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Fourier Analysis of AAPL (Apple Inc.)


AAPL (Apple Inc.) appears to have interesting cyclic behaviour every 188 weeks (4.3744*sine), 171 weeks (3.0007*sine), and 188 weeks (2.0669*cosine).

AAPL (Apple Inc.) has an average price of 17.1 (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 11/28/2016 for AAPL (Apple Inc.), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
017.09835   0 
123.58201 -16.06825 (1*2π)/18771,877 weeks
210.07554 -18.80519 (2*2π)/1877939 weeks
33.22173 -14.30443 (3*2π)/1877626 weeks
41.25708 -10.46663 (4*2π)/1877469 weeks
5-.21231 -8.18928 (5*2π)/1877375 weeks
6.26818 -5.59499 (6*2π)/1877313 weeks
71.09331 -5.74048 (7*2π)/1877268 weeks
8.36555 -6.13811 (8*2π)/1877235 weeks
9-1.0262 -6.08205 (9*2π)/1877209 weeks
10-2.06694 -4.37444 (10*2π)/1877188 weeks
11-2.01814 -3.00075 (11*2π)/1877171 weeks
12-1.60995 -2.13925 (12*2π)/1877156 weeks
13-1.41774 -1.59985 (13*2π)/1877144 weeks
14-1.24356 -.52761 (14*2π)/1877134 weeks
15.36362 .0888 (15*2π)/1877125 weeks
161.41276 -.79464 (16*2π)/1877117 weeks
171.36387 -1.91582 (17*2π)/1877110 weeks
18.41298 -2.18311 (18*2π)/1877104 weeks
19.13532 -1.69197 (19*2π)/187799 weeks
20.1302 -1.65057 (20*2π)/187794 weeks
21.04073 -1.29584 (21*2π)/187789 weeks
22.12707 -1.06741 (22*2π)/187785 weeks
23.51757 -.7603 (23*2π)/187782 weeks
241.10706 -1.16642 (24*2π)/187778 weeks
251.03816 -1.75649 (25*2π)/187775 weeks
26.63663 -2.22632 (26*2π)/187772 weeks
27-.04462 -2.17202 (27*2π)/187770 weeks
28-.42136 -1.7049 (28*2π)/187767 weeks
29-.37065 -1.17956 (29*2π)/187765 weeks
30-.06974 -1.01069 (30*2π)/187763 weeks
31-.0436 -1.07978 (31*2π)/187761 weeks
32.09973 -.94542 (32*2π)/187759 weeks
33.24093 -.96838 (33*2π)/187757 weeks
34.26877 -1.12602 (34*2π)/187755 weeks
35.20225 -1.27346 (35*2π)/187754 weeks
36-.03306 -1.27799 (36*2π)/187752 weeks
37-.22908 -1.15033 (37*2π)/187751 weeks
38-.15194 -.9015 (38*2π)/187749 weeks
39.07352 -.86152 (39*2π)/187748 weeks
40-.13561 -1.05637 (40*2π)/187747 weeks
41-.23947 -.75919 (41*2π)/187746 weeks
42.09988 -.51355 (42*2π)/187745 weeks
43.33825 -.76856 (43*2π)/187744 weeks
44.18474 -1.03645 (44*2π)/187743 weeks
45-.00396 -.90161 (45*2π)/187742 weeks
46.13996 -.78886 (46*2π)/187741 weeks
47.1742 -.95808 (47*2π)/187740 weeks
48.04643 -1.04958 (48*2π)/187739 weeks
49-.0952 -1.04762 (49*2π)/187738 weeks
50-.18927 -.84747 (50*2π)/187738 weeks
51-.10636 -.82628 (51*2π)/187737 weeks
52-.12469 -.86983 (52*2π)/187736 weeks
53-.20107 -.78861 (53*2π)/187735 weeks
54-.18073 -.67114 (54*2π)/187735 weeks
55-.08439 -.67598 (55*2π)/187734 weeks
56-.15739 -.80556 (56*2π)/187734 weeks
57-.32463 -.65973 (57*2π)/187733 weeks
58-.2987 -.37259 (58*2π)/187732 weeks
59.02864 -.2318 (59*2π)/187732 weeks
60.33139 -.49211 (60*2π)/187731 weeks
61.20029 -.76985 (61*2π)/187731 weeks
62-.02368 -.8457 (62*2π)/187730 weeks
63-.14047 -.75395 (63*2π)/187730 weeks
64-.15201 -.67632 (64*2π)/187729 weeks
65-.27455 -.58613 (65*2π)/187729 weeks
66-.20821 -.36807 (66*2π)/187728 weeks
67.0414 -.30897 (67*2π)/187728 weeks
68.21596 -.46954 (68*2π)/187728 weeks
69.17385 -.70594 (69*2π)/187727 weeks
70.0273 -.71377 (70*2π)/187727 weeks
71-.00098 -.71144 (71*2π)/187726 weeks
72-.10163 -.7539 (72*2π)/187726 weeks
73-.22536 -.68515 (73*2π)/187726 weeks
74-.23151 -.47986 (74*2π)/187725 weeks
75.01761 -.42232 (75*2π)/187725 weeks
76.09325 -.67464 (76*2π)/187725 weeks
77-.08306 -.8461 (77*2π)/187724 weeks
78-.34022 -.78892 (78*2π)/187724 weeks
79-.4115 -.6152 (79*2π)/187724 weeks
80-.42075 -.52379 (80*2π)/187723 weeks
81-.41343 -.35847 (81*2π)/187723 weeks
82-.30788 -.22903 (82*2π)/187723 weeks
83-.18517 -.27116 (83*2π)/187723 weeks
84-.07821 -.36278 (84*2π)/187722 weeks
85-.19069 -.42475 (85*2π)/187722 weeks
86-.21617 -.35671 (86*2π)/187722 weeks
87-.21557 -.32283 (87*2π)/187722 weeks
88-.19943 -.31837 (88*2π)/187721 weeks
89-.25992 -.33645 (89*2π)/187721 weeks
90-.26442 -.15398 (90*2π)/187721 weeks
91-.09634 -.10696 (91*2π)/187721 weeks
92-.01195 -.21004 (92*2π)/187720 weeks
93-.0736 -.31556 (93*2π)/187720 weeks
94-.14751 -.22837 (94*2π)/187720 weeks
95-.06574 -.18051 (95*2π)/187720 weeks
96-.07899 -.21215 (96*2π)/187720 weeks
97-.0755 -.14396 (97*2π)/187719 weeks
98.01425 -.06469 (98*2π)/187719 weeks
99.17127 -.10158 (99*2π)/187719 weeks
100.22522 -.27739 (100*2π)/187719 weeks
101.18488 -.37659 (101*2π)/187719 weeks
102.07167 -.40586 (102*2π)/187718 weeks
103.02522 -.34067 (103*2π)/187718 weeks
104.10195 -.35373 (104*2π)/187718 weeks
105.05993 -.41857 (105*2π)/187718 weeks
106.01094 -.40208 (106*2π)/187718 weeks
107.01095 -.34351 (107*2π)/187718 weeks
108.10105 -.37557 (108*2π)/187717 weeks
109.04608 -.50648 (109*2π)/187717 weeks
110-.05476 -.50727 (110*2π)/187717 weeks
111-.11237 -.44985 (111*2π)/187717 weeks
112-.06652 -.40705 (112*2π)/187717 weeks
113-.09763 -.47209 (113*2π)/187717 weeks
114-.20524 -.44813 (114*2π)/187716 weeks
115-.24273 -.35324 (115*2π)/187716 weeks
116-.20063 -.23949 (116*2π)/187716 weeks
117-.11678 -.21636 (117*2π)/187716 weeks
118-.08248 -.24536 (118*2π)/187716 weeks
119-.07028 -.26837 (119*2π)/187716 weeks
120-.07655 -.23746 (120*2π)/187716 weeks
121-.00851 -.2548 (121*2π)/187716 weeks
122.00342 -.35306 (122*2π)/187715 weeks
123-.08915 -.39477 (123*2π)/187715 weeks
124-.15908 -.31994 (124*2π)/187715 weeks
125-.11741 -.28346 (125*2π)/187715 weeks
126-.12503 -.29848 (126*2π)/187715 weeks
127-.1404 -.26537 (127*2π)/187715 weeks
128-.09443 -.22045 (128*2π)/187715 weeks
129-.02973 -.27393 (129*2π)/187715 weeks
130-.09194 -.3467 (130*2π)/187714 weeks
131-.17826 -.3357 (131*2π)/187714 weeks
132-.22094 -.26003 (132*2π)/187714 weeks
133-.17812 -.16968 (133*2π)/187714 weeks
134-.15487 -.16465 (134*2π)/187714 weeks
135-.12578 -.14744 (135*2π)/187714 weeks
136-.11416 -.14437 (136*2π)/187714 weeks
137-.09137 -.11927 (137*2π)/187714 weeks
138-.0521 -.12047 (138*2π)/187714 weeks
139-.00806 -.10911 (139*2π)/187714 weeks
140.03674 -.14193 (140*2π)/187713 weeks
141.04114 -.20385 (141*2π)/187713 weeks
142.03804 -.23988 (142*2π)/187713 weeks
143.01479 -.23839 (143*2π)/187713 weeks
144.03399 -.27287 (144*2π)/187713 weeks
145.02128 -.30228 (145*2π)/187713 weeks
146-.02316 -.35515 (146*2π)/187713 weeks
147-.10465 -.3843 (147*2π)/187713 weeks
148-.19261 -.32011 (148*2π)/187713 weeks
149-.23963 -.23562 (149*2π)/187713 weeks
150-.22591 -.12054 (150*2π)/187713 weeks
151-.13998 -.03901 (151*2π)/187712 weeks
152-.0196 -.0312 (152*2π)/187712 weeks
153.07091 -.13027 (153*2π)/187712 weeks
154.02487 -.19651 (154*2π)/187712 weeks
155.01053 -.20539 (155*2π)/187712 weeks
156.01236 -.2292 (156*2π)/187712 weeks
157-.02579 -.26355 (157*2π)/187712 weeks
158-.09276 -.22194 (158*2π)/187712 weeks
159-.05426 -.11765 (159*2π)/187712 weeks
160.05758 -.13169 (160*2π)/187712 weeks
161.12898 -.24361 (161*2π)/187712 weeks
162.05874 -.37081 (162*2π)/187712 weeks
163-.06203 -.37451 (163*2π)/187712 weeks
164-.0965 -.32686 (164*2π)/187711 weeks
165-.13318 -.31771 (165*2π)/187711 weeks
166-.17362 -.27912 (166*2π)/187711 weeks
167-.20025 -.2124 (167*2π)/187711 weeks
168-.14351 -.15053 (168*2π)/187711 weeks
169-.10129 -.1825 (169*2π)/187711 weeks
170-.12874 -.18565 (170*2π)/187711 weeks
171-.14641 -.14567 (171*2π)/187711 weeks
172-.10944 -.08801 (172*2π)/187711 weeks
173-.01723 -.12895 (173*2π)/187711 weeks
174-.04775 -.18131 (174*2π)/187711 weeks
175-.06322 -.17253 (175*2π)/187711 weeks
176-.07189 -.16404 (176*2π)/187711 weeks
177-.05023 -.16547 (177*2π)/187711 weeks
178-.07344 -.19331 (178*2π)/187711 weeks
179-.06994 -.14601 (179*2π)/187710 weeks
180-.04696 -.15629 (180*2π)/187710 weeks
181-.02731 -.17832 (181*2π)/187710 weeks
182-.04074 -.21318 (182*2π)/187710 weeks
183-.08948 -.20346 (183*2π)/187710 weeks
184-.07546 -.19812 (184*2π)/187710 weeks
185-.09236 -.19437 (185*2π)/187710 weeks
186-.09219 -.18772 (186*2π)/187710 weeks
187-.12108 -.20204 (187*2π)/187710 weeks
188-.12947 -.18551 (188*2π)/187710 weeks
189-.1826 -.17406 (189*2π)/187710 weeks
190-.20535 -.0851 (190*2π)/187710 weeks
191-.15132 -.01572 (191*2π)/187710 weeks
192-.05842 .00838 (192*2π)/187710 weeks
193  -.05875 (193*2π)/187710 weeks
194-.02813 -.09854 (194*2π)/187710 weeks
195-.01692 -.09279 (195*2π)/187710 weeks
196-.00975 -.10601 (196*2π)/187710 weeks
197-.02482 -.14147 (197*2π)/187710 weeks
198-.06909 -.1275 (198*2π)/18779 weeks
199-.05565 -.06922 (199*2π)/18779 weeks
200-.01386 -.06671 (200*2π)/18779 weeks
201.00013 -.08652 (201*2π)/18779 weeks
202.00104 -.10563 (202*2π)/18779 weeks
203-.00498 -.08004 (203*2π)/18779 weeks
204.03317 -.08703 (204*2π)/18779 weeks
205.04872 -.11255 (205*2π)/18779 weeks
206.04974 -.12922 (206*2π)/18779 weeks
207.03702 -.15184 (207*2π)/18779 weeks
208.04576 -.15538 (208*2π)/18779 weeks
209.03111 -.18439 (209*2π)/18779 weeks
210.00858 -.16759 (210*2π)/18779 weeks
211.02013 -.16966 (211*2π)/18779 weeks
212.02375 -.17187 (212*2π)/18779 weeks
213.02031 -.20429 (213*2π)/18779 weeks
214-.01221 -.19691 (214*2π)/18779 weeks
215-.00813 -.18737 (215*2π)/18779 weeks
216-.03296 -.18392 (216*2π)/18779 weeks
217-.00004 -.17485 (217*2π)/18779 weeks
218-.02258 -.1962 (218*2π)/18779 weeks
219-.03735 -.18055 (219*2π)/18779 weeks
220-.02991 -.16975 (220*2π)/18779 weeks
221.00025 -.15227 (221*2π)/18778 weeks
222-.00109 -.21105 (222*2π)/18778 weeks
223-.04285 -.19941 (223*2π)/18778 weeks
224-.04326 -.17333 (224*2π)/18778 weeks
225-.01838 -.17185 (225*2π)/18778 weeks
226-.01756 -.20828 (226*2π)/18778 weeks
227-.06447 -.20403 (227*2π)/18778 weeks
228-.0659 -.17031 (228*2π)/18778 weeks
229-.05026 -.16544 (229*2π)/18778 weeks
230-.03601 -.16196 (230*2π)/18778 weeks
231-.04654 -.18364 (231*2π)/18778 weeks
232-.05111 -.16141 (232*2π)/18778 weeks
233-.01623 -.17474 (233*2π)/18778 weeks
234-.03377 -.20523 (234*2π)/18778 weeks
235-.08094 -.21441 (235*2π)/18778 weeks
236-.11039 -.16422 (236*2π)/18778 weeks
237-.07681 -.12737 (237*2π)/18778 weeks
238-.04637 -.11995 (238*2π)/18778 weeks
239-.00625 -.13238 (239*2π)/18778 weeks
240.01442 -.19876 (240*2π)/18778 weeks
241-.04162 -.24339 (241*2π)/18778 weeks
242-.10551 -.21987 (242*2π)/18778 weeks
243-.09539 -.16869 (243*2π)/18778 weeks
244-.06194 -.19319 (244*2π)/18778 weeks
245-.11166 -.21315 (245*2π)/18778 weeks
246-.15515 -.17529 (246*2π)/18778 weeks
247-.14562 -.12095 (247*2π)/18778 weeks
248-.10065 -.11241 (248*2π)/18778 weeks
249-.09838 -.12281 (249*2π)/18778 weeks
250-.11473 -.1233 (250*2π)/18778 weeks
251-.12981 -.08917 (251*2π)/18777 weeks
252-.08571 -.04998 (252*2π)/18777 weeks
253-.04311 -.07033 (253*2π)/18777 weeks
254-.03077 -.10016 (254*2π)/18777 weeks
255-.04518 -.12053 (255*2π)/18777 weeks
256-.06865 -.10991 (256*2π)/18777 weeks
257-.06724 -.11072 (257*2π)/18777 weeks
258-.07825 -.08028 (258*2π)/18777 weeks
259-.02921 -.04519 (259*2π)/18777 weeks
260.02716 -.06668 (260*2π)/18777 weeks
261.04623 -.14201 (261*2π)/18777 weeks
262-.01535 -.19228 (262*2π)/18777 weeks
263-.05242 -.16466 (263*2π)/18777 weeks
264-.04551 -.14201 (264*2π)/18777 weeks
265-.0341 -.15131 (265*2π)/18777 weeks
266-.05209 -.16216 (266*2π)/18777 weeks
267-.05998 -.15723 (267*2π)/18777 weeks
268-.07302 -.16542 (268*2π)/18777 weeks
269-.09465 -.15917 (269*2π)/18777 weeks
270-.10965 -.12012 (270*2π)/18777 weeks
271-.09673 -.1049 (271*2π)/18777 weeks
272-.08786 -.09118 (272*2π)/18777 weeks
273-.07036 -.07422 (273*2π)/18777 weeks
274-.04953 -.07423 (274*2π)/18777 weeks
275-.02144 -.08509 (275*2π)/18777 weeks
276-.01666 -.11417 (276*2π)/18777 weeks
277-.03441 -.12879 (277*2π)/18777 weeks
278-.0618 -.12255 (278*2π)/18777 weeks
279-.0499 -.08899 (279*2π)/18777 weeks
280-.02896 -.09916 (280*2π)/18777 weeks
281-.02445 -.10495 (281*2π)/18777 weeks
282-.01813 -.10992 (282*2π)/18777 weeks
283-.00847 -.11373 (283*2π)/18777 weeks
284-.00034 -.1502 (284*2π)/18777 weeks
285-.03488 -.15973 (285*2π)/18777 weeks
286-.03615 -.13983 (286*2π)/18777 weeks
287-.02846 -.14186 (287*2π)/18777 weeks
288-.03451 -.17058 (288*2π)/18777 weeks
289-.06731 -.16957 (289*2π)/18776 weeks
290-.07961 -.14185 (290*2π)/18776 weeks
291-.07639 -.12998 (291*2π)/18776 weeks
292-.06348 -.10571 (292*2π)/18776 weeks
293-.03733 -.11518 (293*2π)/18776 weeks
294-.02448 -.13699 (294*2π)/18776 weeks
295-.04187 -.17478 (295*2π)/18776 weeks
296-.07558 -.16622 (296*2π)/18776 weeks
297-.08417 -.14923 (297*2π)/18776 weeks
298-.08507 -.13381 (298*2π)/18776 weeks
299-.07377 -.13482 (299*2π)/18776 weeks
300-.08544 -.14019 (300*2π)/18776 weeks
301-.07575 -.12929 (301*2π)/18776 weeks
302-.06711 -.14172 (302*2π)/18776 weeks
303-.08779 -.16 (303*2π)/18776 weeks
304-.1234 -.15636 (304*2π)/18776 weeks
305-.14293 -.13007 (305*2π)/18776 weeks
306-.13304 -.1008 (306*2π)/18776 weeks
307-.13097 -.08992 (307*2π)/18776 weeks
308-.14138 -.07043 (308*2π)/18776 weeks
309-.12377 -.03915 (309*2π)/18776 weeks
310-.08704 -.02304 (310*2π)/18776 weeks
311-.05786 -.04493 (311*2π)/18776 weeks
312-.0601 -.06169 (312*2π)/18776 weeks
313-.0636 -.06088 (313*2π)/18776 weeks
314-.06166 -.05221 (314*2π)/18776 weeks
315-.04709 -.05648 (315*2π)/18776 weeks
316-.04313 -.06373 (316*2π)/18776 weeks
317-.03941 -.06855 (317*2π)/18776 weeks
318-.04944 -.05722 (318*2π)/18776 weeks
319-.02396 -.04405 (319*2π)/18776 weeks
320-.00069 -.06725 (320*2π)/18776 weeks
321.00215 -.09356 (321*2π)/18776 weeks
322-.00404 -.11297 (322*2π)/18776 weeks
323-.01829 -.13809 (323*2π)/18776 weeks
324-.07214 -.1477 (324*2π)/18776 weeks
325-.10463 -.08673 (325*2π)/18776 weeks
326-.06942 -.05336 (326*2π)/18776 weeks
327-.03714 -.05455 (327*2π)/18776 weeks
328-.02635 -.05389 (328*2π)/18776 weeks
329.00412 -.05616 (329*2π)/18776 weeks
330.02965 -.09725 (330*2π)/18776 weeks
331.00281 -.13326 (331*2π)/18776 weeks
332-.01194 -.13947 (332*2π)/18776 weeks
333-.02582 -.1447 (333*2π)/18776 weeks
334-.0482 -.14927 (334*2π)/18776 weeks
335-.07999 -.12735 (335*2π)/18776 weeks
336-.06621 -.09135 (336*2π)/18776 weeks
337-.04036 -.10172 (337*2π)/18776 weeks
338-.04222 -.10452 (338*2π)/18776 weeks
339-.04605 -.09646 (339*2π)/18776 weeks
340-.03034 -.10154 (340*2π)/18776 weeks
341-.01826 -.12871 (341*2π)/18776 weeks
342-.05001 -.15008 (342*2π)/18775 weeks
343-.08068 -.13363 (343*2π)/18775 weeks
344-.08464 -.10222 (344*2π)/18775 weeks
345-.07577 -.0806 (345*2π)/18775 weeks
346-.04764 -.07134 (346*2π)/18775 weeks
347-.02023 -.09097 (347*2π)/18775 weeks
348-.02364 -.10798 (348*2π)/18775 weeks
349-.02177 -.11209 (349*2π)/18775 weeks
350-.01433 -.13048 (350*2π)/18775 weeks
351-.02902 -.16034 (351*2π)/18775 weeks
352-.06702 -.18267 (352*2π)/18775 weeks
353-.11464 -.15898 (353*2π)/18775 weeks
354-.13172 -.11084 (354*2π)/18775 weeks
355-.11035 -.057 (355*2π)/18775 weeks
356-.06689 -.04489 (356*2π)/18775 weeks
357-.02852 -.05261 (357*2π)/18775 weeks
358.01861 -.08187 (358*2π)/18775 weeks
359.03548 -.14917 (359*2π)/18775 weeks
360-.02027 -.23373 (360*2π)/18775 weeks
361-.12731 -.22243 (361*2π)/18775 weeks
362-.16406 -.14025 (362*2π)/18775 weeks
363-.13921 -.09883 (363*2π)/18775 weeks
364-.11924 -.10051 (364*2π)/18775 weeks
365-.1401 -.07919 (365*2π)/18775 weeks
366-.10757 -.03876 (366*2π)/18775 weeks
367-.06452 -.04699 (367*2π)/18775 weeks
368-.05065 -.08853 (368*2π)/18775 weeks
369-.07899 -.11652 (369*2π)/18775 weeks
370-.1095 -.08357 (370*2π)/18775 weeks
371-.09118 -.05346 (371*2π)/18775 weeks
372-.06308 -.0621 (372*2π)/18775 weeks
373-.05889 -.07668 (373*2π)/18775 weeks
374-.0651 -.0784 (374*2π)/18775 weeks
375-.05426 -.07662 (375*2π)/18775 weeks
376-.05311 -.09798 (376*2π)/18775 weeks
377-.06874 -.10208 (377*2π)/18775 weeks
378-.07781 -.10382 (378*2π)/18775 weeks
379-.09352 -.09603 (379*2π)/18775 weeks
380-.10215 -.08331 (380*2π)/18775 weeks
381-.10335 -.05348 (381*2π)/18775 weeks
382-.07753 -.03506 (382*2π)/18775 weeks
383-.05037 -.03948 (383*2π)/18775 weeks
384-.02574 -.05817 (384*2π)/18775 weeks
385-.0282 -.08409 (385*2π)/18775 weeks
386-.038 -.10501 (386*2π)/18775 weeks
387-.06394 -.11306 (387*2π)/18775 weeks
388-.08107 -.09509 (388*2π)/18775 weeks
389-.07154 -.07393 (389*2π)/18775 weeks
390-.05315 -.07424 (390*2π)/18775 weeks
391-.04666 -.09713 (391*2π)/18775 weeks
392-.05914 -.10223 (392*2π)/18775 weeks
393-.06642 -.10854 (393*2π)/18775 weeks
394-.07558