521 (122*2π)/189316 weeks
123-.02702 -.46285 (123*2π)/189315 weeks
124-.13048 -.48088 (124*2π)/189315 weeks
125-.18302 -.38664 (125*2π)/189315 weeks
126-.13125 -.35674 (126*2π)/189315 weeks
127-.14096 -.36582 (127*2π)/189315 weeks
128-.14199 -.32646 (128*2π)/189315 weeks
129-.0835 -.30142 (129*2π)/189315 weeks
130-.0504 -.37309 (130*2π)/189315 weeks
131-.14249 -.40482 (131*2π)/189314 weeks
132-.20703 -.34231 (132*2π)/189314 weeks
133-.19199 -.24871 (133*2π)/189314 weeks
134-.10012 -.19507 (134*2π)/189314 weeks
135-.0714 -.21627 (135*2π)/189314 weeks
136-.03465 -.22518 (136*2π)/189314 weeks
137-.02086 -.23922 (137*2π)/189314 weeks
138.01208 -.24418 (138*2π)/189314 weeks
139.0387 -.28237 (139*2π)/189314 weeks
140.064 -.31219 (140*2π)/189314 weeks
141.05321 -.37306 (141*2π)/189313 weeks
142-.00327 -.41664 (142*2π)/189313 weeks
143-.03969 -.42313 (143*2π)/189313 weeks
144-.0654 -.3954 (144*2π)/189313 weeks
145-.08441 -.41948 (145*2π)/189313 weeks
146-.12563 -.4035 (146*2π)/189313 weeks
147-.18774 -.37394 (147*2π)/189313 weeks
148-.22433 -.29919 (148*2π)/189313 weeks
149-.17807 -.1876 (149*2π)/189313 weeks
150-.0943 -.13788 (150*2π)/189313 weeks
151.02194 -.14541 (151*2π)/189313 weeks
152.10514 -.23557 (152*2π)/189312 weeks
153.1061 -.36125 (153*2π)/189312 weeks
154.00707 -.45646 (154*2π)/189312 weeks
155-.09055 -.40141 (155*2π)/189312 weeks
156-.09784 -.37085 (156*2π)/189312 weeks
157-.11569 -.362 (157*2π)/189312 weeks
158-.14163 -.32182 (158*2π)/189312 weeks
159-.10048 -.26214 (159*2π)/189312 weeks
160-.01533 -.30398 (160*2π)/189312 weeks
161-.06436 -.41087 (161*2π)/189312 weeks
162-.18736 -.42875 (162*2π)/189312 weeks
163-.28347 -.30772 (163*2π)/189312 weeks
164-.23004 -.17492 (164*2π)/189312 weeks
165-.13837 -.15858 (165*2π)/189311 weeks
166-.10799 -.151 (166*2π)/189311 weeks
167-.05067 -.14535 (167*2π)/189311 weeks
168.00694 -.17081 (168*2π)/189311 weeks
169.03144 -.2551 (169*2π)/189311 weeks
170-.02898 -.28801 (170*2π)/189311 weeks
171-.03082 -.25484 (171*2π)/189311 weeks
172-.00251 -.26654 (172*2π)/189311 weeks
173.00027 -.32263 (173*2π)/189311 weeks
174-.08193 -.37012 (174*2π)/189311 weeks
175-.11914 -.28925 (175*2π)/189311 weeks
176-.08746 -.27354 (176*2π)/189311 weeks
177-.08371 -.27337 (177*2π)/189311 weeks
178-.093 -.28655 (178*2π)/189311 weeks
179-.10487 -.25903 (179*2π)/189311 weeks
180-.06606 -.27555 (180*2π)/189311 weeks
181-.10617 -.2829 (181*2π)/189310 weeks
182-.12228 -.26649 (182*2π)/189310 weeks
183-.11887 -.22832 (183*2π)/189310 weeks
184-.07674 -.20812 (184*2π)/189310 weeks
185-.07277 -.24492 (185*2π)/189310 weeks
186-.06316 -.23445 (186*2π)/189310 weeks
187-.05834 -.24579 (187*2π)/189310 weeks
188-.05623 -.23664 (188*2π)/189310 weeks
189-.03315 -.26573 (189*2π)/189310 weeks
190-.02134 -.2724 (190*2π)/189310 weeks
191-.00955 -.34398 (191*2π)/189310 weeks
192-.08936 -.40246 (192*2π)/189310 weeks
193-.18164 -.38918 (193*2π)/189310 weeks
194-.24303 -.29993 (194*2π)/189310 weeks
195-.20155 -.22974 (195*2π)/189310 weeks
196-.17898 -.24153 (196*2π)/189310 weeks
197-.17901 -.2173 (197*2π)/189310 weeks
198-.16646 -.1935 (198*2π)/189310 weeks
199-.1276 -.20739 (199*2π)/189310 weeks
200-.1433 -.25079 (200*2π)/18939 weeks
201-.1956 -.22515 (201*2π)/18939 weeks
202-.19691 -.18026 (202*2π)/18939 weeks
203-.1812 -.16121 (203*2π)/18939 weeks
204-.16075 -.1628 (204*2π)/18939 weeks
205-.18791 -.14688 (205*2π)/18939 weeks
206-.16854 -.10852 (206*2π)/18939 weeks
207-.13584 -.09338 (207*2π)/18939 weeks
208-.112 -.08634 (208*2π)/18939 weeks
209-.09435 -.10214 (209*2π)/18939 weeks
210-.07336 -.09163 (210*2π)/18939 weeks
211-.04872 -.11965 (211*2π)/18939 weeks
212-.06648 -.12512 (212*2π)/18939 weeks
213-.05268 -.12014 (213*2π)/18939 weeks
214-.04128 -.11479 (214*2π)/18939 weeks
215-.01278 -.14278 (215*2π)/18939 weeks
216-.03348 -.16197 (216*2π)/18939 weeks
217-.03067 -.1575 (217*2π)/18939 weeks
218-.05396 -.17146 (218*2π)/18939 weeks
219-.02806 -.1492 (219*2π)/18939 weeks
220-.03221 -.17973 (220*2π)/18939 weeks
221-.05179 -.17858 (221*2π)/18939 weeks
222-.05249 -.16899 (222*2π)/18939 weeks
223-.03012 -.13711 (223*2π)/18938 weeks
224-.00333 -.19198 (224*2π)/18938 weeks
225-.04258 -.20305 (225*2π)/18938 weeks
226-.05432 -.18211 (226*2π)/18938 weeks
227-.03139 -.17274 (227*2π)/18938 weeks
228-.01768 -.20973 (228*2π)/18938 weeks
229-.06395 -.22179 (229*2π)/18938 weeks
230-.07596 -.19162 (230*2π)/18938 weeks
231-.06359 -.18379 (231*2π)/18938 weeks
232-.04987 -.17809 (232*2π)/18938 weeks
233-.05792 -.20166 (233*2π)/18938 weeks
234-.06539 -.18099 (234*2π)/18938 weeks
235-.0304 -.19287 (235*2π)/18938 weeks
236-.04781 -.22519 (236*2π)/18938 weeks
237-.09702 -.23453 (237*2π)/18938 weeks
238-.12593 -.18228 (238*2π)/18938 weeks
239-.0895 -.14686 (239*2π)/18938 weeks
240-.05778 -.14398 (240*2π)/18938 weeks
241-.02118 -.16468 (241*2π)/18938 weeks
242-.01647 -.23453 (242*2π)/18938 weeks
243-.08563 -.26395 (243*2π)/18938 weeks
244-.143 -.22134 (244*2π)/18938 weeks
245-.11893 -.17208 (245*2π)/18938 weeks
246-.0958 -.20202 (246*2π)/18938 weeks
247-.15032 -.19865 (247*2π)/18938 weeks
248-.17106 -.14203 (248*2π)/18938 weeks
249-.1331 -.09616 (249*2π)/18938 weeks
250-.08514 -.10918 (250*2π)/18938 weeks
251-.0881 -.1202 (251*2π)/18938 weeks
252-.09822 -.11201 (252*2π)/18938 weeks
253-.0859 -.07937 (253*2π)/18937 weeks
254-.02508 -.07905 (254*2π)/18937 weeks
255-.00651 -.12853 (255*2π)/18937 weeks
256-.02158 -.15963 (256*2π)/18937 weeks
257-.0483 -.16282 (257*2π)/18937 weeks
258-.05823 -.13995 (258*2π)/18937 weeks
259-.0506 -.14395 (259*2π)/18937 weeks
260-.0347 -.1229 (260*2π)/18937 weeks
261.01737 -.14545 (261*2π)/18937 weeks
262.01676 -.20747 (262*2π)/18937 weeks
263-.04581 -.25734 (263*2π)/18937 weeks
264-.12173 -.22225 (264*2π)/18937 weeks
265-.10899 -.16674 (265*2π)/18937 weeks
266-.08256 -.16137 (266*2π)/18937 weeks
267-.08628 -.17359 (267*2π)/18937 weeks
268-.1041 -.15925 (268*2π)/18937 weeks
269-.0985 -.14563 (269*2π)/18937 weeks
270-.10347 -.13647 (270*2π)/18937 weeks
271-.0938 -.11491 (271*2π)/18937 weeks
272-.05906 -.09569 (272*2π)/18937 weeks
273-.03957 -.1182 (273*2π)/18937 weeks
274-.02889 -.13203 (274*2π)/18937 weeks
275-.01877 -.15077 (275*2π)/18937 weeks
276-.02806 -.17508 (276*2π)/18937 weeks
277-.04448 -.19629 (277*2π)/18937 weeks
278-.07731 -.19262 (278*2π)/18937 weeks
279-.08923 -.1669 (279*2π)/18937 weeks
280-.0796 -.14483 (280*2π)/18937 weeks
281-.04978 -.15873 (281*2π)/18937 weeks
282-.0703 -.18185 (282*2π)/18937 weeks
283-.08287 -.17742 (283*2π)/18937 weeks
284-.09197 -.17561 (284*2π)/18937 weeks
285-.1018 -.17255 (285*2π)/18937 weeks
286-.12906 -.16477 (286*2π)/18937 weeks
287-.1212 -.12251 (287*2π)/18937 weeks
288-.09276 -.12477 (288*2π)/18937 weeks
289-.0992 -.12796 (289*2π)/18937 weeks
290-.11329 -.11371 (290*2π)/18937 weeks
291-.08788 -.08759 (291*2π)/18937 weeks
292-.05545 -.0978 (292*2π)/18936 weeks
293-.05405 -.11826 (293*2π)/18936 weeks
294-.05096 -.1345 (294*2π)/18936 weeks
295-.08023 -.14485 (295*2π)/18936 weeks
296-.0978 -.12711 (296*2π)/18936 weeks
297-.1009 -.09357 (297*2π)/18936 weeks
298-.05828 -.07838 (298*2π)/18936 weeks
299-.03855 -.09792 (299*2π)/18936 weeks
300-.03519 -.11252 (300*2π)/18936 weeks
301-.04555 -.12303 (301*2π)/18936 weeks
302-.0452 -.1139 (302*2π)/18936 weeks
303-.03771 -.12838 (303*2π)/18936 weeks
304-.04708 -.12196 (304*2π)/18936 weeks
305-.03563 -.10282 (305*2π)/18936 weeks
306-.00658 -.10849 (306*2π)/18936 weeks
307.00984 -.14395 (307*2π)/18936 weeks
308.00016 -.18102 (308*2π)/18936 weeks
309-.01993 -.18748 (309*2π)/18936 weeks
310-.02914 -.19625 (310*2π)/18936 weeks
311-.05311 -.22183 (311*2π)/18936 weeks
312-.09277 -.22109 (312*2π)/18936 weeks
313-.1246 -.18879 (313*2π)/18936 weeks
314-.11506 -.15895 (314*2π)/18936 weeks
315-.10487 -.15585 (315*2π)/18936 weeks
316-.1072 -.15568 (316*2π)/18936 weeks
317-.12082 -.14914 (317*2π)/18936 weeks
318-.11843 -.13428 (318*2π)/18936 weeks
319-.11348 -.12809 (319*2π)/18936 weeks
320-.1051 -.12356 (320*2π)/18936 weeks
321-.1232 -.12598 (321*2π)/18936 weeks
322-.1319 -.09246 (322*2π)/18936 weeks
323-.10666 -.07082 (323*2π)/18936 weeks
324-.07852 -.0687 (324*2π)/18936 weeks
325-.05534 -.0742 (325*2π)/18936 weeks
326-.02596 -.09593 (326*2π)/18936 weeks
327-.03547 -.15517 (327*2π)/18936 weeks
328-.10396 -.15812 (328*2π)/18936 weeks
329-.12089 -.11776 (329*2π)/18936 weeks
330-.10685 -.09103 (330*2π)/18936 weeks
331-.10467 -.07489 (331*2π)/18936 weeks
332-.08332 -.04461 (332*2π)/18936 weeks
333-.03 -.04695 (333*2π)/18936 weeks
334-.01619 -.08737 (334*2π)/18936 weeks
335-.01408 -.10575 (335*2π)/18936 weeks
336-.01496 -.12293 (336*2π)/18936 weeks
337-.02604 -.14659 (337*2π)/18936 weeks
338-.06655 -.1528 (338*2π)/18936 weeks
339-.07883 -.11759 (339*2π)/18936 weeks
340-.0542 -.11338 (340*2π)/18936 weeks
341-.05284 -.11608 (341*2π)/18936 weeks
342-.05996 -.10928 (342*2π)/18936 weeks
343-.04392 -.10646 (343*2π)/18936 weeks
344-.0196 -.12818 (344*2π)/18936 weeks
345-.03989 -.16265 (345*2π)/18935 weeks
346-.07579 -.16116 (346*2π)/18935 weeks
347-.09184 -.13378 (347*2π)/18935 weeks
348-.09172 -.10915 (348*2π)/18935 weeks
349-.06725 -.0921 (349*2π)/18935 weeks
350-.03582 -.10588 (350*2π)/18935 weeks
351-.0355 -.12409 (351*2π)/18935 weeks
352-.03308 -.12957 (352*2π)/18935 weeks
353-.02492 -.14911 (353*2π)/18935 weeks
354-.04015 -.1814 (354*2π)/18935 weeks
355-.08121 -.20475 (355*2π)/18935 weeks
356-.13144 -.1785 (356*2π)/18935 weeks
357-.14681 -.12659 (357*2π)/18935 weeks
358-.11957 -.07341 (358*2π)/18935 weeks
359-.07304 -.06783 (359*2π)/18935 weeks
360-.03618 -.08483 (360*2π)/18935 weeks
361.0006 -.12626 (361*2π)/18935 weeks
362-.00688 -.19673 (362*2π)/18935 weeks
363-.09053 -.25728 (363*2π)/18935 weeks
364-.19119 -.2041 (364*2π)/18935 weeks
365-.19407 -.10718 (365*2π)/18935 weeks
366-.14984 -.07637 (366*2π)/18935 weeks
367-.12831 -.0842 (367*2π)/18935 weeks
368-.13412 -.05716 (368*2π)/18935 weeks
369-.08358 -.03925 (369*2π)/18935 weeks
370-.05246 -.07287 (370*2π)/18935 weeks
371-.06626 -.11492 (371*2π)/18935 weeks
372-.10447 -.11657 (372*2π)/18935 weeks
373-.10679 -.06962 (373*2π)/18935 weeks
374-.0707 -.06132 (374*2π)/18935 weeks
375-.05547 -.08963 (375*2π)/18935 weeks
376-.06528 -.10283 (376*2π)/18935 weeks
377-.07281 -.09925 (377*2π)/18935 weeks
378-.06637 -.10418 (378*2π)/18935 weeks
379-.08244 -.11665 (379*2π)/18935 weeks
380-.09543 -.1025 (380*2π)/18935 weeks
381-.09763 -.09296 (381*2π)/18935 weeks
382-.09571 -.07515 (382*2π)/18935 weeks
383-.08281 -.06425 (383*2π)/18935 weeks
384-.0568 -.05534 (384*2π)/18935 weeks
385-.03206 -.07794 (385*2π)/18935 weeks
386-.03313 -.10885 (386*2π)/18935 weeks
387-.0489 -.13362 (387*2π)/18935 weeks
388-.08062 -.13334