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# Fourier Analysis of PSF (Cohen & Steers Select Preferred and Income Fund)

PSF (Cohen & Steers Select Preferred and Income Fund) appears to have interesting cyclic behaviour every 39 weeks (.5594*sine), 35 weeks (.3482*sine), and 35 weeks (.2025*cosine).

PSF (Cohen & Steers Select Preferred and Income Fund) has an average price of 19.19 (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.

## Fourier Analysis

Using data from 11/26/2010 to 4/16/2018 for PSF (Cohen & Steers Select Preferred and Income Fund), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
019.19044   0
1.74087 -4.47479 (1*2π)/387387 weeks
2-.03603 -2.90061 (2*2π)/387194 weeks
3-.0514 -2.12385 (3*2π)/387129 weeks
4.37455 -.70282 (4*2π)/38797 weeks
5-.31016 -1.07662 (5*2π)/38777 weeks
6-.35667 -.76928 (6*2π)/38765 weeks
7-.05507 -.23883 (7*2π)/38755 weeks
8-.16388 -.57522 (8*2π)/38748 weeks
9.06398 -.46912 (9*2π)/38743 weeks
10-.11262 -.55939 (10*2π)/38739 weeks
11-.20249 -.34815 (11*2π)/38735 weeks
12.08102 -.26448 (12*2π)/38732 weeks
13-.04242 -.25171 (13*2π)/38730 weeks
14-.18568 -.28252 (14*2π)/38728 weeks
15-.13411 -.25505 (15*2π)/38726 weeks
16-.01587 -.18255 (16*2π)/38724 weeks
17.04504 -.12635 (17*2π)/38723 weeks
18.03954 -.19074 (18*2π)/38722 weeks
19.00413 -.19804 (19*2π)/38720 weeks
20-.10014 -.25284 (20*2π)/38719 weeks
21-.07184 -.13886 (21*2π)/38718 weeks
22-.00976 -.18361 (22*2π)/38718 weeks
23-.02865 -.24135 (23*2π)/38717 weeks
24.05217 -.17874 (24*2π)/38716 weeks
25.02863 -.16598 (25*2π)/38715 weeks
26-.0454 -.177 (26*2π)/38715 weeks
27-.00743 -.13131 (27*2π)/38714 weeks
28-.03863 -.09338 (28*2π)/38714 weeks
29-.08004 -.13876 (29*2π)/38713 weeks
30.06122 -.22611 (30*2π)/38713 weeks
31-.06864 -.15994 (31*2π)/38712 weeks
32-.11184 -.11939 (32*2π)/38712 weeks
33-.0323 -.13458 (33*2π)/38712 weeks
34-.09713 -.07037 (34*2π)/38711 weeks
35-.06803 -.14246 (35*2π)/38711 weeks
36-.05198 -.12755 (36*2π)/38711 weeks
37-.0862 -.0931 (37*2π)/38710 weeks
38-.06455 -.07637 (38*2π)/38710 weeks
39.05568 -.03645 (39*2π)/38710 weeks
40-.06395 -.03948 (40*2π)/38710 weeks
41-.04728 -.10718 (41*2π)/3879 weeks
42-.03721 -.06478 (42*2π)/3879 weeks
43-.05469 -.06259 (43*2π)/3879 weeks
44-.08084 -.0883 (44*2π)/3879 weeks
45.0206 -.08613 (45*2π)/3879 weeks
46-.0272 -.05219 (46*2π)/3878 weeks
47-.04648 -.09923 (47*2π)/3878 weeks
48.00705 -.03246 (48*2π)/3878 weeks
49.01062 -.06616 (49*2π)/3878 weeks
50-.02542 -.07464 (50*2π)/3878 weeks
51-.01841 -.04804 (51*2π)/3878 weeks
52-.00617 -.07691 (52*2π)/3877 weeks
53-.05014 -.06199 (53*2π)/3877 weeks
54-.05458 -.07228 (54*2π)/3877 weeks
55-.01022 -.11492 (55*2π)/3877 weeks
56-.00264 -.1099 (56*2π)/3877 weeks
57-.0311 -.07257 (57*2π)/3877 weeks
58-.02117 -.03671 (58*2π)/3877 weeks
59-.0029 -.10387 (59*2π)/3877 weeks
60-.0107 -.06549 (60*2π)/3876 weeks
61-.06357 -.05978 (61*2π)/3876 weeks
62-.04938 -.05884 (62*2π)/3876 weeks
63-.02053 -.04787 (63*2π)/3876 weeks
64-.03616 -.06187 (64*2π)/3876 weeks
65-.06414 -.06995 (65*2π)/3876 weeks
66-.04241 -.05083 (66*2π)/3876 weeks
67-.05564 -.04793 (67*2π)/3876 weeks
68-.04339 -.06048 (68*2π)/3876 weeks
69.00198 -.04802 (69*2π)/3876 weeks
70-.01461 -.04085 (70*2π)/3876 weeks
71-.02851 -.08761 (71*2π)/3875 weeks
72-.06761 -.04175 (72*2π)/3875 weeks
73-.05321 -.01285 (73*2π)/3875 weeks
74-.03605 -.02128 (74*2π)/3875 weeks
75-.04582 -.04066 (75*2π)/3875 weeks
76-.03473 -.04809 (76*2π)/3875 weeks
77-.03145 -.04868 (77*2π)/3875 weeks
78-.04659 -.01342 (78*2π)/3875 weeks
79-.01292 -.02255 (79*2π)/3875 weeks
80.00709 -.05637 (80*2π)/3875 weeks
81-.02644 -.05314 (81*2π)/3875 weeks
82-.0264 -.03857 (82*2π)/3875 weeks
83-.02099 -.04978 (83*2π)/3875 weeks
84-.05882 -.03429 (84*2π)/3875 weeks
85-.04205 -.02295 (85*2π)/3875 weeks
86-.0449 -.05624 (86*2π)/3875 weeks
87-.03147 -.05932 (87*2π)/3874 weeks
88-.07378 .00769 (88*2π)/3874 weeks
89-.01318 -.03299 (89*2π)/3874 weeks
90-.03581 -.03848 (90*2π)/3874 weeks
91-.03612 -.05689 (91*2π)/3874 weeks
92-.0453 -.03434 (92*2π)/3874 weeks
93-.02462 -.03592 (93*2π)/3874 weeks
94-.03391 -.02929 (94*2π)/3874 weeks
95-.04804 -.00258 (95*2π)/3874 weeks
96-.03968 -.04471 (96*2π)/3874 weeks
97-.04504 -.02195 (97*2π)/3874 weeks
98-.02884 -.01111 (98*2π)/3874 weeks
99.00511 -.03149 (99*2π)/3874 weeks
100-.01627 -.02946 (100*2π)/3874 weeks
101-.03923 -.03503 (101*2π)/3874 weeks
102-.03823 -.01122 (102*2π)/3874 weeks
103-.04707 -.04293 (103*2π)/3874 weeks
104-.03478 -.01052 (104*2π)/3874 weeks
105-.0185 -.02826 (105*2π)/3874 weeks
106-.01637 -.02504 (106*2π)/3874 weeks
107-.03946 -.03644 (107*2π)/3874 weeks
108-.01841 .00635 (108*2π)/3874 weeks
109-.01011 -.00473 (109*2π)/3874 weeks
110-.0303 -.02754 (110*2π)/3874 weeks
111-.02752 -.04223 (111*2π)/3873 weeks
112-.01657 -.02569 (112*2π)/3873 weeks
113-.02799 -.02341 (113*2π)/3873 weeks
114-.01807 -.02543 (114*2π)/3873 weeks
115-.00543 -.02408 (115*2π)/3873 weeks
116-.05106 -.02471 (116*2π)/3873 weeks
117-.04456 -.05416 (117*2π)/3873 weeks
118-.04231 .00244 (118*2π)/3873 weeks
119-.01808 .00704 (119*2π)/3873 weeks
120-.02552 -.02765 (120*2π)/3873 weeks
121-.03491 -.02126 (121*2π)/3873 weeks
122-.00073 -.02103 (122*2π)/3873 weeks
123-.01422 -.02768 (123*2π)/3873 weeks
124-.0314 -.0313 (124*2π)/3873 weeks
125-.03428 -.017 (125*2π)/3873 weeks
126-.01413 -.00132 (126*2π)/3873 weeks
127-.02091 -.02173 (127*2π)/3873 weeks
128-.03253 -.02646 (128*2π)/3873 weeks
129-.02186 -.03704 (129*2π)/3873 weeks
130-.03972 -.0358 (130*2π)/3873 weeks
131-.05287 -.04458 (131*2π)/3873 weeks
132-.03043 -.02092 (132*2π)/3873 weeks
133-.03046 -.03109 (133*2π)/3873 weeks
134-.04898 -.02403 (134*2π)/3873 weeks
135-.03292 -.00326 (135*2π)/3873 weeks
136-.04943 -.02983 (136*2π)/3873 weeks
137-.04291 -.04328 (137*2π)/3873 weeks
138-.06244 .0058 (138*2π)/3873 weeks
139-.03627 .00244 (139*2π)/3873 weeks
140-.01097 -.0231 (140*2π)/3873 weeks
141-.03468 -.01709 (141*2π)/3873 weeks
142-.04689 -.01493 (142*2π)/3873 weeks
143-.05037 -.01531 (143*2π)/3873 weeks
144-.02984 -.00283 (144*2π)/3873 weeks
145-.03174 -.02151 (145*2π)/3873 weeks
146-.02907 -.02116 (146*2π)/3873 weeks
147-.05598 -.01018 (147*2π)/3873 weeks
148-.02073 -.00397 (148*2π)/3873 weeks
149-.01388 -.01144 (149*2π)/3873 weeks
150-.03913 .01178 (150*2π)/3873 weeks
151-.04264 -.00914 (151*2π)/3873 weeks
152-.01211 .00297 (152*2π)/3873 weeks
153-.04207 -.00417 (153*2π)/3873 weeks
154-.03219 -.009 (154*2π)/3873 weeks
155-.02212 -.00728 (155*2π)/3872 weeks
156-.03658 -.02066 (156*2π)/3872 weeks
157-.03232 -.0185 (157*2π)/3872 weeks
158-.01753 .0078 (158*2π)/3872 weeks
159-.04965 -.00553 (159*2π)/3872 weeks
160-.01012 -.01354 (160*2π)/3872 weeks
161-.01297 .00109 (161*2π)/3872 weeks
162-.03842 .00397 (162*2π)/3872 weeks
163-.03496 -.02681 (163*2π)/3872 weeks
164-.03612 -.00664 (164*2π)/3872 weeks
165-.04777 -.00331 (165*2π)/3872 weeks
166-.04278 -.01532 (166*2π)/3872 weeks
167-.01466 .00036 (167*2π)/3872 weeks
168-.03319 -.00729 (168*2π)/3872 weeks
169-.03361 -.01753 (169*2π)/3872 weeks
170-.03155 .00055 (170*2π)/3872 weeks
171-.02955 -.00506 (171*2π)/3872 weeks
172-.01363 -.01233 (172*2π)/3872 weeks
173-.04041 .00641 (173*2π)/3872 weeks
174-.02214 -.00661 (174*2π)/3872 weeks
175-.03364 -.00465 (175*2π)/3872 weeks
176-.03847 .0016 (176*2π)/3872 weeks
177-.05603 -.01376 (177*2π)/3872 weeks
178-.02619 .01623 (178*2π)/3872 weeks
179-.0334 .0036 (179*2π)/3872 weeks
180-.03593 -.0027 (180*2π)/3872 weeks
181-.02124 -.00976 (181*2π)/3872 weeks
182-.02097 -.00096 (182*2π)/3872 weeks
183-.01284 -.01776 (183*2π)/3872 weeks
184-.02747 -.02622 (184*2π)/3872 weeks
185-.04014 -.0046 (185*2π)/3872 weeks
186-.03328 -.00741 (186*2π)/3872 weeks
187-.02595 .00591 (187*2π)/3872 weeks
188-.04608 -.01161 (188*2π)/3872 weeks
189-.03471 .00416 (189*2π)/3872 weeks
190-.01934 -.00983 (190*2π)/3872 weeks
191-.0378 .01351 (191*2π)/3872 weeks
192-.01714 .00246 (192*2π)/3872 weeks
193-.03628 -.00396 (193*2π)/3872 weeks
194-.03628 .00396 (194*2π)/3872 weeks
195-.01714 -.00246 (195*2π)/3872 weeks
196-.0378 -.01351 (196*2π)/3872 weeks
197-.01934 .00983 (197*2π)/3872 weeks
198-.03471 -.00416 (198*2π)/3872 weeks
199-.04608 .01161 (199*2π)/3872 weeks
200-.02595 -.00591 (200*2π)/3872 weeks
201-.03328 .00741 (201*2π)/3872 weeks
202-.04014 .0046 (202*2π)/3872 weeks
203-.02747 .02622 (203*2π)/3872 weeks
204-.01284 .01776 (204*2π)/3872 weeks
205-.02097 .00096 (205*2π)/3872 weeks
206-.02124 .00976 (206*2π)/3872 weeks
207-.03593 .0027 (207*2π)/3872 weeks
208-.0334 -.0036 (208*2π)/3872 weeks
209-.02619 -.01623 (209*2π)/3872 weeks
210-.05603 .01376 (210*2π)/3872 weeks
211-.03847 -.0016 (211*2π)/3872 weeks
212-.03364 .00465 (212*2π)/3872 weeks
213-.02214 .00661 (213*2π)/3872 weeks
214-.04041 -.00641 (214*2π)/3872 weeks
215-.01363 .01233 (215*2π)/3872 weeks
216-.02955 .00506 (216*2π)/3872 weeks
217-.03155 -.00055 (217*2π)/3872 weeks
218-.03361 .01753 (218*2π)/3872 weeks
219-.03319 .00729 (219*2π)/3872 weeks
220-.01466 -.00036 (220*2π)/3872 weeks
221-.04278 .01532 (221*2π)/3872 weeks
222-.04777 .00331 (222*2π)/3872 weeks
223-.03612 .00664 (223*2π)/3872 weeks
224-.03496 .02681 (224*2π)/3872 weeks
225-.03842 -.00397 (225*2π)/3872 weeks
226-.01297 -.00109 (226*2π)/3872 weeks
227-.01012 .01354 (227*2π)/3872 weeks
228-.04965 .00553 (228*2π)/3872 weeks
229-.01753 -.0078 (229*2π)/3872 weeks
230-.03232 .0185 (230*2π)/3872 weeks
231-.03658 .02066 (231*2π)/3872 weeks
232-.02212 .00728 (232*2π)/3872 weeks
233-.03219 .009 (233*2π)/3872 weeks
234-.04207 .00417 (234*2π)/3872 weeks
235-.01211 -.00297 (235*2π)/3872 weeks
236-.04264 .00914 (236*2π)/3872 weeks
237-.03913 -.01178 (237*2π)/3872 weeks
238-.01388 .01144 (238*2π)/3872 weeks
239-.02073 .00397 (239*2π)/3872 weeks
240-.05598 .01018 (240*2π)/3872 weeks
241-.02907 .02116 (241*2π)/3872 weeks
242-.03174 .02151 (242*2π)/3872 weeks
243-.02984 .00283 (243*2π)/3872 weeks
244-.05037 .01531 (244*2π)/3872 weeks
245-.04689 .01493 (245*2π)/3872 weeks
246-.03468 .01709 (246*2π)/3872 weeks
247-.01097 .0231 (247*2π)/3872 weeks
248-.03627 -.00244 (248*2π)/3872 weeks
249-.06244 -.0058 (249*2π)/3872 weeks
250-.04291 .04328 (250*2π)/3872 weeks
251-.04943 .02983 (251*2π)/3872 weeks
252-.03292 .00326 (252*2π)/3872 weeks
253-.04898 .02403 (253*2π)/3872 weeks
254-.03046 .03109 (254*2π)/3872 weeks
255-.03043 .02092 (255*2π)/3872 weeks
256-.05287 .04458 (256*2π)/3872 weeks
257-.03972 .0358 (257*2π)/3872 weeks
258-.02186 .03704 (258*2π)/3872 weeks
259-.03253 .02646 (259*2π)/3871 weeks
260-.02091 .02173 (260*2π)/3871 weeks
261-.01413 .00132 (261*2π)/3871 weeks
262-.03428 .017 (262*2π)/3871 weeks
263-.0314 .0313 (263*2π)/3871 weeks
264-.01422 .02768 (264*2π)/3871 weeks
265-.00073 .02103 (265*2π)/3871 weeks
266-.03491 .02126 (266*2π)/3871 weeks
267-.02552 .02765 (267*2π)/3871 weeks
268-.01808 -.00704 (268*2π)/3871 weeks
269-.04231 -.00244 (269*2π)/3871 weeks
270-.04456 .05416 (270*2π)/3871 weeks
271-.05106 .02471 (271*2π)/3871 weeks
272-.00543 .02408 (272*2π)/3871 weeks
273-.01807 .02543 (273*2π)/3871 weeks
274-.02799 .02341 (274*2π)/3871 weeks
275-.01657 .02569 (275*2π)/3871 weeks
276-.02752 .04223 (276*2π)/3871 weeks
277-.0303 .02754 (277*2π)/3871 weeks
278-.01011 .00473 (278*2π)/3871 weeks
279-.01841 -.00635 (279*2π)/3871 weeks
280-.03946 .03644 (280*2π)/3871 weeks
281-.01637 .02504 (281*2π)/3871 weeks
282-.0185 .02826 (282*2π)/3871 weeks
283-.03478 .01052 (283*2π)/3871 weeks
284-.04707 .04293 (284*2π)/3871 weeks
285-.03823 .01122 (285*2π)/3871 weeks
286-.03923 .03503 (286*2π)/3871 weeks
287-.01627 .02946 (287*2π)/3871 weeks
288.00511 .03149 (288*2π)/3871 weeks
289-.02884 .01111 (289*2π)/3871 weeks
290-.04504 .02195 (290*2π)/3871 weeks
291-.03968 .04471 (291*2π)/3871 weeks
292-.04804 .00258 (292*2π)/3871 weeks
293-.03391 .02929 (293*2π)/3871 weeks
294-.02462 .03592 (294*2π)/3871 weeks
295-.0453 .03434 (295*2π)/3871 weeks
296-.03612 .05689 (296*2π)/3871 weeks
297-.03581 .03848 (297*2π)/3871 weeks
298-.01318 .03299 (298*2π)/3871 weeks
299-.07378 -.00769 (299*2π)/3871 weeks
300-.03147 .05932 (300*2π)/3871 weeks
301-.0449 .05624 (301*2π)/3871 weeks
302-.04205 .02295 (302*2π)/3871 weeks
303-.05882 .03429 (303*2π)/3871 weeks
304-.02099 .04978 (304*2π)/3871 weeks
305-.0264 .03857 (305*2π)/3871 weeks
306-.02644 .05314 (306*2π)/3871 weeks
307.00709 .05637 (307*2π)/3871 weeks
308-.01292 .02255 (308*2π)/3871 weeks
309-.04659 .01342 (309*2π)/3871 weeks
310-.03145 .04868 (310*2π)/3871 weeks
311-.03473 .04809 (311*2π)/3871 weeks
312-.04582 .04066 (312*2π)/3871 weeks
313-.03605 .02128 (313*2π)/3871 weeks
314-.05321 .01285 (314*2π)/3871 weeks
315-.06761 .04175 (315*2π)/3871 weeks
316-.02851 .08761 (316*2π)/3871 weeks
317-.01461 .04085 (317*2π)/3871 weeks
318.00198 .04802 (318*2π)/3871 weeks
319-.04339 .06048 (319*2π)/3871 weeks
320-.05564 .04793 (320*2π)/3871 weeks
321-.04241 .05083 (321*2π)/3871 weeks
322-.06414 .06995 (322*2π)/3871 weeks
323-.03616 .06187 (323*2π)/3871 weeks
324-.02053 .04787 (324*2π)/3871 weeks
325-.04938 .05884 (325*2π)/3871 weeks
326-.06357 .05978 (326*2π)/3871 weeks
327-.0107 .06549 (327*2π)/3871 weeks
328-.0029 .10387 (328*2π)/3871 weeks
329-.02117 .03671 (329*2π)/3871 weeks
330-.0311 .07257 (330*2π)/3871 weeks
331-.00264 .1099 (331*2π)/3871 weeks
332-.01022 .11492 (332*2π)/3871 weeks
333-.05458 .07228 (333*2π)/3871 weeks
334-.05014 .06199 (334*2π)/3871 weeks
335-.00617 .07691 (335*2π)/3871 weeks
336-.01841 .04804 (336*2π)/3871 weeks
337-.02542 .07464 (337*2π)/3871 weeks
338.01062 .06616 (338*2π)/3871 weeks
339.00705 .03246 (339*2π)/3871 weeks
340-.04648 .09923 (340*2π)/3871 weeks
341-.0272 .05219 (341*2π)/3871 weeks
342.0206 .08613 (342*2π)/3871 weeks
343-.08084 .0883 (343*2π)/3871 weeks
344-.05469 .06259 (344*2π)/3871 weeks
345-.03721 .06478 (345*2π)/3871 weeks
346-.04728 .10718 (346*2π)/3871 weeks
347-.06395 .03948 (347*2π)/3871 weeks
348.05568 .03645 (348*2π)/3871 weeks
349-.06455 .07637 (349*2π)/3871 weeks
350-.0862 .0931 (350*2π)/3871 weeks
351-.05198 .12755 (351*2π)/3871 weeks
352-.06803 .14246 (352*2π)/3871 weeks
353-.09713 .07037 (353*2π)/3871 weeks
354-.0323 .13458 (354*2π)/3871 weeks
355-.11184 .11939 (355*2π)/3871 weeks
356-.06864 .15994 (356*2π)/3871 weeks
357.06122 .22611 (357*2π)/3871 weeks
358-.08004 .13876 (358*2π)/3871 weeks
359-.03863 .09338 (359*2π)/3871 weeks
360-.00743 .13131 (360*2π)/3871 weeks
361-.0454 .177 (361*2π)/3871 weeks
362.02863 .16598 (362*2π)/3871 weeks
363.05217 .17874 (363*2π)/3871 weeks
364-.02865 .24135 (364*2π)/3871 weeks
365-.00976 .18361 (365*2π)/3871 weeks
366-.07184 .13886 (366*2π)/3871 weeks
367-.10014 .25284 (367*2π)/3871 weeks
368.00413 .19804 (368*2π)/3871 weeks
369.03954 .19074 (369*2π)/3871 weeks
370.04504 .12635 (370*2π)/3871 weeks
371-.01587 .18255 (371*2π)/3871 weeks
372-.13411 .25505 (372*2π)/3871 weeks
373-.18568 .28252 (373*2π)/3871 weeks
374-.04242 .25171 (374*2π)/3871 weeks
375.08102 .26448 (375*2π)/3871 weeks
376-.20249 .34815 (376*2π)/3871 weeks
377-.11262 .55939 (377*2π)/3871 weeks
378.06398 .46912 (378*2π)/3871 weeks
379-.16388 .57522 (379*2π)/3871 weeks
380-.05507 .23883 (380*2π)/3871 weeks
381-.35667 .76928 (381*2π)/3871 weeks
382-.31016 1.07662 (382*2π)/3871 weeks
383.37455 .70282 (383*2π)/3871 weeks
384-.0514 2.12385 (384*2π)/3871 weeks
385-.03603 2.90061 (385*2π)/3871 weeks