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Fourier Analysis of PSA (Public Storage Common Stock)


PSA (Public Storage Common Stock) appears to have interesting cyclic behaviour every 189 weeks (8.6692*sine), 157 weeks (7.8218*sine), and 171 weeks (7.7619*sine).

PSA (Public Storage Common Stock) has an average price of 42.67 (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 11/18/1980 to 1/9/2017 for PSA (Public Storage Common Stock), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
042.67078   0 
139.69348 -41.61991 (1*2π)/18861,886 weeks
215.55058 -30.71632 (2*2π)/1886943 weeks
39.5178 -22.58341 (3*2π)/1886629 weeks
45.0615 -22.54895 (4*2π)/1886472 weeks
5-.27004 -15.62213 (5*2π)/1886377 weeks
61.64854 -10.86199 (6*2π)/1886314 weeks
73.89821 -10.82159 (7*2π)/1886269 weeks
81.85696 -12.67514 (8*2π)/1886236 weeks
9-.24575 -9.88302 (9*2π)/1886210 weeks
10-.36377 -8.66915 (10*2π)/1886189 weeks
11-.05194 -7.76186 (11*2π)/1886171 weeks
12-.28066 -7.82176 (12*2π)/1886157 weeks
13-1.15261 -6.94479 (13*2π)/1886145 weeks
14-.92008 -5.83022 (14*2π)/1886135 weeks
15-1.28462 -5.75728 (15*2π)/1886126 weeks
16-1.15032 -4.51052 (16*2π)/1886118 weeks
17-.30794 -4.62306 (17*2π)/1886111 weeks
18-1.24458 -4.8135 (18*2π)/1886105 weeks
19-1.70267 -4.16392 (19*2π)/188699 weeks
20-1.57414 -3.0823 (20*2π)/188694 weeks
21-.58507 -2.78769 (21*2π)/188690 weeks
22-.4238 -3.74254 (22*2π)/188686 weeks
23-1.8359 -3.50522 (23*2π)/188682 weeks
24-1.58227 -1.98012 (24*2π)/188679 weeks
25-.52843 -1.97922 (25*2π)/188675 weeks
26-.83546 -2.50268 (26*2π)/188673 weeks
27-1.32309 -2.08413 (27*2π)/188670 weeks
28-1.07 -1.08302 (28*2π)/188667 weeks
29.06171 -1.17386 (29*2π)/188665 weeks
30-.06555 -1.77207 (30*2π)/188663 weeks
31-.43043 -1.77412 (31*2π)/188661 weeks
32-.32698 -1.17602 (32*2π)/188659 weeks
33.1627 -1.46055 (33*2π)/188657 weeks
34-.14805 -1.50795 (34*2π)/188655 weeks
35-.1488 -1.23656 (35*2π)/188654 weeks
36.19822 -1.05872 (36*2π)/188652 weeks
37.32308 -1.41075 (37*2π)/188651 weeks
38.32368 -1.29809 (38*2π)/188650 weeks
39.54587 -1.50829 (39*2π)/188648 weeks
40.39424 -1.91445 (40*2π)/188647 weeks
41-.04407 -1.77703 (41*2π)/188646 weeks
42-.01825 -1.54498 (42*2π)/188645 weeks
43.10884 -1.41408 (43*2π)/188644 weeks
44.18605 -1.78961 (44*2π)/188643 weeks
45-.36341 -1.80918 (45*2π)/188642 weeks
46-.49096 -1.20592 (46*2π)/188641 weeks
47-.11515 -1.16492 (47*2π)/188640 weeks
48-.16398 -1.23104 (48*2π)/188639 weeks
49-.22096 -.95765 (49*2π)/188638 weeks
50.09224 -.897 (50*2π)/188638 weeks
51.06529 -1.06625 (51*2π)/188637 weeks
52.1122 -1.01923 (52*2π)/188636 weeks
53.19043 -.99871 (53*2π)/188636 weeks
54.27318 -1.11588 (54*2π)/188635 weeks
55.21883 -1.08888 (55*2π)/188634 weeks
56.38032 -1.11587 (56*2π)/188634 weeks
57.34973 -1.25006 (57*2π)/188633 weeks
58.28303 -1.48847 (58*2π)/188633 weeks
59.05567 -1.54883 (59*2π)/188632 weeks
60-.32728 -1.48365 (60*2π)/188631 weeks
61-.27052 -.92472 (61*2π)/188631 weeks
62-.06534 -1.01456 (62*2π)/188630 weeks
63-.0507 -.99048 (63*2π)/188630 weeks
64-.06552 -.98938 (64*2π)/188629 weeks
65.12792 -.79759 (65*2π)/188629 weeks
66.35241 -1.14952 (66*2π)/188629 weeks
67-.00866 -1.39328 (67*2π)/188628 weeks
68-.2513 -1.08087 (68*2π)/188628 weeks
69-.03778 -.85621 (69*2π)/188627 weeks
70.12209 -1.10139 (70*2π)/188627 weeks
71-.24237 -1.17084 (71*2π)/188627 weeks
72-.2523 -.7599 (72*2π)/188626 weeks
73.0871 -.80601 (73*2π)/188626 weeks
74.16474 -.94386 (74*2π)/188625 weeks
75-.0182 -1.07786 (75*2π)/188625 weeks
76-.09418 -.94818 (76*2π)/188625 weeks
77-.12786 -.84396 (77*2π)/188624 weeks
78-.00382 -.88703 (78*2π)/188624 weeks
79.01628 -.90789 (79*2π)/188624 weeks
80.01179 -1.04873 (80*2π)/188624 weeks
81-.17483 -.98513 (81*2π)/188623 weeks
82-.22231 -.94233 (82*2π)/188623 weeks
83-.28001 -.80929 (83*2π)/188623 weeks
84-.28582 -.69154 (84*2π)/188622 weeks
85-.18495 -.49035 (85*2π)/188622 weeks
86.18131 -.4647 (86*2π)/188622 weeks
87.20723 -.81599 (87*2π)/188622 weeks
88-.07848 -.83921 (88*2π)/188621 weeks
89-.06409 -.4754 (89*2π)/188621 weeks
90.41763 -.65955 (90*2π)/188621 weeks
91.23281 -1.09762 (91*2π)/188621 weeks
92-.14768 -1.08736 (92*2π)/188621 weeks
93-.24912 -.82147 (93*2π)/188620 weeks
94-.09707 -.67207 (94*2π)/188620 weeks
95-.01957 -.73371 (95*2π)/188620 weeks
96-.10285 -.70842 (96*2π)/188620 weeks
97.00853 -.57277 (97*2π)/188619 weeks
98.18635 -.69128 (98*2π)/188619 weeks
99.14391 -.8388 (99*2π)/188619 weeks
100.07525 -.88034 (100*2π)/188619 weeks
101.02615 -.90948 (101*2π)/188619 weeks
102-.08392 -.87315 (102*2π)/188618 weeks
103-.04301 -.80752 (103*2π)/188618 weeks
104-.06163 -.94092 (104*2π)/188618 weeks
105-.29556 -.95811 (105*2π)/188618 weeks
106-.2874 -.67749 (106*2π)/188618 weeks
107-.09033 -.68355 (107*2π)/188618 weeks
108-.11365 -.82853 (108*2π)/188617 weeks
109-.28432 -.90697 (109*2π)/188617 weeks
110-.45797 -.66026 (110*2π)/188617 weeks
111-.31778 -.46519 (111*2π)/188617 weeks
112-.04276 -.46753 (112*2π)/188617 weeks
113-.03911 -.79169 (113*2π)/188617 weeks
114-.34926 -.75442 (114*2π)/188617 weeks
115-.34546 -.48465 (115*2π)/188616 weeks
116-.16236 -.40964 (116*2π)/188616 weeks
117-.07965 -.5963 (117*2π)/188616 weeks
118-.29308 -.62691 (118*2π)/188616 weeks
119-.37368 -.40526 (119*2π)/188616 weeks
120-.17817 -.22116 (120*2π)/188616 weeks
121.01215 -.34052 (121*2π)/188616 weeks
122-.02021 -.45237 (122*2π)/188615 weeks
123-.06509 -.45597 (123*2π)/188615 weeks
124-.07517 -.43978 (124*2π)/188615 weeks
125-.06603 -.36918 (125*2π)/188615 weeks
126.13592 -.35504 (126*2π)/188615 weeks
127.14228 -.53655 (127*2π)/188615 weeks
128-.00843 -.59942 (128*2π)/188615 weeks
129-.02046 -.46585 (129*2π)/188615 weeks
130.02185 -.51932 (130*2π)/188615 weeks
131.06023 -.50429 (131*2π)/188614 weeks
132-.01578 -.58648 (132*2π)/188614 weeks
133.01493 -.46754 (133*2π)/188614 weeks
134.10989 -.51936 (134*2π)/188614 weeks
135.15191 -.61307 (135*2π)/188614 weeks
136.00022 -.71544 (136*2π)/188614 weeks
137-.05092 -.66601 (137*2π)/188614 weeks
138-.11022 -.66157 (138*2π)/188614 weeks
139-.07802 -.61325 (139*2π)/188614 weeks
140-.15046 -.66835 (140*2π)/188613 weeks
141-.28583 -.61187 (141*2π)/188613 weeks
142-.31632 -.2591 (142*2π)/188613 weeks
143.02981 -.22977 (143*2π)/188613 weeks
144.14467 -.37757 (144*2π)/188613 weeks
145.16707 -.50323 (145*2π)/188613 weeks
146.23226 -.58888 (146*2π)/188613 weeks
147.11801 -.78971 (147*2π)/188613 weeks
148.0013 -.75562 (148*2π)/188613 weeks
149-.04457 -.81012 (149*2π)/188613 weeks
150-.25017 -.76936 (150*2π)/188613 weeks
151-.25033 -.55081 (151*2π)/188612 weeks
152-.05329 -.56181 (152*2π)/188612 weeks
153-.12163 -.72131 (153*2π)/188612 weeks
154-.2365 -.68308 (154*2π)/188612 weeks
155-.26519 -.56718 (155*2π)/188612 weeks
156-.20319 -.58574 (156*2π)/188612 weeks
157-.28538 -.5875 (157*2π)/188612 weeks
158-.30051 -.52991 (158*2π)/188612 weeks
159-.30113 -.47956 (159*2π)/188612 weeks
160-.29223 -.49301 (160*2π)/188612 weeks
161-.38663 -.39892 (161*2π)/188612 weeks
162-.31342 -.23826 (162*2π)/188612 weeks
163-.19727 -.20345 (163*2π)/188612 weeks
164-.04607 -.2536 (164*2π)/188612 weeks
165-.0477 -.34499 (165*2π)/188611 weeks
166.07112 -.35229 (166*2π)/188611 weeks
167.00244 -.56186 (167*2π)/188611 weeks
168-.12342 -.54068 (168*2π)/188611 weeks
169-.15175 -.50281 (169*2π)/188611 weeks
170-.2065 -.5173 (170*2π)/188611 weeks
171-.27463 -.44154 (171*2π)/188611 weeks
172-.26302 -.35699 (172*2π)/188611 weeks
173-.19423 -.21802 (173*2π)/188611 weeks
174.03314 -.25562 (174*2π)/188611 weeks
175.02596 -.42293 (175*2π)/188611 weeks
176-.05387 -.47817 (176*2π)/188611 weeks
177-.0817 -.45648 (177*2π)/188611 weeks
178-.08328 -.48688 (178*2π)/188611 weeks
179-.14192 -.55265 (179*2π)/188611 weeks
180-.22605 -.44582 (180*2π)/188610 weeks
181-.12731 -.37021 (181*2π)/188610 weeks
182-.07264 -.46888 (182*2π)/188610 weeks
183-.17218 -.5039 (183*2π)/188610 weeks
184-.19069 -.48432 (184*2π)/188610 weeks
185-.21204 -.46432 (185*2π)/188610 weeks
186-.26505 -.49962 (186*2π)/188610 weeks
187-.34573 -.40062 (187*2π)/188610 weeks
188-.28576 -.2851 (188*2π)/188610 weeks
189-.19558 -.3163 (189*2π)/188610 weeks
190-.2331 -.36507 (190*2π)/188610 weeks
191-.27377 -.32972 (191*2π)/188610 weeks
192-.25922 -.26795 (192*2π)/188610 weeks
193-.25903 -.24942 (193*2π)/188610 weeks
194-.23335 -.17663 (194*2π)/188610 weeks
195-.13934 -.13632 (195*2π)/188610 weeks
196-.05937 -.17896 (196*2π)/188610 weeks
197-.02057 -.24172 (197*2π)/188610 weeks
198-.03287 -.30277 (198*2π)/188610 weeks
199-.07142 -.29467 (199*2π)/18869 weeks
200.03357 -.31218 (200*2π)/18869 weeks
201-.06374 -.46264 (201*2π)/18869 weeks
202-.17594 -.38573 (202*2π)/18869 weeks
203-.16399 -.32648 (203*2π)/18869 weeks
204-.12648 -.37213 (204*2π)/18869 weeks
205-.26847 -.32836 (205*2π)/18869 weeks
206-.16237 -.20207 (206*2π)/18869 weeks
207-.12317 -.26085 (207*2π)/18869 weeks
208-.13055 -.24891 (208*2π)/18869 weeks
209-.08246 -.21823 (209*2π)/18869 weeks
210-.04795 -.31822 (210*2π)/18869 weeks
211-.1602 -.36385 (211*2π)/18869 weeks
212-.23495 -.21335 (212*2π)/18869 weeks
213-.08577 -.08467 (213*2π)/18869 weeks
214.05145 -.19009 (214*2π)/18869 weeks
215.01804 -.31732 (215*2π)/18869 weeks
216-.04614 -.31051 (216*2π)/18869 weeks
217-.01147 -.29798 (217*2π)/18869 weeks
218-.03654 -.34352 (218*2π)/18869 weeks
219-.09208 -.36094 (219*2π)/18869 weeks
220-.1175 -.26523 (220*2π)/18869 weeks
221-.02969 -.23127 (221*2π)/18869 weeks
222.05692 -.28678 (222*2π)/18868 weeks
223.03605 -.44508 (223*2π)/18868 weeks
224-.12905 -.42691 (224*2π)/18868 weeks
225-.07754 -.34013 (225*2π)/18868 weeks
226-.04578 -.38001 (226*2π)/18868 weeks
227-.09361 -.417 (227*2π)/18868 weeks
228-.09319 -.36956 (228*2π)/18868 weeks
229-.06745 -.44133 (229*2π)/18868 weeks
230-.17938 -.48886 (230*2π)/18868 weeks
231-.24579 -.38565 (231*2π)/18868 weeks
232-.19097 -.3029 (232*2π)/18868 weeks
233-.13108 -.33742 (233*2π)/18868 weeks
234-.17533 -.3509 (234*2π)/18868 weeks
235-.17772 -.32903 (235*2π)/18868 weeks
236-.12847 -.30666 (236*2π)/18868 weeks
237-.10519 -.4227 (237*2π)/18868 weeks
238-.22868 -.42742 (238*2π)/18868 weeks
239-.2721 -.35525 (239*2π)/18868 weeks
240-.28511 -.27947 (240*2π)/18868 weeks
241-.21538 -.19538 (241*2π)/18868 weeks
242-.08031 -.26217 (242*2π)/18868 weeks
243-.17774 -.41332 (243*2π)/18868 weeks
244-.30134 -.34126 (244*2π)/18868 weeks
245-.31849 -.22471 (245*2π)/18868 weeks
246-.21048 -.1779 (246*2π)/18868 weeks
247-.18911 -.21475 (247*2π)/18868 weeks
248-.19517 -.21675 (248*2π)/18868 weeks
249-.19554 -.21227 (249*2π)/18868 weeks
250-.16689 -.19473 (250*2π)/18868 weeks
251-.1588 -.24413 (251*2π)/18868 weeks
252-.2285 -.24689 (252*2π)/18867 weeks
253-.25111 -.15968 (253*2π)/18867 weeks
254-.22078 -.07755 (254*2π)/18867 weeks
255-.08717 -.04437 (255*2π)/18867 weeks
256-.00174 -.12135 (256*2π)/18867 weeks
257.02083 -.27784 (257*2π)/18867 weeks
258-.14713 -.33784 (258*2π)/18867 weeks
259-.20846 -.17415 (259*2π)/18867 weeks
260-.08322 -.1313 (260*2π)/18867 weeks
261-.04857 -.2185 (261*2π)/18867 weeks
262-.06977 -.24459 (262*2π)/18867 weeks
263-.0897 -.28121 (263*2π)/18867 weeks
264-.1581 -.25808 (264*2π)/18867 weeks
265-.11642 -.21402 (265*2π)/18867 weeks
266-.16625 -.24549 (266*2π)/18867 weeks
267-.16237 -.15816 (267*2π)/18867 weeks
268-.09551 -.15444 (268*2π)/18867 weeks
269-.0324 -.18988 (269*2π)/18867 weeks
270-.08088 -.30562 (270*2π)/18867 weeks
271-.20921 -.24612 (271*2π)/18867 weeks
272-.14316 -.12781 (272*2π)/18867 weeks
273-.06816 -.13314 (273*2π)/18867 weeks
274-.03731 -.18125 (274*2π)/18867 weeks
275-.04965 -.18342 (275*2π)/18867 weeks
276-.02452 -.19084 (276*2π)/18867 weeks
277.0375 -.24911 (277*2π)/18867 weeks
278-.04181 -.34971 (278*2π)/18867 weeks
279-.14097 -.30116 (279*2π)/18867 weeks
280-.1312 -.21123 (280*2π)/18867 weeks
281-.0463 -.19547 (281*2π)/18867 weeks
282-.02622 -.27574 (282*2π)/18867 weeks
283-.04759 -.29176 (283*2π)/18867 weeks
284-.07508 -.30829 (284*2π)/18867 weeks
285-.04861 -.32984 (285*2π)/18867 weeks
286-.1016 -.39931 (286*2π)/18867 weeks
287-.23785 -.38925 (287*2π)/18867 weeks
288-.27749 -.24075 (288*2π)/18867 weeks
289-.18526 -.15555 (289*2π)/18867 weeks
290-.06295 -.19008 (290*2π)/18867 weeks
291-.07501 -.31783 (291*2π)/18866 weeks
292-.17704 -.34574 (292*2π)/18866 weeks
293-.25149 -.28207 (293*2π)/18866 weeks
294-.23209 -.1863 (294*2π)/18866 weeks
295-.15879 -.16271 (295*2π)/18866 weeks
296-.11715 -.23244 (296*2π)/18866 weeks
297-.19525 -.25859 (297*2π)/18866 weeks
298-.20756 -.17616 (298*2π)/18866 weeks
299-.14449 -.15836 (299*2π)/18866 weeks
300-.11955 -.20729 (300*2π)/18866 weeks
301-.14478 -.22648 (301*2π)/18866 weeks
302-.15063 -.20779 (302*2π)/18866 weeks
303-.14499 -.22975 (303*2π)/18866 weeks
304-.1578 -.22719 (304*2π)/18866 weeks
305-.19265 -.23827 (305*2π)/18866 weeks
306-.19505 -.19199 (306*2π)/18866 weeks
307-.19261 -.20098 (307*2π)/18866 weeks
308-.19851 -.20229 (308*2π)/18866 weeks
309-.2531 -.17802 (309*2π)/18866 weeks
310-.21071 -.12578 (310*2π)/18866 weeks
311-.22266 -.07629 (311*2π)/18866 weeks
312-.11754 -.07699 (312*2π)/18866 weeks
313-.14311 -.10205 (313*2π)/18866 weeks
314-.09003 -.11711 (314*2π)/18866 weeks
315-.13977 -.15649 (315*2π)/18866 weeks
316-.15078 -.09755 (316*2π)/18866 weeks
317-.0886 -.09594 (317*2π)/18866 weeks
318-.06551 -.14334 (318*2π)/18866 weeks
319-.11999 -.14251 (319*2π)/18866 weeks
320-.09414 -.11091 (320*2π)/18866 weeks
321-.06112 -.10065 (321*2π)/18866 weeks
322-.01652 -.13542 (322*2π)/18866 weeks
323-.01048 -.20533 (323*2π)/18866 weeks
324-.06629 -.25001 (324*2π)/18866 weeks
325-.13001 -.19979 (325*2π)/18866 weeks
326-.05622 -.1682 (326*2π)/18866 weeks
327-.10025 -.24575 (327*2π)/18866 weeks
328-.1746 -.21882 (328*2π)/18866 weeks
329-.16187 -.11136 (329*2π)/18866 weeks
330-.02727 -.14453 (330*2π)/18866 weeks
331-.06926 -.25751 (331*2π)/18866 weeks
332-.17163 -.24268 (332*2π)/18866 weeks
333-.19082 -.11606 (333*2π)/18866 weeks
334-.05695 -.10287 (334*2π)/18866 weeks
335-.04063 -.21509 (335*2π)/18866 weeks
336-.14207 -.2444 (336*2π)/18866 weeks
337-.14992 -.14413 (337*2π)/18866 weeks
338-.06153 -.16802 (338*2π)/18866 weeks
339-.10666 -.22594 (339*2π)/18866 weeks
340-.15783 -.22698 (340*2π)/18866 weeks
341-.20406 -.15643 (341*2π)/18866 weeks
342-.1362 -.11467 (342*2π)/18866 weeks
343-.10704 -.14374 (343*2π)/18865 weeks
344-.12373 -.14575 (344*2π)/18865 weeks
345-.0898 -.12612 (345*2π)/18865 weeks
346-.06322 -.1647 (346*2π)/18865 weeks
347-.10201 -.20787 (347*2π)/18865 weeks
348-.15377 -.19129 (348*2π)/18865 weeks
349-.15727 -.15189 (349*2π)/18865 weeks
350-.16583 -.15055 (350*2π)/18865 weeks
351-.16963 -.06735 (351*2π)/18865 weeks
352-.0546 -.04495 (352*2π)/18865 weeks
353-.01497 -.13626 (353*2π)/18865 weeks
354-.10194 -.18033 (354*2π)/18865 weeks
355-.1241 -.09958 (355*2π)/18865 weeks
356-.03977 -.09107 (356*2π)/18865 weeks
357-.0033 -.17135 (357*2π)/18865 weeks
358-.07592 -.18337 (358*2π)/18865 weeks
359-.03676 -.13042 (359*2π)/18865 weeks
360.01484 -.1992 (360*2π)/18865 weeks
361-.04428 -.2737 (361*2π)/18865 weeks
362-.1386 -.24566 (362*2π)/18865 weeks
363-.11815 -.16563 (363*2π)/18865 weeks
364-.05569 -.19045 (364*2π)/18865 weeks
365-.09537 -.24374 (365*2π)/18865 weeks
366-.14078 -.21071 (366*2π)/18865 weeks
367-.11081 -.17746 (367*2π)/18865 weeks
368-.11112 -.23241 (368*2π)/18865 weeks
369-.15018 -.19692 (369*2π)/18865 weeks
370-.1662 -.17532 (370*2π)/18865 weeks
371-.13797 -.13349 (371*2π)/18865 weeks
372-.12114 -.12271 (372*2π)/18865 weeks
373-.04329 -.12693 (373*2π)/18865 weeks
374-.05893 -.22091 (374*2π)/18865 weeks
375-.12619 -.25004 (375*2π)/18865 weeks
376-.2001 -.17688 (376*2π)/18865 weeks
377-.10787 -.10291 (377*2π)/18865 weeks
378-.06621 -.16075 (378*2π)/18865 weeks
379-.08431 -.18782 (379*2π)/18865 weeks
380-.09239 -.17708 (380*2π)/18865 weeks
381-.07741 -.2197 (381*2π)/18865 weeks
382-.10894 -.2245 (382*2π)/18865 weeks
383-.10747 -.25943 (383*2π)/18865 weeks
384-.17666 -.26269 (384*2π)/18865 weeks
385-.23131 -.2173 (385*2π)/18865 weeks
386-.21752 -.13538