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Fourier Analysis of PSA (Public Storage Common Stock)


PSA (Public Storage Common Stock) appears to have interesting cyclic behaviour every 190 weeks (8.4571*sine), 172 weeks (7.5999*sine), and 100 weeks (1.6765*cosine).

PSA (Public Storage Common Stock) has an average price of 43.22 (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 3/20/2017 for PSA (Public Storage Common Stock), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
043.22084   0 
140.26967 -42.34708 (1*2π)/18961,896 weeks
215.67224 -31.41151 (2*2π)/1896948 weeks
39.39723 -23.28537 (3*2π)/1896632 weeks
44.46996 -22.95168 (4*2π)/1896474 weeks
5-.53876 -15.56688 (5*2π)/1896379 weeks
61.67228 -11.12677 (6*2π)/1896316 weeks
73.55096 -11.47346 (7*2π)/1896271 weeks
8.93544 -12.92 (8*2π)/1896237 weeks
9-.89647 -9.70169 (9*2π)/1896211 weeks
10-.88872 -8.45709 (10*2π)/1896190 weeks
11-.55596 -7.59989 (11*2π)/1896172 weeks
12-.94488 -7.52072 (12*2π)/1896158 weeks
13-1.66886 -6.3573 (13*2π)/1896146 weeks
14-1.23303 -5.28866 (14*2π)/1896135 weeks
15-1.59442 -5.07652 (15*2π)/1896126 weeks
16-1.14557 -3.9134 (16*2π)/1896119 weeks
17-.51077 -4.26161 (17*2π)/1896112 weeks
18-1.54537 -4.04982 (18*2π)/1896105 weeks
19-1.67649 -3.19229 (19*2π)/1896100 weeks
20-1.10781 -2.28234 (20*2π)/189695 weeks
21-.17315 -2.47774 (21*2π)/189690 weeks
22-.55109 -3.31475 (22*2π)/189686 weeks
23-1.66028 -2.36949 (23*2π)/189682 weeks
24-.63756 -1.17521 (24*2π)/189679 weeks
25.21949 -1.77062 (25*2π)/189676 weeks
26-.37988 -2.0557 (26*2π)/189673 weeks
27-.50687 -1.41681 (27*2π)/189670 weeks
28.26654 -.84591 (28*2π)/189668 weeks
291.04044 -1.64431 (29*2π)/189665 weeks
30.43466 -2.0559 (30*2π)/189663 weeks
31.14372 -1.79189 (31*2π)/189661 weeks
32.54827 -1.42274 (32*2π)/189659 weeks
33.6909 -1.97125 (33*2π)/189657 weeks
34.3403 -1.79366 (34*2π)/189656 weeks
35.50278 -1.62568 (35*2π)/189654 weeks
36.77542 -1.77971 (36*2π)/189653 weeks
37.53449 -2.13456 (37*2π)/189651 weeks
38.49913 -2.01565 (38*2π)/189650 weeks
39.39875 -2.27452 (39*2π)/189649 weeks
40-.04499 -2.31468 (40*2π)/189647 weeks
41-.21904 -1.81939 (41*2π)/189646 weeks
42.0042 -1.69003 (42*2π)/189645 weeks
43.1033 -1.71195 (43*2π)/189644 weeks
44-.16054 -1.92548 (44*2π)/189643 weeks
45-.43712 -1.43438 (45*2π)/189642 weeks
46.02855 -1.0504 (46*2π)/189641 weeks
47.25783 -1.41972 (47*2π)/189640 weeks
48.12311 -1.4157 (48*2π)/189640 weeks
49.2697 -1.26627 (49*2π)/189639 weeks
50.39644 -1.53569 (50*2π)/189638 weeks
51.14802 -1.60316 (51*2π)/189637 weeks
52.176 -1.58864 (52*2π)/189636 weeks
53.15427 -1.63001 (53*2π)/189636 weeks
54.03644 -1.70942 (54*2π)/189635 weeks
55-.02569 -1.60137 (55*2π)/189634 weeks
56-.04314 -1.69003 (56*2π)/189634 weeks
57-.25853 -1.62546 (57*2π)/189633 weeks
58-.46261 -1.54683 (58*2π)/189633 weeks
59-.5071 -1.25044 (59*2π)/189632 weeks
60-.43402 -.9286 (60*2π)/189632 weeks
61.10053 -.8872 (61*2π)/189631 weeks
62-.01401 -1.21322 (62*2π)/189631 weeks
63-.04834 -1.18972 (63*2π)/189630 weeks
64-.08083 -1.19751 (64*2π)/189630 weeks
65.04149 -1.29052 (65*2π)/189629 weeks
66-.30338 -1.46572 (66*2π)/189629 weeks
67-.51826 -1.05227 (67*2π)/189628 weeks
68-.16651 -.8076 (68*2π)/189628 weeks
69.01716 -1.04471 (69*2π)/189627 weeks
70-.24091 -1.17136 (70*2π)/189627 weeks
71-.29801 -.81718 (71*2π)/189627 weeks
72.09037 -.85669 (72*2π)/189626 weeks
73-.02749 -1.21482 (73*2π)/189626 weeks
74-.21754 -1.14041 (74*2π)/189626 weeks
75-.32111 -.91316 (75*2π)/189625 weeks
76-.1449 -.83808 (76*2π)/189625 weeks
77-.10465 -.85778 (77*2π)/189625 weeks
78-.16659 -.98585 (78*2π)/189624 weeks
79-.20463 -.92733 (79*2π)/189624 weeks
80-.27971 -.86657 (80*2π)/189624 weeks
81-.16008 -.67867 (81*2π)/189623 weeks
82-.07522 -.72335 (82*2π)/189623 weeks
83.04007 -.74383 (83*2π)/189623 weeks
84.08304 -.84324 (84*2π)/189623 weeks
85.11871 -1.00052 (85*2π)/189622 weeks
86-.06225 -1.21841 (86*2π)/189622 weeks
87-.4108 -1.00717 (87*2π)/189622 weeks
88-.27172 -.71557 (88*2π)/189622 weeks
89-.03207 -.85761 (89*2π)/189621 weeks
90-.3917 -1.13008 (90*2π)/189621 weeks
91-.62287 -.64739 (91*2π)/189621 weeks
92-.2865 -.38308 (92*2π)/189621 weeks
93.00547 -.55096 (93*2π)/189620 weeks
94-.01809 -.78033 (94*2π)/189620 weeks
95-.16704 -.77622 (95*2π)/189620 weeks
96-.14585 -.69352 (96*2π)/189620 weeks
97-.13014 -.80751 (97*2π)/189620 weeks
98-.33114 -.80265 (98*2π)/189619 weeks
99-.36566 -.59344 (99*2π)/189619 weeks
100-.26944 -.49818 (100*2π)/189619 weeks
101-.19855 -.46154 (101*2π)/189619 weeks
102-.10351 -.42386 (102*2π)/189619 weeks
103-.07301 -.50299 (103*2π)/189618 weeks
104-.13794 -.4379 (104*2π)/189618 weeks
105.01767 -.36026 (105*2π)/189618 weeks
106.17881 -.59364 (106*2π)/189618 weeks
107-.02962 -.69248 (107*2π)/189618 weeks
108-.08736 -.52304 (108*2π)/189618 weeks
109.04041 -.45216 (109*2π)/189617 weeks
110.24958 -.58749 (110*2π)/189617 weeks
111.11025 -.83872 (111*2π)/189617 weeks
112-.1228 -.85257 (112*2π)/189617 weeks
113-.23315 -.56989 (113*2π)/189617 weeks
114.08758 -.47846 (114*2π)/189617 weeks
115.15215 -.76263 (115*2π)/189616 weeks
116-.06499 -.83644 (116*2π)/189616 weeks
117-.20008 -.68046 (117*2π)/189616 weeks
118-.0215 -.57039 (118*2π)/189616 weeks
119.05311 -.76838 (119*2π)/189616 weeks
120-.14325 -.91434 (120*2π)/189616 weeks
121-.37157 -.76001 (121*2π)/189616 weeks
122-.31176 -.57133 (122*2π)/189616 weeks
123-.23041 -.56361 (123*2π)/189615 weeks
124-.22542 -.58627 (124*2π)/189615 weeks
125-.23809 -.6048 (125*2π)/189615 weeks
126-.34159 -.60372 (126*2π)/189615 weeks
127-.33315 -.37367 (127*2π)/189615 weeks
128-.16354 -.33475 (128*2π)/189615 weeks
129-.10751 -.47519 (129*2π)/189615 weeks
130-.21457 -.4404 (130*2π)/189615 weeks
131-.17 -.42894 (131*2π)/189614 weeks
132-.15203 -.35471 (132*2π)/189614 weeks
133-.10606 -.46081 (133*2π)/189614 weeks
134-.19476 -.38644 (134*2π)/189614 weeks
135-.13015 -.29898 (135*2π)/189614 weeks
136.00495 -.24297 (136*2π)/189614 weeks
137.0621 -.39636 (137*2π)/189614 weeks
138.04262 -.43083 (138*2π)/189614 weeks
139.02195 -.50395 (139*2π)/189614 weeks
140.02575 -.46232 (140*2π)/189614 weeks
141.05961 -.56596 (141*2π)/189613 weeks
142-.0309 -.7228 (142*2π)/189613 weeks
143-.39477 -.59202 (143*2π)/189613 weeks
144-.31134 -.29095 (144*2π)/189613 weeks
145-.16083 -.21259 (145*2π)/189613 weeks
146-.04523 -.22054 (146*2π)/189613 weeks
147.10634 -.17226 (147*2π)/189613 weeks
148.23438 -.36805 (148*2π)/189613 weeks
149.19111 -.44051 (149*2π)/189613 weeks
150.2451 -.53846 (150*2π)/189613 weeks
151.09354 -.70301 (151*2π)/189613 weeks
152-.08456 -.58718 (152*2π)/189612 weeks
153.04771 -.45329 (153*2π)/189612 weeks
154.1195 -.60673 (154*2π)/189612 weeks
155.03078 -.68223 (155*2π)/189612 weeks
156-.07315 -.62967 (156*2π)/189612 weeks
157-.02074 -.61571 (157*2π)/189612 weeks
158-.08543 -.67402 (158*2π)/189612 weeks
159-.13965 -.65519 (159*2π)/189612 weeks
160-.18198 -.62053 (160*2π)/189612 weeks
161-.17413 -.64031 (161*2π)/189612 weeks
162-.32052 -.62486 (162*2π)/189612 weeks
163-.37461 -.45012 (163*2π)/189612 weeks
164-.32575 -.33491 (164*2π)/189612 weeks
165-.17536 -.27654 (165*2π)/189611 weeks
166-.13121 -.33489 (166*2π)/189611 weeks
167.00119 -.27145 (167*2π)/189611 weeks
168.051 -.48235 (168*2π)/189611 weeks
169-.05387 -.53131 (169*2π)/189611 weeks
170-.09297 -.51953 (170*2π)/189611 weeks
171-.14185 -.56373 (171*2π)/189611 weeks
172-.24184 -.52748 (172*2π)/189611 weeks
173-.27722 -.44925 (173*2π)/189611 weeks
174-.27161 -.28301 (174*2π)/189611 weeks
175-.04305 -.23178 (175*2π)/189611 weeks
176.01264 -.38141 (176*2π)/189611 weeks
177-.04008 -.46002 (177*2π)/189611 weeks
178-.06977 -.45069 (178*2π)/189611 weeks
179-.06431 -.48268 (179*2π)/189611 weeks
180-.1102 -.56568 (180*2π)/189611 weeks
181-.21733 -.48043 (181*2π)/189610 weeks
182-.13795 -.38693 (182*2π)/189610 weeks
183-.06958 -.47333 (183*2π)/189610 weeks
184-.16384 -.52053 (184*2π)/189610 weeks
185-.18848 -.50409 (185*2π)/189610 weeks
186-.21479 -.48426 (186*2π)/189610 weeks
187-.26973 -.51987 (187*2π)/189610 weeks
188-.35775 -.42057 (188*2π)/189610 weeks
189-.3022 -.29845 (189*2π)/189610 weeks
190-.21212 -.32425 (190*2π)/189610 weeks
191-.24974 -.3677 (191*2π)/189610 weeks
192-.28754 -.32594 (192*2π)/189610 weeks
193-.26683 -.26091 (193*2π)/189610 weeks
194-.26023 -.23901 (194*2π)/189610 weeks
195-.22132 -.16838 (195*2π)/189610 weeks
196-.11841 -.14307 (196*2π)/189610 weeks
197-.04386 -.20179 (197*2π)/189610 weeks
198-.01816 -.27348 (198*2π)/189610 weeks
199-.04438 -.33175 (199*2π)/189610 weeks
200-.08143 -.31821 (200*2π)/18969 weeks
201.00806 -.35787 (201*2π)/18969 weeks
202-.1284 -.47427 (202*2π)/18969 weeks
203-.21549 -.36122 (203*2π)/18969 weeks
204-.18201 -.30705 (204*2π)/18969 weeks
205-.15893 -.35455 (205*2π)/18969 weeks
206-.27013 -.26733 (206*2π)/18969 weeks
207-.12019 -.18755 (207*2π)/18969 weeks
208-.10467 -.26536 (208*2π)/18969 weeks
209-.10783 -.2535 (209*2π)/18969 weeks
210-.05771 -.25087 (210*2π)/18969 weeks
211-.07445 -.3528 (211*2π)/18969 weeks
212-.18894 -.33122 (212*2π)/18969 weeks
213-.16876 -.16814 (213*2π)/18969 weeks
214.02324 -.1519 (214*2π)/18969 weeks
215.06777 -.32901 (215*2π)/18969 weeks
216-.04426 -.41346 (216*2π)/18969 weeks
217-.09912 -.36357 (217*2π)/18969 weeks
218-.06821 -.36593 (218*2π)/18969 weeks
219-.12168 -.38524 (219*2π)/18969 weeks
220-.16806 -.3586 (220*2π)/18969 weeks
221-.12677 -.27346 (221*2π)/18969 weeks
222-.04564 -.3182 (222*2π)/18969 weeks
223-.04469 -.41651 (223*2π)/18969 weeks
224-.17618 -.49613 (224*2π)/18968 weeks
225-.2779 -.35606 (225*2π)/18968 weeks
226-.16909 -.3232 (226*2π)/18968 weeks
227-.18467 -.3719 (227*2π)/18968 weeks
228-.24418 -.35361 (228*2π)/18968 weeks
229-.21346 -.31134 (229*2π)/18968 weeks
230-.24892 -.36284 (230*2π)/18968 weeks
231-.33815 -.28942 (231*2π)/18968 weeks
232-.2724 -.17239 (232*2π)/18968 weeks
233-.16949 -.18248 (233*2π)/18968 weeks
234-.16995 -.25354 (234*2π)/18968 weeks
235-.21284 -.22227 (235*2π)/18968 weeks
236-.18869 -.21105 (236*2π)/18968 weeks
237-.15559 -.2359 (237*2π)/18968 weeks
238-.2344 -.29342 (238*2π)/18968 weeks
239-.28072 -.1664 (239*2π)/18968 weeks
240-.20471 -.10079 (240*2π)/18968 weeks
241-.13275 -.0851 (241*2π)/18968 weeks
242-.04693 -.13583 (242*2π)/18968 weeks
243-.07695 -.26888 (243*2π)/18968 weeks
244-.24409 -.21594 (244*2π)/18968 weeks
245-.1814 -.0674 (245*2π)/18968 weeks
246-.0628 -.05434 (246*2π)/18968 weeks
247.00729 -.16191 (247*2π)/18968 weeks
248-.04535 -.19761 (248*2π)/18968 weeks
249-.05423 -.18937 (249*2π)/18968 weeks
250-.05027 -.19397 (250*2π)/18968 weeks
251-.03383 -.21309 (251*2π)/18968 weeks
252-.07591 -.22748 (252*2π)/18968 weeks
253-.0764 -.16616 (253*2π)/18967 weeks
254.01105 -.15396 (254*2π)/18967 weeks
255.06318 -.21372 (255*2π)/18967 weeks
256.06506 -.3424 (256*2π)/18967 weeks
257-.05419 -.40047 (257*2π)/18967 weeks
258-.18737 -.37947 (258*2π)/18967 weeks
259-.21236 -.20233 (259*2π)/18967 weeks
260-.03812 -.16057 (260*2π)/18967 weeks
261-.02135 -.30655 (261*2π)/18967 weeks
262-.13227 -.32316 (262*2π)/18967 weeks
263-.14883 -.26903 (263*2π)/18967 weeks
264-.15797 -.24014 (264*2π)/18967 weeks
265-.12089 -.1847 (265*2π)/18967 weeks
266-.07113 -.23179 (266*2π)/18967 weeks
267-.11008 -.2052 (267*2π)/18967 weeks
268-.03414 -.22802 (268*2π)/18967 weeks
269-.07138 -.30041 (269*2π)/18967 weeks
270-.12758 -.31258 (270*2π)/18967 weeks
271-.20157 -.23424 (271*2π)/18967 weeks
272-.09498 -.14929 (272*2π)/18967 weeks
273-.0096 -.26762 (273*2π)/18967 weeks
274-.08744 -.32511 (274*2π)/18967 weeks
275-.15396 -.30982 (275*2π)/18967 weeks
276-.15946 -.26854 (276*2π)/18967 weeks
277-.17961 -.27463 (277*2π)/18967 weeks
278-.22666 -.27001 (278*2π)/18967 weeks
279-.25172 -.15107 (279*2π)/18967 weeks
280-.13435 -.10787 (280*2π)/18967 weeks
281-.07706 -.18478 (281*2π)/18967 weeks
282-.12914 -.24968 (282*2π)/18967 weeks
283-.2071 -.20544 (283*2π)/18967 weeks
284-.17777 -.15112 (284*2π)/18967 weeks
285-.16453 -.12515 (285*2π)/18967 weeks
286-.15278 -.13171 (286*2π)/18967 weeks
287-.14207 -.06208 (287*2π)/18967 weeks
288-.03736 -.02215 (288*2π)/18967 weeks
289.07312 -.13235 (289*2π)/18967 weeks
290.013 -.25983 (290*2π)/18967 weeks
291-.1058 -.27215 (291*2π)/18967 weeks
292-.16094 -.15123 (292*2π)/18966 weeks
293-.06303 -.08359 (293*2π)/18966 weeks
294.02775 -.13103 (294*2π)/18966 weeks
295.03782 -.23085 (295*2π)/18966 weeks
296-.03936 -.27349 (296*2π)/18966 weeks
297-.10489 -.23115 (297*2π)/18966 weeks
298-.056 -.16695 (298*2π)/18966 weeks
299-.0043 -.233 (299*2π)/18966 weeks
300-.06993 -.27346 (300*2π)/18966 weeks
301-.11422 -.23016 (301*2π)/18966 weeks
302-.08514 -.19593 (302*2π)/18966 weeks
303-.06177 -.20943 (303*2π)/18966 weeks
304-.07765 -.20822 (304*2π)/18966 weeks
305-.05298 -.20289 (305*2π)/18966 weeks
306-.04405 -.20126 (306*2π)/18966 weeks
307-.02293 -.24379 (307*2π)/18966 weeks
308-.05699 -.2463 (308*2π)/18966 weeks
309-.05103 -.25306 (309*2π)/18966 weeks
310-.03366 -.26118 (310*2π)/18966 weeks
311-.0623 -.33394 (311*2π)/18966 weeks
312-.09217 -.31504 (312*2π)/18966 weeks
313-.17663 -.33473 (313*2π)/18966 weeks
314-.17098 -.24124 (314*2π)/18966 weeks
315-.18421 -.25482 (315*2π)/18966 weeks
316-.15632 -.19615 (316*2π)/18966 weeks
317-.1314 -.24753 (317*2π)/18966 weeks
318-.19501 -.24989 (318*2π)/18966 weeks
319-.19694 -.19244 (319*2π)/18966 weeks
320-.1434 -.17043 (320*2π)/18966 weeks
321-.16246 -.21407 (321*2π)/18966 weeks
322-.18622 -.18818 (322*2π)/18966 weeks
323-.20124 -.1439 (323*2π)/18966 weeks
324-.16526 -.09444 (324*2π)/18966 weeks
325-.09002 -.09187 (325*2π)/18966 weeks
326-.04527 -.15375 (326*2π)/18966 weeks
327-.10878 -.19678 (327*2π)/18966 weeks
328-.09387 -.11385 (328*2π)/18966 weeks
329-.04238 -.17942 (329*2π)/18966 weeks
330-.08999 -.25081 (330*2π)/18966 weeks
331-.19438 -.1974 (331*2π)/18966 weeks
332-.10658 -.09161 (332*2π)/18966 weeks
333-.02047 -.16948 (333*2π)/18966 weeks
334-.0672 -.26221 (334*2π)/18966 weeks
335-.19385 -.2202 (335*2π)/18966 weeks
336-.14368 -.09914 (336*2π)/18966 weeks
337-.03961 -.13394 (337*2π)/18966 weeks
338-.06643 -.23622 (338*2π)/18966 weeks
339-.14812 -.18618 (339*2π)/18966 weeks
340-.07414 -.13318 (340*2π)/18966 weeks
341-.05356 -.19468 (341*2π)/18966 weeks
342-.07701 -.24523 (342*2π)/18966 weeks
343-.16658 -.2387 (343*2π)/18966 weeks
344-.15866 -.16713 (344*2π)/18966 weeks
345-.12242 -.16267 (345*2π)/18965 weeks
346-.1355 -.17151 (346*2π)/18965 weeks
347-.1218 -.13059 (347*2π)/18965 weeks
348-.07158 -.13559 (348*2π)/18965 weeks
349-.06653 -.19218 (349*2π)/18965 weeks
350-.1138 -.217 (350*2π)/18965 weeks
351-.14117 -.19346 (351*2π)/18965 weeks
352-.15657 -.20483 (352*2π)/18965 weeks
353-.21457 -.13561 (353*2π)/18965 weeks
354-.13435 -.04645 (354*2π)/18965 weeks
355-.04582 -.09234 (355*2π)/18965 weeks
356-.09312 -.17289 (356*2π)/18965 weeks
357-.15264 -.11473 (357*2π)/18965 weeks
358-.08573 -.0647 (358*2π)/18965 weeks
359-.01174 -.11859 (359*2π)/18965 weeks
360-.06767 -.15986 (360*2π)/18965 weeks
361-.04971 -.09686 (361*2π)/18965 weeks
362.0289 -.13931 (362*2π)/18965 weeks
363.0083 -.23436 (363*2π)/18965 weeks
364-.08985 -.24774 (364*2π)/18965 weeks
365-.09969 -.16953 (365*2π)/18965 weeks
366-.03378 -.17458 (366*2π)/18965 weeks
367-.0561 -.23786 (367*2π)/18965 weeks
368-.10936 -.22082 (368*2π)/18965 weeks
369-.0897 -.18262 (369*2π)/18965 weeks
370-.08075 -.23763 (370*2π)/18965 weeks
371-.12545 -.21218 (371*2π)/18965 weeks
372-.14828 -.19351 (372*2π)/18965 weeks
373-.12806 -.14767 (373*2π)/18965 weeks
374-.11349 -.13265 (374*2π)/18965 weeks
375-.03456 -.12881 (375*2π)/18965 weeks
376-.04181 -.22388 (376*2π)/18965 weeks
377-.10811 -.2588 (377*2π)/18965 weeks
378-.18595 -.18881 (378*2π)/18965 weeks
379-.09617 -.11363 (379*2π)/18965 weeks
380-.05513 -.17185 (380*2π)/18965 weeks
381-.07483 -.19929 (381*2π)/18965 weeks
382-.08387 -.18943 (382*2π)/1896