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Fourier Analysis of AAPL (Apple Inc.)


AAPL (Apple Inc.) appears to have interesting cyclic behaviour every 189 weeks (3.6062*sine), 111 weeks (2.7942*sine), and 172 weeks (2.25*sine).

AAPL (Apple Inc.) has an average price of 17.69 (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 12/12/1980 to 2/21/2017 for AAPL (Apple Inc.), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
017.69464   0 
124.31233 -16.79854 (1*2π)/18891,889 weeks
210.14128 -19.4634 (2*2π)/1889945 weeks
33.09367 -14.62551 (3*2π)/1889630 weeks
41.14396 -10.60708 (4*2π)/1889472 weeks
5-.2563 -8.15605 (5*2π)/1889378 weeks
6.40455 -5.66375 (6*2π)/1889315 weeks
71.01063 -5.96293 (7*2π)/1889270 weeks
8.00924 -6.15942 (8*2π)/1889236 weeks
9-1.44793 -5.65164 (9*2π)/1889210 weeks
10-2.07937 -3.60623 (10*2π)/1889189 weeks
11-1.62124 -2.25004 (11*2π)/1889172 weeks
12-.94461 -1.54863 (12*2π)/1889157 weeks
13-.55014 -1.12811 (13*2π)/1889145 weeks
14.02407 -.30311 (14*2π)/1889135 weeks
151.693 -.47817 (15*2π)/1889126 weeks
162.11938 -1.83342 (16*2π)/1889118 weeks
171.40379 -2.79423 (17*2π)/1889111 weeks
18.33162 -2.53407 (18*2π)/1889105 weeks
19.29219 -1.91617 (19*2π)/188999 weeks
20.31669 -1.87493 (20*2π)/188994 weeks
21.38543 -1.53582 (21*2π)/188990 weeks
22.56092 -1.4566 (22*2π)/188986 weeks
23.95518 -1.50017 (23*2π)/188982 weeks
241.05173 -2.19277 (24*2π)/188979 weeks
25.46744 -2.54293 (25*2π)/188976 weeks
26-.19628 -2.49815 (26*2π)/188973 weeks
27-.64948 -1.88361 (27*2π)/188970 weeks
28-.53017 -1.2469 (28*2π)/188967 weeks
29-.09693 -.95019 (29*2π)/188965 weeks
30.20501 -1.10124 (30*2π)/188963 weeks
31.12831 -1.21477 (31*2π)/188961 weeks
32.26841 -1.2179 (32*2π)/188959 weeks
33.25272 -1.33525 (33*2π)/188957 weeks
34.07648 -1.42424 (34*2π)/188956 weeks
35-.10736 -1.38595 (35*2π)/188954 weeks
36-.24755 -1.14731 (36*2π)/188952 weeks
37-.20788 -.9269 (37*2π)/188951 weeks
38.05309 -.87546 (38*2π)/188950 weeks
39.14759 -1.03037 (39*2π)/188948 weeks
40-.13812 -.97301 (40*2π)/188947 weeks
41.09022 -.7596 (41*2π)/188946 weeks
42.38088 -.97365 (42*2π)/188945 weeks
43.13837 -1.27048 (43*2π)/188944 weeks
44-.19093 -1.15922 (44*2π)/188943 weeks
45-.13068 -.88819 (45*2π)/188942 weeks
46.00254 -.96124 (46*2π)/188941 weeks
47-.18268 -1.0139 (47*2π)/188940 weeks
48-.29017 -.8575 (48*2π)/188939 weeks
49-.26428 -.69738 (49*2π)/188939 weeks
50-.09256 -.56428 (50*2π)/188938 weeks
51-.05105 -.67339 (51*2π)/188937 weeks
52-.08924 -.65464 (52*2π)/188936 weeks
53-.0189 -.5617 (53*2π)/188936 weeks
54.07602 -.58398 (54*2π)/188935 weeks
55.05499 -.67353 (55*2π)/188934 weeks
56-.05662 -.61485 (56*2π)/188934 weeks
57.10137 -.46511 (57*2π)/188933 weeks
58.31883 -.56526 (58*2π)/188933 weeks
59.321 -.89329 (59*2π)/188932 weeks
60-.02927 -1.06472 (60*2π)/188931 weeks
61-.29818 -.77498 (61*2π)/188931 weeks
62-.25591 -.5191 (62*2π)/188930 weeks
63-.07351 -.44277 (63*2π)/188930 weeks
64.03358 -.47595 (64*2π)/188930 weeks
65.09752 -.44103 (65*2π)/188929 weeks
66.22902 -.59605 (66*2π)/188929 weeks
67.12686 -.81601 (67*2π)/188928 weeks
68-.12594 -.82518 (68*2π)/188928 weeks
69-.28654 -.62622 (69*2π)/188927 weeks
70-.17632 -.4279 (70*2π)/188927 weeks
71-.10588 -.41038 (71*2π)/188927 weeks
72-.07529 -.33579 (72*2π)/188926 weeks
73.05826 -.31114 (73*2π)/188926 weeks
74.18689 -.42394 (74*2π)/188926 weeks
75.07779 -.61687 (75*2π)/188925 weeks
76-.16472 -.48645 (76*2π)/188925 weeks
77-.10239 -.23188 (77*2π)/188925 weeks
78.1486 -.13653 (78*2π)/188924 weeks
79.33184 -.29365 (79*2π)/188924 weeks
80.34569 -.43325 (80*2π)/188924 weeks
81.38171 -.54876 (81*2π)/188923 weeks
82.2967 -.6815 (82*2π)/188923 weeks
83.10982 -.71386 (83*2π)/188923 weeks
84.02449 -.66622 (84*2π)/188922 weeks
85.05759 -.51052 (85*2π)/188922 weeks
86.14026 -.56077 (86*2π)/188922 weeks
87.11889 -.59342 (87*2π)/188922 weeks
88.08759 -.6119 (88*2π)/188921 weeks
89.08433 -.59663 (89*2π)/188921 weeks
90.14899 -.69583 (90*2π)/188921 weeks
91-.02356 -.77723 (91*2π)/188921 weeks
92-.1529 -.65954 (92*2π)/188921 weeks
93-.12542 -.53446 (93*2π)/188920 weeks
94-.0127 -.5613 (94*2π)/188920 weeks
95-.0804 -.6388 (95*2π)/188920 weeks
96-.13082 -.5711 (96*2π)/188920 weeks
97-.11782 -.5959 (97*2π)/188919 weeks
98-.19447 -.61707 (98*2π)/188919 weeks
99-.32538 -.54057 (99*2π)/188919 weeks
100-.35713 -.3519 (100*2π)/188919 weeks
101-.2217 -.25169 (101*2π)/188919 weeks
102-.09576 -.22689 (102*2π)/188919 weeks
103-.04469 -.30482 (103*2π)/188918 weeks
104-.10539 -.33475 (104*2π)/188918 weeks
105-.06704 -.25405 (105*2π)/188918 weeks
106.00002 -.28581 (106*2π)/188918 weeks
107-.00075 -.32688 (107*2π)/188918 weeks
108-.06097 -.30708 (108*2π)/188917 weeks
109-.00354 -.20201 (109*2π)/188917 weeks
110.12055 -.26702 (110*2π)/188917 weeks
111.13425 -.36139 (111*2π)/188917 weeks
112.08 -.41615 (112*2π)/188917 weeks
113.07465 -.36305 (113*2π)/188917 weeks
114.13779 -.41929 (114*2π)/188917 weeks
115.09238 -.52715 (115*2π)/188916 weeks
116-.00486 -.56258 (116*2π)/188916 weeks
117-.1038 -.49465 (117*2π)/188916 weeks
118-.11023 -.4094 (118*2π)/188916 weeks
119-.08611 -.38141 (119*2π)/188916 weeks
120-.06205 -.37787 (120*2π)/188916 weeks
121-.09874 -.35126 (121*2π)/188916 weeks
122-.05077 -.28981 (122*2π)/188915 weeks
123.04823 -.32514 (123*2π)/188915 weeks
124.04624 -.42626 (124*2π)/188915 weeks
125-.05011 -.4424 (125*2π)/188915 weeks
126-.05459 -.39763 (126*2π)/188915 weeks
127-.05475 -.41585 (127*2π)/188915 weeks
128-.09482 -.40776 (128*2π)/188915 weeks
129-.09967 -.33726 (129*2π)/188915 weeks
130-.01111 -.32215 (130*2π)/188915 weeks
131.00144 -.41227 (131*2π)/188914 weeks
132-.06574 -.47211 (132*2π)/188914 weeks
133-.15332 -.45474 (133*2π)/188914 weeks
134-.18092 -.35853 (134*2π)/188914 weeks
135-.17886 -.33223 (135*2π)/188914 weeks
136-.16904 -.29465 (136*2π)/188914 weeks
137-.16583 -.27814 (137*2π)/188914 weeks
138-.16157 -.23659 (138*2π)/188914 weeks
139-.12904 -.21082 (139*2π)/188914 weeks
140-.09077 -.16942 (140*2π)/188913 weeks
141-.02954 -.16802 (141*2π)/188913 weeks
142.00734 -.21684 (142*2π)/188913 weeks
143.0278 -.25342 (143*2π)/188913 weeks
144.01283 -.25997 (144*2π)/188913 weeks
145.04678 -.28902 (145*2π)/188913 weeks
146.0513 -.32344 (146*2π)/188913 weeks
147.02726 -.39183 (147*2π)/188913 weeks
148-.04492 -.45008 (148*2π)/188913 weeks
149-.14971 -.41422 (149*2π)/188913 weeks
150-.22192 -.3413 (150*2π)/188913 weeks
151-.23569 -.22018 (151*2π)/188913 weeks
152-.16493 -.11762 (152*2π)/188912 weeks
153-.04211 -.08703 (153*2π)/188912 weeks
154.06474 -.17476 (154*2π)/188912 weeks
155.02926 -.246 (155*2π)/188912 weeks
156.01732 -.25846 (156*2π)/188912 weeks
157.02022 -.28456 (157*2π)/188912 weeks
158-.01845 -.32013 (158*2π)/188912 weeks
159-.08388 -.27684 (159*2π)/188912 weeks
160-.03813 -.1765 (160*2π)/188912 weeks
161.07306 -.20436 (161*2π)/188912 weeks
162.12729 -.32804 (162*2π)/188912 weeks
163.03296 -.44501 (163*2π)/188912 weeks
164-.09272 -.42489 (164*2π)/188912 weeks
165-.12075 -.36518 (165*2π)/188911 weeks
166-.15477 -.34269 (166*2π)/188911 weeks
167-.18263 -.28906 (167*2π)/188911 weeks
168-.18458 -.21519 (168*2π)/188911 weeks
169-.10816 -.17278 (169*2π)/188911 weeks
170-.07618 -.21696 (170*2π)/188911 weeks
171-.10214 -.2091 (171*2π)/188911 weeks
172-.09848 -.16653 (172*2π)/188911 weeks
173-.0388 -.13579 (173*2π)/188911 weeks
174.02645 -.21436 (174*2π)/188911 weeks
175-.02997 -.24921 (175*2π)/188911 weeks
176-.04082 -.23074 (176*2π)/188911 weeks
177-.04367 -.22111 (177*2π)/188911 weeks
178-.0266 -.23276 (178*2π)/188911 weeks
179-.05821 -.24443 (179*2π)/188911 weeks
180-.03135 -.20573 (180*2π)/188910 weeks
181-.02019 -.23322 (181*2π)/188910 weeks
182-.02299 -.26007 (182*2π)/188910 weeks
183-.05832 -.27201 (183*2π)/188910 weeks
184-.08923 -.23113 (184*2π)/188910 weeks
185-.06801 -.23136 (185*2π)/188910 weeks
186-.07766 -.21525 (186*2π)/188910 weeks
187-.07113 -.20698 (187*2π)/188910 weeks
188-.09433 -.19668 (188*2π)/188910 weeks
189-.07745 -.17187 (189*2π)/188910 weeks
190-.08818 -.13089 (190*2π)/188910 weeks
191-.02012 -.07355 (191*2π)/188910 weeks
192.0702 -.1024 (192*2π)/188910 weeks
193.12434 -.18168 (193*2π)/188910 weeks
194.08228 -.27172 (194*2π)/188910 weeks
195.02151 -.26621 (195*2π)/188910 weeks
196.02999 -.26501 (196*2π)/188910 weeks
197.01328 -.27456 (197*2π)/188910 weeks
198-.02224 -.27493 (198*2π)/188910 weeks
199-.02292 -.23171 (199*2π)/18899 weeks
200.03314 -.22735 (200*2π)/18899 weeks
201.03899 -.27553 (201*2π)/18899 weeks
202.01154 -.2975 (202*2π)/18899 weeks
203-.00954 -.30268 (203*2π)/18899 weeks
204-.0006 -.2883 (204*2π)/18899 weeks
205-.00616 -.32811 (205*2π)/18899 weeks
206-.03994 -.34006 (206*2π)/18899 weeks
207-.06588 -.33117 (207*2π)/18899 weeks
208-.09387 -.31814 (208*2π)/18899 weeks
209-.09454 -.31264 (209*2π)/18899 weeks
210-.12324 -.29614 (210*2π)/18899 weeks
211-.11041 -.26421 (211*2π)/18899 weeks
212-.10957 -.27533 (212*2π)/18899 weeks
213-.11752 -.26831 (213*2π)/18899 weeks
214-.14297 -.26029 (214*2π)/18899 weeks
215-.1327 -.2204 (215*2π)/18899 weeks
216-.11635 -.22339 (216*2π)/18899 weeks
217-.11914 -.20656 (217*2π)/18899 weeks
218-.10358 -.23222 (218*2π)/18899 weeks
219-.12907 -.20652 (219*2π)/18899 weeks
220-.10733 -.19525 (220*2π)/18899 weeks
221-.09851 -.20885 (221*2π)/18899 weeks
222-.09567 -.22342 (222*2π)/18899 weeks
223-.14931 -.20989 (223*2π)/18898 weeks
224-.11837 -.16347 (224*2π)/18898 weeks
225-.09272 -.17701 (225*2π)/18898 weeks
226-.10174 -.19662 (226*2π)/18898 weeks
227-.12788 -.18031 (227*2π)/18898 weeks
228-.10309 -.13907 (228*2π)/18898 weeks
229-.06927 -.16061 (229*2π)/18898 weeks
230-.07871 -.18209 (230*2π)/18898 weeks
231-.08524 -.18436 (231*2π)/18898 weeks
232-.10225 -.16855 (232*2π)/18898 weeks
233-.07914 -.16834 (233*2π)/18898 weeks
234-.09872 -.18577 (234*2π)/18898 weeks
235-.10737 -.14398 (235*2π)/18898 weeks
236-.07826 -.11729 (236*2π)/18898 weeks
237-.02729 -.13969 (237*2π)/18898 weeks
238-.0352 -.19619 (238*2π)/18898 weeks
239-.0708 -.20577 (239*2π)/18898 weeks
240-.10651 -.19967 (240*2π)/18898 weeks
241-.14215 -.1565 (241*2π)/18898 weeks
242-.10437 -.08864 (242*2π)/18898 weeks
243-.03338 -.08974 (243*2π)/18898 weeks
244-.01044 -.15047 (244*2π)/18898 weeks
245-.05004 -.16231 (245*2π)/18898 weeks
246-.0259 -.12053 (246*2π)/18898 weeks
247.01974 -.15067 (247*2π)/18898 weeks
248.0162 -.21148 (248*2π)/18898 weeks
249-.03175 -.23753 (249*2π)/18898 weeks
250-.04862 -.2111 (250*2π)/18898 weeks
251-.04374 -.2054 (251*2π)/18898 weeks
252-.03637 -.22644 (252*2π)/18897 weeks
253-.07047 -.26289 (253*2π)/18897 weeks
254-.12426 -.23563 (254*2π)/18897 weeks
255-.12802 -.19418 (255*2π)/18897 weeks
256-.10783 -.16851 (256*2π)/18897 weeks
257-.08461 -.1712 (257*2π)/18897 weeks
258-.09548 -.18771 (258*2π)/18897 weeks
259-.08931 -.19715 (259*2π)/18897 weeks
260-.12592 -.21661 (260*2π)/18897 weeks
261-.16915 -.16878 (261*2π)/18897 weeks
262-.16343 -.09774 (262*2π)/18897 weeks
263-.08921 -.06345 (263*2π)/18897 weeks
264-.03931 -.118 (264*2π)/18897 weeks
265-.0555 -.14933 (265*2π)/18897 weeks
266-.07021 -.14084 (266*2π)/18897 weeks
267-.05467 -.13038 (267*2π)/18897 weeks
268-.04601 -.14734 (268*2π)/18897 weeks
269-.04588 -.15211 (269*2π)/18897 weeks
270-.03687 -.17064 (270*2π)/18897 weeks
271-.04183 -.19781 (271*2π)/18897 weeks
272-.08213 -.20224 (272*2π)/18897 weeks
273-.09718 -.19365 (273*2π)/18897 weeks
274-.11231 -.18422 (274*2π)/18897 weeks
275-.12645 -.1601 (275*2π)/18897 weeks
276-.12608 -.13788 (276*2π)/18897 weeks
277-.10476 -.11147 (277*2π)/18897 weeks
278-.07461 -.11467 (278*2π)/18897 weeks
279-.06468 -.13369 (279*2π)/18897 weeks
280-.0842 -.15575 (280*2π)/18897 weeks
281-.10397 -.12677 (281*2π)/18897 weeks
282-.08732 -.11494 (282*2π)/18897 weeks
283-.07958 -.11088 (283*2π)/18897 weeks
284-.07058 -.10613 (284*2π)/18897 weeks
285-.05899 -.09534 (285*2π)/18897 weeks
286-.02204 -.1146 (286*2π)/18897 weeks
287-.03479 -.14635 (287*2π)/18897 weeks
288-.04486 -.13567 (288*2π)/18897 weeks
289-.03603 -.13059 (289*2π)/18897 weeks
290-.01982 -.15907 (290*2π)/18897 weeks
291-.04323 -.18312 (291*2π)/18896 weeks
292-.06986 -.17245 (292*2π)/18896 weeks
293-.07843 -.16397 (293*2π)/18896 weeks
294-.08307 -.13466 (294*2π)/18896 weeks
295-.05778 -.12597 (295*2π)/18896 weeks
296-.03267 -.13555 (296*2π)/18896 weeks
297-.02746 -.17903 (297*2π)/18896 weeks
298-.05941 -.19029 (298*2π)/18896 weeks
299-.07615 -.18189 (299*2π)/18896 weeks
300-.08561 -.1683 (300*2π)/18896 weeks
301-.07637 -.16499 (301*2π)/18896 weeks
302-.08732 -.17354 (302*2π)/18896 weeks
303-.08229 -.16034 (303*2π)/18896 weeks
304-.07008 -.16916 (304*2π)/18896 weeks
305-.08496 -.19267 (305*2π)/18896 weeks
306-.12235 -.19878 (306*2π)/18896 weeks
307-.15062 -.17739 (307*2π)/18896 weeks
308-.14897 -.1452 (308*2π)/18896 weeks
309-.14998 -.1312 (309*2π)/18896 weeks
310-.16381 -.11005 (310*2π)/18896 weeks
311-.14975 -.07373 (311*2π)/18896 weeks
312-.11279 -.05142 (312*2π)/18896 weeks
313-.0799 -.0697 (313*2π)/18896 weeks
314-.07927 -.08588 (314*2π)/18896 weeks
315-.08093 -.08482 (315*2π)/18896 weeks
316-.07699 -.07616 (316*2π)/18896 weeks
317-.06084 -.08135 (317*2π)/18896 weeks
318-.0559 -.08949 (318*2π)/18896 weeks
319-.05149 -.09516 (319*2π)/18896 weeks
320-.05855 -.0841 (320*2π)/18896 weeks
321-.03029 -.0771 (321*2π)/18896 weeks
322-.01153 -.10684 (322*2π)/18896 weeks
323-.01577 -.13499 (323*2π)/18896 weeks
324-.02886 -.15292 (324*2π)/18896 weeks
325-.05154 -.17164 (325*2π)/18896 weeks
326-.10503 -.1626 (326*2π)/18896 weeks
327-.11397 -.09397 (327*2π)/18896 weeks
328-.06506 -.077 (328*2π)/18896 weeks
329-.03462 -.09358 (329*2π)/18896 weeks
330-.02617 -.10203 (330*2π)/18896 weeks
331-.00323 -.12088 (331*2π)/18896 weeks
332-.00408 -.17 (332*2π)/18896 weeks
333-.04991 -.1884 (333*2π)/18896 weeks
334-.06827 -.18162 (334*2π)/18896 weeks
335-.08461 -.17473 (335*2π)/18896 weeks
336-.10513 -.16241 (336*2π)/18896 weeks
337-.11621 -.12625 (337*2π)/18896 weeks
338-.08212 -.10689 (338*2π)/18896 weeks
339-.06726 -.13279 (339*2π)/18896 weeks
340-.07434 -.13319 (340*2π)/18896 weeks
341-.07547 -.12651 (341*2π)/18896 weeks
342-.06957 -.14172 (342*2π)/18896 weeks
343-.08227 -.16433 (343*2π)/18896 weeks
344-.11992 -.15106 (344*2π)/18895 weeks
345-.12358 -.11381 (345*2π)/18895 weeks
346-.09828 -.09183 (346*2π)/18895 weeks
347-.07587 -.09231 (347*2π)/18895 weeks
348-.05505 -.11367 (348*2π)/18895 weeks
349-.05992 -.1464 (349*2π)/18895 weeks
350-.08283 -.14943 (350*2π)/18895 weeks
351-.0901 -.14762 (351*2π)/18895 weeks
352-.10533 -.1561 (352*2π)/18895 weeks
353-.13817 -.14876 (353*2π)/18895 weeks
354-.16448 -.1173 (354*2π)/18895 weeks
355-.15121 -.06211 (355*2π)/18895 weeks
356-.10381 -.03604 (356*2π)/18895 weeks
357-.04914 -.04753 (357*2π)/18895 weeks
358-.03279 -.09609 (358*2π)/18895 weeks
359-.04319 -.13631 (359*2π)/18895 weeks
360-.07033 -.17579 (360*2π)/18895 weeks
361-.13714 -.18548 (361*2π)/18895 weeks
362-.2151 -.13213 (362*2π)/18895 weeks
363-.20185 -.01866 (363*2π)/18895 weeks
364-.10914 .02117 (364*2π)/18895 weeks
365-.05957 -.01736 (365*2π)/18895 weeks
366-.05736 -.04777 (366*2π)/18895 weeks
367-.04664 -.03492 (367*2π)/18895 weeks
368-.01034 -.06931 (368*2π)/18895 weeks
369-.03086 -.11306 (369*2π)/18895 weeks
370-.07512 -.12031 (370*2π)/18895 weeks
371-.09334 -.08706 (371*2π)/18895 weeks
372-.05649 -.05824 (372*2π)/18895 weeks
373-.03196 -.08692 (373*2π)/18895 weeks
374-.04946 -.11619 (374*2π)/18895 weeks
375-.06817 -.11208 (375*2π)/18895 weeks
376-.07083 -.10153 (376*2π)/18895 weeks
377-.07006 -.1069 (377*2π)/18895 weeks
378-.08829 -.10182 (378*2π)/18895 weeks
379-.08371 -.08152 (379*2π)/18895 weeks
380-.07486 -.0762 (380*2π)/18895 weeks
381-.0606 -.06905 (381*2π)/18895 weeks
382-.04522 -.07595 (382*2π)/18895 weeks
383-.02728 -.09073 (383*2π)/18895 weeks
384-.03326 -.12345 (384*2π)/18895 weeks
385-.0609 -.13904 (385*2π)/18895 weeks
386-.08852 -.13739 (386*2π)/18895 weeks
387-.10804 -.11014 (387*2π)/18895 weeks
388-.10793 -.08781 (388*2π)/18895 weeks
389-.0922 -.06622 (389*2π)/1889