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Fourier Analysis of AAPL (Apple Inc.)


AAPL (Apple Inc.) appears to have interesting cyclic behaviour every 188 weeks (3.9974*sine), 171 weeks (2.6088*sine), and 188 weeks (2.1534*cosine).

AAPL (Apple Inc.) has an average price of 17.42 (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 1/9/2017 for AAPL (Apple Inc.), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
017.41519   0 
123.9631 -16.46724 (1*2π)/18831,883 weeks
210.09579 -19.17605 (2*2π)/1883942 weeks
33.12843 -14.49834 (3*2π)/1883628 weeks
41.16502 -10.56193 (4*2π)/1883471 weeks
5-.27558 -8.19106 (5*2π)/1883377 weeks
6.29876 -5.63908 (6*2π)/1883314 weeks
71.01938 -5.86777 (7*2π)/1883269 weeks
8.14598 -6.17462 (8*2π)/1883235 weeks
9-1.2995 -5.89391 (9*2π)/1883209 weeks
10-2.15343 -3.99736 (10*2π)/1883188 weeks
11-1.90204 -2.60879 (11*2π)/1883171 weeks
12-1.35327 -1.80825 (12*2π)/1883157 weeks
13-1.0532 -1.31032 (13*2π)/1883145 weeks
14-.66006 -.33281 (14*2π)/1883135 weeks
151.03067 -.1054 (15*2π)/1883126 weeks
161.80495 -1.2643 (16*2π)/1883118 weeks
171.41452 -2.35261 (17*2π)/1883111 weeks
18.36689 -2.36665 (18*2π)/1883105 weeks
19.1972 -1.79488 (19*2π)/188399 weeks
20.20712 -1.74696 (20*2π)/188394 weeks
21.2008 -1.38558 (21*2π)/188390 weeks
22.34988 -1.22128 (22*2π)/188386 weeks
23.78036 -1.09251 (23*2π)/188382 weeks
241.15347 -1.69263 (24*2π)/188378 weeks
25.80412 -2.22181 (25*2π)/188375 weeks
26.21235 -2.4655 (26*2π)/188372 weeks
27-.42103 -2.10704 (27*2π)/188370 weeks
28-.57323 -1.49541 (28*2π)/188367 weeks
29-.30503 -1.03544 (29*2π)/188365 weeks
30.03654 -1.02201 (30*2π)/188363 weeks
31.02366 -1.12353 (31*2π)/188361 weeks
32.1844 -1.06142 (32*2π)/188359 weeks
33.26171 -1.15535 (33*2π)/188357 weeks
34.1785 -1.30957 (34*2π)/188355 weeks
35.02322 -1.38229 (35*2π)/188354 weeks
36-.20246 -1.25153 (36*2π)/188352 weeks
37-.29464 -1.03837 (37*2π)/188351 weeks
38-.09637 -.85828 (38*2π)/188350 weeks
39.09187 -.93484 (39*2π)/188348 weeks
40-.18717 -1.01004 (40*2π)/188347 weeks
41-.10802 -.70265 (41*2π)/188346 weeks
42.28502 -.69912 (42*2π)/188345 weeks
43.29372 -1.06082 (43*2π)/188344 weeks
44-.014 -1.17427 (44*2π)/188343 weeks
45-.10626 -.93344 (45*2π)/188342 weeks
46.05931 -.91727 (46*2π)/188341 weeks
47-.03974 -1.06934 (47*2π)/188340 weeks
48-.21167 -1.03439 (48*2π)/188339 weeks
49-.30722 -.91409 (49*2π)/188338 weeks
50-.2574 -.69333 (50*2π)/188338 weeks
51-.16955 -.73704 (51*2π)/188337 weeks
52-.20997 -.74865 (52*2π)/188336 weeks
53-.21466 -.62841 (53*2π)/188336 weeks
54-.12503 -.56259 (54*2π)/188335 weeks
55-.06949 -.63271 (55*2π)/188334 weeks
56-.20087 -.66764 (56*2π)/188334 weeks
57-.20076 -.4409 (57*2π)/188333 weeks
58.027 -.3028 (58*2π)/188332 weeks
59.31373 -.48679 (59*2π)/188332 weeks
60.26492 -.87542 (60*2π)/188331 weeks
61-.08691 -.91925 (61*2π)/188331 weeks
62-.27891 -.7569 (62*2π)/188330 weeks
63-.25283 -.58235 (63*2π)/188330 weeks
64-.17697 -.5126 (64*2π)/188329 weeks
65-.1726 -.39307 (65*2π)/188329 weeks
66.04005 -.34764 (66*2π)/188329 weeks
67.19883 -.53864 (67*2π)/188328 weeks
68.11211 -.76293 (68*2π)/188328 weeks
69-.12889 -.82257 (69*2π)/188327 weeks
70-.22862 -.65629 (70*2π)/188327 weeks
71-.22871 -.60164 (71*2π)/188327 weeks
72-.30043 -.52915 (72*2π)/188326 weeks
73-.27716 -.3889 (73*2π)/188326 weeks
74-.10692 -.30244 (74*2π)/188325 weeks
75.03619 -.48861 (75*2π)/188325 weeks
76-.17875 -.65285 (76*2π)/188325 weeks
77-.39745 -.51945 (77*2π)/188324 weeks
78-.41843 -.24581 (78*2π)/188324 weeks
79-.24141 -.11738 (79*2π)/188324 weeks
80-.12741 -.10972 (80*2π)/188324 weeks
81.02051 -.07847 (81*2π)/188323 weeks
82.14686 -.16188 (82*2π)/188323 weeks
83.12759 -.32466 (83*2π)/188323 weeks
84.07434 -.42371 (84*2π)/188322 weeks
85-.04225 -.33052 (85*2π)/188322 weeks
86.02496 -.27182 (86*2π)/188322 weeks
87.05279 -.27509 (87*2π)/188322 weeks
88.06316 -.29625 (88*2π)/188321 weeks
89.04261 -.27039 (89*2π)/188321 weeks
90.19511 -.22209 (90*2π)/188321 weeks
91.25626 -.3907 (91*2π)/188321 weeks
92.14204 -.49167 (92*2π)/188320 weeks
93.0254 -.44811 (93*2π)/188320 weeks
94.0883 -.34743 (94*2π)/188320 weeks
95.1535 -.42184 (95*2π)/188320 weeks
96.09884 -.43558 (96*2π)/188320 weeks
97.14997 -.43105 (97*2π)/188319 weeks
98.19911 -.50985 (98*2π)/188319 weeks
99.13736 -.65167 (99*2π)/188319 weeks
100-.05164 -.69707 (100*2π)/188319 weeks
101-.14576 -.60514 (101*2π)/188319 weeks
102-.17865 -.47482 (102*2π)/188318 weeks
103-.1139 -.42095 (103*2π)/188318 weeks
104-.10532 -.48919 (104*2π)/188318 weeks
105-.17915 -.44068 (105*2π)/188318 weeks
106-.15471 -.3787 (106*2π)/188318 weeks
107-.10878 -.37101 (107*2π)/188318 weeks
108-.13864 -.44021 (108*2π)/188317 weeks
109-.26336 -.37688 (109*2π)/188317 weeks
110-.22858 -.25861 (110*2π)/188317 weeks
111-.15033 -.21439 (111*2π)/188317 weeks
112-.09437 -.25561 (112*2π)/188317 weeks
113-.15058 -.23247 (113*2π)/188317 weeks
114-.10377 -.14161 (114*2π)/188317 weeks
115.00922 -.14593 (115*2π)/188316 weeks
116.09564 -.21655 (116*2π)/188316 weeks
117.07439 -.31176 (117*2π)/188316 weeks
118.01228 -.33668 (118*2π)/188316 weeks
119-.01678 -.33352 (119*2π)/188316 weeks
120-.00868 -.31527 (120*2π)/188316 weeks
121-.04061 -.36593 (121*2π)/188316 weeks
122-.12599 -.34081 (122*2π)/188315 weeks
123-.12651 -.23171 (123*2π)/188315 weeks
124-.03113 -.18723 (124*2π)/188315 weeks
125.00305 -.25559 (125*2π)/188315 weeks
126-.02091 -.25606 (126*2π)/188315 weeks
127.009 -.25217 (127*2π)/188315 weeks
128.02754 -.2977 (128*2π)/188315 weeks
129-.03991 -.32808 (129*2π)/188315 weeks
130-.08611 -.23807 (130*2π)/188314 weeks
131-.02345 -.17753 (131*2π)/188314 weeks
132.06768 -.19286 (132*2π)/188314 weeks
133.12073 -.27052 (133*2π)/188314 weeks
134.07399 -.31112 (134*2π)/188314 weeks
135.06276 -.33925 (135*2π)/188314 weeks
136.03856 -.35088 (136*2π)/188314 weeks
137.03376 -.37183 (137*2π)/188314 weeks
138-.00032 -.40022 (138*2π)/188314 weeks
139-.02576 -.41076 (139*2π)/188314 weeks
140-.08858 -.40829 (140*2π)/188313 weeks
141-.14333 -.36605 (141*2π)/188313 weeks
142-.14556 -.32667 (142*2π)/188313 weeks
143-.12842 -.28443 (143*2π)/188313 weeks
144-.14479 -.28341 (144*2π)/188313 weeks
145-.1431 -.23445 (145*2π)/188313 weeks
146-.14025 -.17835 (146*2π)/188313 weeks
147-.08552 -.12678 (147*2π)/188313 weeks
148.02793 -.11824 (148*2π)/188313 weeks
149.09626 -.17922 (149*2π)/188313 weeks
150.13335 -.28036 (150*2π)/188313 weeks
151.08896 -.3906 (151*2π)/188312 weeks
152-.01923 -.44812 (152*2π)/188312 weeks
153-.14655 -.41578 (153*2π)/188312 weeks
154-.16394 -.29347 (154*2π)/188312 weeks
155-.132 -.26931 (155*2π)/188312 weeks
156-.13064 -.25449 (156*2π)/188312 weeks
157-.11813 -.21452 (157*2π)/188312 weeks
158-.05189 -.20373 (158*2π)/188312 weeks
159-.02203 -.28828 (159*2π)/188312 weeks
160-.13108 -.33519 (160*2π)/188312 weeks
161-.22647 -.2654 (161*2π)/188312 weeks
162-.21883 -.1162 (162*2π)/188312 weeks
163-.0922 -.05201 (163*2π)/188312 weeks
164-.00884 -.10333 (164*2π)/188311 weeks
165.00957 -.12316 (165*2π)/188311 weeks
166.05236 -.15177 (166*2π)/188311 weeks
167.07771 -.20343 (167*2π)/188311 weeks
168.05308 -.28419 (168*2π)/188311 weeks
169-.01944 -.28155 (169*2π)/188311 weeks
170-.00803 -.24564 (170*2π)/188311 weeks
171.01078 -.26677 (171*2π)/188311 weeks
172-.01033 -.3156 (172*2π)/188311 weeks
173-.09974 -.32685 (173*2π)/188311 weeks
174-.10506 -.23506 (174*2π)/188311 weeks
175-.06617 -.23206 (175*2π)/188311 weeks
176-.06315 -.23499 (176*2π)/188311 weeks
177-.07428 -.24608 (177*2π)/188311 weeks
178-.07888 -.21799 (178*2π)/188311 weeks
179-.04371 -.24205 (179*2π)/188311 weeks
180-.0852 -.24236 (180*2π)/188310 weeks
181-.09623 -.22387 (181*2π)/188310 weeks
182-.08621 -.18829 (182*2π)/188310 weeks
183-.0425 -.17546 (183*2π)/188310 weeks
184-.04277 -.21392 (184*2π)/188310 weeks
185-.03289 -.20397 (185*2π)/188310 weeks
186-.02884 -.21564 (186*2π)/188310 weeks
187-.02631 -.20633 (187*2π)/188310 weeks
188-.00294 -.23529 (188*2π)/188310 weeks
189.01038 -.2406 (189*2π)/188310 weeks
190.02729 -.31104 (190*2π)/188310 weeks
191-.04501 -.37415 (191*2π)/188310 weeks
192-.13375 -.37131 (192*2π)/188310 weeks
193-.2014 -.29274 (193*2π)/188310 weeks
194-.16803 -.22215 (194*2π)/188310 weeks
195-.1446 -.23396 (195*2π)/188310 weeks
196-.14789 -.2131 (196*2π)/188310 weeks
197-.14036 -.18884 (197*2π)/188310 weeks
198-.09855 -.19626 (198*2π)/188310 weeks
199-.10174 -.24583 (199*2π)/18839 weeks
200-.15712 -.23882 (200*2π)/18839 weeks
201-.17198 -.20099 (201*2π)/18839 weeks
202-.16542 -.18149 (202*2π)/18839 weeks
203-.14633 -.18127 (203*2π)/18839 weeks
204-.18013 -.17849 (204*2π)/18839 weeks
205-.18028 -.14028 (205*2π)/18839 weeks
206-.16057 -.11564 (206*2π)/18839 weeks
207-.14541 -.09826 (207*2π)/18839 weeks
208-.12799 -.10544 (208*2π)/18839 weeks
209-.11551 -.08496 (209*2π)/18839 weeks
210-.08223 -.09805 (210*2π)/18839 weeks
211-.0965 -.10942 (211*2π)/18839 weeks
212-.08921 -.09938 (212*2π)/18839 weeks
213-.08519 -.08474 (213*2π)/18839 weeks
214-.04624 -.09146 (214*2π)/18839 weeks
215-.05178 -.11578 (215*2π)/18839 weeks
216-.04865 -.10965 (216*2π)/18839 weeks
217-.06394 -.13481 (217*2π)/18839 weeks
218-.05378 -.10121 (218*2π)/18839 weeks
219-.03922 -.1248 (219*2π)/18839 weeks
220-.05418 -.13713 (220*2π)/18839 weeks
221-.06321 -.13499 (221*2π)/18839 weeks
222-.06972 -.08888 (222*2π)/18838 weeks
223-.01378 -.1074 (223*2π)/18838 weeks
224-.02808 -.13963 (224*2π)/18838 weeks
225-.05142 -.13533 (225*2π)/18838 weeks
226-.04471 -.10882 (226*2π)/18838 weeks
227-.00336 -.11923 (227*2π)/18838 weeks
228-.01864 -.16085 (228*2π)/18838 weeks
229-.04725 -.15562 (229*2π)/18838 weeks
230-.04894 -.1448 (230*2π)/18838 weeks
231-.045 -.12557 (231*2π)/18838 weeks
232-.0324 -.14585 (232*2π)/18838 weeks
233-.05495 -.13833 (233*2π)/18838 weeks
234-.02311 -.11201 (234*2π)/18838 weeks
235.00421 -.13375 (235*2π)/18838 weeks
236-.00165 -.18583 (236*2π)/18838 weeks
237-.05909 -.19734 (237*2π)/18838 weeks
238-.08077 -.1592 (238*2π)/18838 weeks
239-.08307 -.12533 (239*2π)/18838 weeks
240-.0573 -.08432 (240*2π)/18838 weeks
241.01703 -.09171 (241*2π)/18838 weeks
242.03973 -.15875 (242*2π)/18838 weeks
243-.00734 -.20714 (243*2π)/18838 weeks
244-.0426 -.17651 (244*2π)/18838 weeks
245.00066 -.16753 (245*2π)/18838 weeks
246-.00634 -.22087 (246*2π)/18838 weeks
247-.06175 -.2441 (247*2π)/18838 weeks
248-.10675 -.21236 (248*2π)/18838 weeks
249-.09124 -.17567 (249*2π)/18838 weeks
250-.0835 -.17669 (250*2π)/18838 weeks
251-.09496 -.19191 (251*2π)/18838 weeks
252-.13819 -.18472 (252*2π)/18837 weeks
253-.14576 -.12453 (253*2π)/18837 weeks
254-.10906 -.09934 (254*2π)/18837 weeks
255-.07654 -.10306 (255*2π)/18837 weeks
256-.06662 -.12441 (256*2π)/18837 weeks
257-.0889 -.13141 (257*2π)/18837 weeks
258-.08901 -.13699 (258*2π)/18837 weeks
259-.12318 -.12362 (259*2π)/18837 weeks
260-.1159 -.06069 (260*2π)/18837 weeks
261-.06112 -.0249 (261*2π)/18837 weeks
262.011 -.05925 (262*2π)/18837 weeks
263.00558 -.13691 (263*2π)/18837 weeks
264-.03374 -.14588 (264*2π)/18837 weeks
265-.04161 -.12723 (265*2π)/18837 weeks
266-.02518 -.12805 (266*2π)/18837 weeks
267-.0311 -.14746 (267*2π)/18837 weeks
268-.03752 -.15006 (268*2π)/18837 weeks
269-.0426 -.16772 (269*2π)/18837 weeks
270-.06331 -.18097 (270*2π)/18837 weeks
271-.09911 -.15907 (271*2π)/18837 weeks
272-.10213 -.14119 (272*2π)/18837 weeks
273-.10583 -.12452 (273*2π)/18837 weeks
274-.10237 -.09827 (274*2π)/18837 weeks
275-.08725 -.08342 (275*2π)/18837 weeks
276-.05603 -.07502 (276*2π)/18837 weeks
277-.03415 -.09552 (277*2π)/18837 weeks
278-.03866 -.11715 (278*2π)/18837 weeks
279-.06616 -.12627 (279*2π)/18837 weeks
280-.07082 -.09113 (280*2π)/18837 weeks
281-.04905 -.08953 (281*2π)/18837 weeks
282-.04129 -.09111 (282*2π)/18837 weeks
283-.03221 -.09194 (283*2π)/18837 weeks
284-.0196 -.08939 (284*2π)/18837 weeks
285.00458 -.12104 (285*2π)/18837 weeks
286-.02165 -.14455 (286*2π)/18837 weeks
287-.02878 -.12876 (287*2π)/18837 weeks
288-.02004 -.12759 (288*2π)/18837 weeks
289-.01534 -.15848 (289*2π)/18837 weeks
290-.04619 -.17099 (290*2π)/18836 weeks
291-.06759 -.15044 (291*2π)/18836 weeks
292-.07073 -.13889 (292*2π)/18836 weeks
293-.06608 -.11058 (293*2π)/18836 weeks
294-.0388 -.11088 (294*2π)/18836 weeks
295-.01885 -.12774 (295*2π)/18836 weeks
296-.02551 -.17013 (296*2π)/18836 weeks
297-.05989 -.1717 (297*2π)/18836 weeks
298-.0733 -.1584 (298*2π)/18836 weeks
299-.07862 -.14328 (299*2π)/18836 weeks
300-.06811 -.14195 (300*2π)/18836 weeks
301-.07955 -.14893 (301*2π)/18836 weeks
302-.07206 -.13666 (302*2π)/18836 weeks
303-.06145 -.14748 (303*2π)/18836 weeks
304-.07946 -.16866 (304*2π)/18836 weeks
305-.11637 -.16982 (305*2π)/18836 weeks
306-.14043 -.14563 (306*2π)/18836 weeks
307-.13449 -.11461 (307*2π)/18836 weeks
308-.13379 -.10211 (308*2π)/18836 weeks
309-.14581 -.08175 (309*2π)/18836 weeks
310-.12979 -.0479 (310*2π)/18836 weeks
311-.09273 -.02875 (311*2π)/18836 weeks
312-.06156 -.04901 (312*2π)/18836 weeks
313-.06235 -.06563 (313*2π)/18836 weeks
314-.06493 -.06477 (314*2π)/18836 weeks
315-.06196 -.05615 (315*2π)/18836 weeks
316-.04655 -.06094 (316*2π)/18836 weeks
317-.04206 -.06869 (317*2π)/18836 weeks
318-.03795 -.07399 (318*2π)/18836 weeks
319-.04646 -.06275 (319*2π)/18836 weeks
320-.01934 -.05263 (320*2π)/18836 weeks
321.00198 -.07934 (321*2π)/18836 weeks
322.00142 -.10693 (322*2π)/18836 weeks
323-.00823 -.12601 (323*2π)/18836 weeks
324-.02699 -.14842 (324*2π)/18836 weeks
325-.08158 -.14872 (325*2π)/18836 weeks
326-.10265 -.08274 (326*2π)/18836 weeks
327-.05965 -.05676 (327*2π)/18836 weeks
328-.02722 -.06572 (328*2π)/18836 weeks
329-.01674 -.06983 (329*2π)/18836 weeks
330.01131 -.08112 (330*2π)/18836 weeks
331.02434 -.12832 (331*2π)/18836 weeks
332-.01311 -.15727 (332*2π)/18836 weeks
333-.03077 -.15764 (333*2π)/18836 weeks
334-.04702 -.15727 (334*2π)/18836 weeks
335-.07009 -.15331 (335*2π)/18836 weeks
336-.09275 -.12247 (336*2π)/18836 weeks
337-.06731 -.09302 (337*2π)/18836 weeks
338-.0454 -.11212 (338*2π)/18836 weeks
339-.04992 -.11449 (339*2π)/18836 weeks
340-.05205 -.1072 (340*2π)/18836 weeks
341-.04016 -.11876 (341*2π)/18836 weeks
342-.04131 -.14675 (342*2π)/18836 weeks
343-.08023 -.15166 (343*2π)/18835 weeks
344-.1002 -.12154 (344*2π)/18835 weeks
345-.08848 -.09098 (345*2π)/18835 weeks
346-.06951 -.07852 (346*2π)/18835 weeks
347-.04055 -.08584 (347*2π)/18835 weeks
348-.02729 -.11684 (348*2π)/18835 weeks
349-.04216 -.13049 (349*2π)/18835 weeks
350-.04607 -.13397 (350*2π)/18835 weeks
351-.05224 -.15154 (351*2π)/18835 weeks
352-.08278 -.16602 (352*2π)/18835 weeks
353-.1247 -.15906 (353*2π)/18835 weeks
354-.14776 -.1089 (354*2π)/18835 weeks
355-.12879 -.05965 (355*2π)/18835 weeks
356-.07856 -.03232 (356*2π)/18835 weeks
357-.03636 -.05535 (357*2π)/18835 weeks
358-.01521 -.08989 (358*2π)/18835 weeks
359-.00411 -.14056 (359*2π)/18835 weeks
360-.04245 -.19699 (360*2π)/18835 weeks
361-.13898 -.21617 (361*2π)/18835 weeks
362-.20837 -.12877 (362*2π)/18835 weeks
363-.17358 -.03917 (363*2π)/18835 weeks
364-.11934 -.02936 (364*2π)/18835 weeks
365-.10076 -.04675 (365*2π)/18835 weeks
366-.1012 -.02293 (366*2π)/18835 weeks
367-.04976 -.01951 (367*2π)/18835 weeks
368-.02938 -.0605 (368*2π)/18835 weeks
369-.05247 -.0988 (369*2π)/18835 weeks
370-.09041 -.09343 (370*2π)/18835 weeks
371-.08639 -.04695 (371*2π)/18835 weeks
372-.05024 -.04405 (372*2π)/18835 weeks
373-.03876 -.07403 (373*2π)/18835 weeks
374-.05026 -.08618 (374*2π)/18835 weeks
375-.05792 -.08205 (375*2π)/18835 weeks
376-.05165 -.08708 (376*2π)/18835 weeks
377-.06771 -.09974 (377*2π)/18835 weeks
378-.08095 -.08633 (378*2π)/18835 weeks
379-.08392 -.07765 (379*2π)/18835 weeks
380-.08394 -.06029 (380*2π)/18835 weeks
381-.07331 -.04841 (381*2π)/18835 weeks
382-.04934 -.03579 (382*2π)/18835 weeks
383-.02202 -.05342 (383*2π)/18835 weeks
384-.01729 -.08282 (384*2π)/18835 weeks
385-.02662 -.11022 (385*2π)/18835 weeks
386-.05611 -.1172 (386*2π)/18835 weeks
387-.07806 -.11262 (387*2π)/18835 weeks
388-.09389 -.09064 (388*2π)/18835 weeks
389-.08204 -.06682 (389*2π)/18835 weeks
390-.0584 -.06717 (390*2π)/18835 weeks
391-.05415 -.08502 (391*2π)/18835 weeks
392-.07248 -.09901 (392*2π)/18835 weeks
393-.08412 -.08472