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# Fourier Analysis of PENTX (PIMCO REALRETIREMENT 2025 FUND INSTITUTIONAL CLASS)

PENTX (PIMCO REALRETIREMENT 2025 FUND INSTITUTIONAL CLASS) appears to have interesting cyclic behaviour every 36 weeks (.0931*sine), 32 weeks (.0747*sine), and 36 weeks (.0445*cosine).

PENTX (PIMCO REALRETIREMENT 2025 FUND INSTITUTIONAL CLASS) has an average price of 7.85 (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 7/1/2011 to 4/16/2018 for PENTX (PIMCO REALRETIREMENT 2025 FUND INSTITUTIONAL CLASS), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
07.84967   0
1.03692 -.55272 (1*2π)/356356 weeks
2.19001 -.55197 (2*2π)/356178 weeks
3-.11827 -.40981 (3*2π)/356119 weeks
4.08427 -.22508 (4*2π)/35689 weeks
5.02965 -.24468 (5*2π)/35671 weeks
6-.09417 -.15866 (6*2π)/35659 weeks
7.03944 -.12645 (7*2π)/35651 weeks
8.0109 -.15845 (8*2π)/35645 weeks
9.00505 -.10923 (9*2π)/35640 weeks
10-.04449 -.09306 (10*2π)/35636 weeks
11.03334 -.07473 (11*2π)/35632 weeks
12.01619 -.05429 (12*2π)/35630 weeks
13-.02464 -.03223 (13*2π)/35627 weeks
14-.00565 -.05989 (14*2π)/35625 weeks
15-.03913 -.05017 (15*2π)/35624 weeks
16-.00698 -.01687 (16*2π)/35622 weeks
17.01512 -.06386 (17*2π)/35621 weeks
18-.01278 -.05928 (18*2π)/35620 weeks
19-.0148 -.00615 (19*2π)/35619 weeks
20.01509 -.03834 (20*2π)/35618 weeks
21-.01679 -.0371 (21*2π)/35617 weeks
22.01396 -.01683 (22*2π)/35616 weeks
23.01458 -.02639 (23*2π)/35615 weeks
24-.00984 -.02198 (24*2π)/35615 weeks
25-.00807 -.03461 (25*2π)/35614 weeks
26.00374 -.02791 (26*2π)/35614 weeks
27-.00309 -.01357 (27*2π)/35613 weeks
28-.01189 -.04209 (28*2π)/35613 weeks
29-.0167 -.02151 (29*2π)/35612 weeks
30.00825 -.03593 (30*2π)/35612 weeks
31-.03167 -.02672 (31*2π)/35611 weeks
32.0054 -.04467 (32*2π)/35611 weeks
33-.00464 -.02947 (33*2π)/35611 weeks
34-.01363 -.01181 (34*2π)/35610 weeks
35-.00828 -.01978 (35*2π)/35610 weeks
36.00297 -.03536 (36*2π)/35610 weeks
37-.01477 -.0108 (37*2π)/35610 weeks
38-.01003 -.02662 (38*2π)/3569 weeks
39-.00185 -.02002 (39*2π)/3569 weeks
40.00062 -.01416 (40*2π)/3569 weeks
41-.00762 -.01118 (41*2π)/3569 weeks
42-.01378 -.01353 (42*2π)/3568 weeks
43.00772 -.00653 (43*2π)/3568 weeks
44-.00722 -.0004 (44*2π)/3568 weeks
45-.00339 -.006 (45*2π)/3568 weeks
46-.00409 -.01272 (46*2π)/3568 weeks
47-.00337 -.00512 (47*2π)/3568 weeks
48-.01029 -.01342 (48*2π)/3567 weeks
49-.00465 -.01191 (49*2π)/3567 weeks
50-.01117 -.01036 (50*2π)/3567 weeks
51-.00664 -.01277 (51*2π)/3567 weeks
52-.00697 -.01198 (52*2π)/3567 weeks
53-.0107 -.01293 (53*2π)/3567 weeks
54-.0022 -.01951 (54*2π)/3567 weeks
55-.01233 -.02701 (55*2π)/3566 weeks
56-.00636 -.02684 (56*2π)/3566 weeks
57-.00493 -.01414 (57*2π)/3566 weeks
58-.00423 -.02492 (58*2π)/3566 weeks
59-.01322 -.02274 (59*2π)/3566 weeks
60-.01134 -.01126 (60*2π)/3566 weeks
61-.00904 -.01533 (61*2π)/3566 weeks
62-.0045 -.01632 (62*2π)/3566 weeks
63-.01192 -.01111 (63*2π)/3566 weeks
64-.00596 -.0087 (64*2π)/3566 weeks
65-.00168 -.02032 (65*2π)/3565 weeks
66-.02029 -.01863 (66*2π)/3565 weeks
67-.00837 -.00388 (67*2π)/3565 weeks
68-.00554 -.00976 (68*2π)/3565 weeks
69-.01653 -.01145 (69*2π)/3565 weeks
70-.00602 -.00968 (70*2π)/3565 weeks
71-.01008 -.01705 (71*2π)/3565 weeks
72-.01379 -.00491 (72*2π)/3565 weeks
73-.00223 -.01097 (73*2π)/3565 weeks
74-.00199 -.01075 (74*2π)/3565 weeks
75-.01384 -.00528 (75*2π)/3565 weeks
76-.00005 -.00989 (76*2π)/3565 weeks
77-.00633 -.01415 (77*2π)/3565 weeks
78-.01062 -.00226 (78*2π)/3565 weeks
79-.00362 -.01091 (79*2π)/3565 weeks
80-.00168 -.01376 (80*2π)/3564 weeks
81-.00938 .00148 (81*2π)/3564 weeks
82.00141 -.00626 (82*2π)/3564 weeks
83-.00998 -.00949 (83*2π)/3564 weeks
84-.00577 -.01283 (84*2π)/3564 weeks
85-.01142 -.00348 (85*2π)/3564 weeks
86-.00429 -.01082 (86*2π)/3564 weeks
87-.01554 -.0089 (87*2π)/3564 weeks
88-.00263 -.00967 (88*2π)/3564 weeks
89-.01244 -.01442 (89*2π)/3564 weeks
90-.00814 -.00674 (90*2π)/3564 weeks
91-.00265 -.01585 (91*2π)/3564 weeks
92-.01022 -.01164 (92*2π)/3564 weeks
93-.01409 -.00556 (93*2π)/3564 weeks
94-.00212 -.00663 (94*2π)/3564 weeks
95-.0096 -.0091 (95*2π)/3564 weeks
96-.00541 -.00483 (96*2π)/3564 weeks
97-.00791 -.00396 (97*2π)/3564 weeks
98-.0086 -.00097 (98*2π)/3564 weeks
99-.00666 -.00186 (99*2π)/3564 weeks
100-.00588 -.00587 (100*2π)/3564 weeks
101-.00778 -.00468 (101*2π)/3564 weeks
102-.00686 .00047 (102*2π)/3563 weeks
103-.00919 .00138 (103*2π)/3563 weeks
104-.00451 -.00333 (104*2π)/3563 weeks
105-.00262 -.00301 (105*2π)/3563 weeks
106-.0082 -.00746 (106*2π)/3563 weeks
107-.00346 -.00386 (107*2π)/3563 weeks
108-.0037 -.00168 (108*2π)/3563 weeks
109-.00467 -.00304 (109*2π)/3563 weeks
110-.00267 -.00338 (110*2π)/3563 weeks
111-.00816 -.00569 (111*2π)/3563 weeks
112.00368 -.00022 (112*2π)/3563 weeks
113-.00025 -.00804 (113*2π)/3563 weeks
114-.00595 -.00531 (114*2π)/3563 weeks
115-.00272 -.00581 (115*2π)/3563 weeks
116-.00154 -.00747 (116*2π)/3563 weeks
117-.00714 -.00761 (117*2π)/3563 weeks
118-.00713 -.00722 (118*2π)/3563 weeks
119-.01067 -.0095 (119*2π)/3563 weeks
120-.00719 -.00414 (120*2π)/3563 weeks
121-.0079 -.00764 (121*2π)/3563 weeks
122-.01226 -.00867 (122*2π)/3563 weeks
123-.00438 -.00679 (123*2π)/3563 weeks
124-.0116 -.00641 (124*2π)/3563 weeks
125-.00692 -.00592 (125*2π)/3563 weeks
126-.01023 -.01096 (126*2π)/3563 weeks
127-.00908 .00278 (127*2π)/3563 weeks
128-.00897 -.00199 (128*2π)/3563 weeks
129-.00532 -.00485 (129*2π)/3563 weeks
130-.0065 .00078 (130*2π)/3563 weeks
131-.00871 .00306 (131*2π)/3563 weeks
132-.01138 -.00055 (132*2π)/3563 weeks
133-.01237 -.00253 (133*2π)/3563 weeks
134-.00916 .00079 (134*2π)/3563 weeks
135-.01178 -.0012 (135*2π)/3563 weeks
136-.00736 -.00023 (136*2π)/3563 weeks
137-.01055 -.00243 (137*2π)/3563 weeks
138-.01018 .00586 (138*2π)/3563 weeks
139-.01244 -.0061 (139*2π)/3563 weeks
140-.00792 .00035 (140*2π)/3563 weeks
141-.00811 -.00448 (141*2π)/3563 weeks
142-.00881 .00089 (142*2π)/3563 weeks
143-.00441 -.00395 (143*2π)/3562 weeks
144-.00923 -.001 (144*2π)/3562 weeks
145-.00854 -.00172 (145*2π)/3562 weeks
146-.00789 -.00031 (146*2π)/3562 weeks
147-.00778 -.00143 (147*2π)/3562 weeks
148-.01287 .00074 (148*2π)/3562 weeks
149-.00399 -.00109 (149*2π)/3562 weeks
150-.0098 -.0061 (150*2π)/3562 weeks
151-.0099 .0015 (151*2π)/3562 weeks
152-.009 .00061 (152*2π)/3562 weeks
153-.00742 -.00114 (153*2π)/3562 weeks
154-.00714 -.00023 (154*2π)/3562 weeks
155-.01282 -.00619 (155*2π)/3562 weeks
156-.01126 -.00224 (156*2π)/3562 weeks
157-.00318 -.00102 (157*2π)/3562 weeks
158-.00626 .00067 (158*2π)/3562 weeks
159-.00466 -.00228 (159*2π)/3562 weeks
160-.00969 -.00539 (160*2π)/3562 weeks
161-.00475 .00117 (161*2π)/3562 weeks
162-.00717 -.0006 (162*2π)/3562 weeks
163-.0075 -.00239 (163*2π)/3562 weeks
164-.00653 .00218 (164*2π)/3562 weeks
165-.0013 -.00091 (165*2π)/3562 weeks
166-.00727 .00068 (166*2π)/3562 weeks
167-.00644 .00116 (167*2π)/3562 weeks
168-.00334 .00377 (168*2π)/3562 weeks
169-.00495 -.00115 (169*2π)/3562 weeks
170-.01333 -.00174 (170*2π)/3562 weeks
171-.00446 .00337 (171*2π)/3562 weeks
172-.00204 -.00161 (172*2π)/3562 weeks
173-.00962 .00159 (173*2π)/3562 weeks
174-.00463 .00117 (174*2π)/3562 weeks
175-.00677 -.00325 (175*2π)/3562 weeks
176-.00781 .00524 (176*2π)/3562 weeks
177-.00605 -.00061 (177*2π)/3562 weeks
178-.00864   (178*2π)/3562 weeks
179-.00605 .00061 (179*2π)/3562 weeks
180-.00781 -.00524 (180*2π)/3562 weeks
181-.00677 .00325 (181*2π)/3562 weeks
182-.00463 -.00117 (182*2π)/3562 weeks
183-.00962 -.00159 (183*2π)/3562 weeks
184-.00204 .00161 (184*2π)/3562 weeks
185-.00446 -.00337 (185*2π)/3562 weeks
186-.01333 .00174 (186*2π)/3562 weeks
187-.00495 .00115 (187*2π)/3562 weeks
188-.00334 -.00377 (188*2π)/3562 weeks
189-.00644 -.00116 (189*2π)/3562 weeks
190-.00727 -.00068 (190*2π)/3562 weeks
191-.0013 .00091 (191*2π)/3562 weeks
192-.00653 -.00218 (192*2π)/3562 weeks
193-.0075 .00239 (193*2π)/3562 weeks
194-.00717 .0006 (194*2π)/3562 weeks
195-.00475 -.00117 (195*2π)/3562 weeks
196-.00969 .00539 (196*2π)/3562 weeks
197-.00466 .00228 (197*2π)/3562 weeks
198-.00626 -.00067 (198*2π)/3562 weeks
199-.00318 .00102 (199*2π)/3562 weeks
200-.01126 .00224 (200*2π)/3562 weeks
201-.01282 .00619 (201*2π)/3562 weeks
202-.00714 .00023 (202*2π)/3562 weeks
203-.00742 .00114 (203*2π)/3562 weeks
204-.009 -.00061 (204*2π)/3562 weeks
205-.0099 -.0015 (205*2π)/3562 weeks
206-.0098 .0061 (206*2π)/3562 weeks
207-.00399 .00109 (207*2π)/3562 weeks
208-.01287 -.00074 (208*2π)/3562 weeks
209-.00778 .00143 (209*2π)/3562 weeks
210-.00789 .00031 (210*2π)/3562 weeks
211-.00854 .00172 (211*2π)/3562 weeks
212-.00923 .001 (212*2π)/3562 weeks
213-.00441 .00395 (213*2π)/3562 weeks
214-.00881 -.00089 (214*2π)/3562 weeks
215-.00811 .00448 (215*2π)/3562 weeks
216-.00792 -.00035 (216*2π)/3562 weeks
217-.01244 .0061 (217*2π)/3562 weeks
218-.01018 -.00586 (218*2π)/3562 weeks
219-.01055 .00243 (219*2π)/3562 weeks
220-.00736 .00023 (220*2π)/3562 weeks
221-.01178 .0012 (221*2π)/3562 weeks
222-.00916 -.00079 (222*2π)/3562 weeks
223-.01237 .00253 (223*2π)/3562 weeks
224-.01138 .00055 (224*2π)/3562 weeks
225-.00871 -.00306 (225*2π)/3562 weeks
226-.0065 -.00078 (226*2π)/3562 weeks
227-.00532 .00485 (227*2π)/3562 weeks
228-.00897 .00199 (228*2π)/3562 weeks
229-.00908 -.00278 (229*2π)/3562 weeks
230-.01023 .01096 (230*2π)/3562 weeks
231-.00692 .00592 (231*2π)/3562 weeks
232-.0116 .00641 (232*2π)/3562 weeks
233-.00438 .00679 (233*2π)/3562 weeks
234-.01226 .00867 (234*2π)/3562 weeks
235-.0079 .00764 (235*2π)/3562 weeks
236-.00719 .00414 (236*2π)/3562 weeks
237-.01067 .0095 (237*2π)/3562 weeks
238-.00713 .00722 (238*2π)/3561 weeks
239-.00714 .00761 (239*2π)/3561 weeks
240-.00154 .00747 (240*2π)/3561 weeks
241-.00272 .00581 (241*2π)/3561 weeks
242-.00595 .00531 (242*2π)/3561 weeks
243-.00025 .00804 (243*2π)/3561 weeks
244.00368 .00022 (244*2π)/3561 weeks
245-.00816 .00569 (245*2π)/3561 weeks
246-.00267 .00338 (246*2π)/3561 weeks
247-.00467 .00304 (247*2π)/3561 weeks
248-.0037 .00168 (248*2π)/3561 weeks
249-.00346 .00386 (249*2π)/3561 weeks
250-.0082 .00746 (250*2π)/3561 weeks
251-.00262 .00301 (251*2π)/3561 weeks
252-.00451 .00333 (252*2π)/3561 weeks
253-.00919 -.00138 (253*2π)/3561 weeks
254-.00686 -.00047 (254*2π)/3561 weeks
255-.00778 .00468 (255*2π)/3561 weeks
256-.00588 .00587 (256*2π)/3561 weeks
257-.00666 .00186 (257*2π)/3561 weeks
258-.0086 .00097 (258*2π)/3561 weeks
259-.00791 .00396 (259*2π)/3561 weeks
260-.00541 .00483 (260*2π)/3561 weeks
261-.0096 .0091 (261*2π)/3561 weeks
262-.00212 .00663 (262*2π)/3561 weeks
263-.01409 .00556 (263*2π)/3561 weeks
264-.01022 .01164 (264*2π)/3561 weeks
265-.00265 .01585 (265*2π)/3561 weeks
266-.00814 .00674 (266*2π)/3561 weeks
267-.01244 .01442 (267*2π)/3561 weeks
268-.00263 .00967 (268*2π)/3561 weeks
269-.01554 .0089 (269*2π)/3561 weeks
270-.00429 .01082 (270*2π)/3561 weeks
271-.01142 .00348 (271*2π)/3561 weeks
272-.00577 .01283 (272*2π)/3561 weeks
273-.00998 .00949 (273*2π)/3561 weeks
274.00141 .00626 (274*2π)/3561 weeks
275-.00938 -.00148 (275*2π)/3561 weeks
276-.00168 .01376 (276*2π)/3561 weeks
277-.00362 .01091 (277*2π)/3561 weeks
278-.01062 .00226 (278*2π)/3561 weeks
279-.00633 .01415 (279*2π)/3561 weeks
280-.00005 .00989 (280*2π)/3561 weeks
281-.01384 .00528 (281*2π)/3561 weeks
282-.00199 .01075 (282*2π)/3561 weeks
283-.00223 .01097 (283*2π)/3561 weeks
284-.01379 .00491 (284*2π)/3561 weeks
285-.01008 .01705 (285*2π)/3561 weeks
286-.00602 .00968 (286*2π)/3561 weeks
287-.01653 .01145 (287*2π)/3561 weeks
288-.00554 .00976 (288*2π)/3561 weeks
289-.00837 .00388 (289*2π)/3561 weeks
290-.02029 .01863 (290*2π)/3561 weeks
291-.00168 .02032 (291*2π)/3561 weeks
292-.00596 .0087 (292*2π)/3561 weeks
293-.01192 .01111 (293*2π)/3561 weeks
294-.0045 .01632 (294*2π)/3561 weeks
295-.00904 .01533 (295*2π)/3561 weeks
296-.01134 .01126 (296*2π)/3561 weeks
297-.01322 .02274 (297*2π)/3561 weeks
298-.00423 .02492 (298*2π)/3561 weeks
299-.00493 .01414 (299*2π)/3561 weeks
300-.00636 .02684 (300*2π)/3561 weeks
301-.01233 .02701 (301*2π)/3561 weeks
302-.0022 .01951 (302*2π)/3561 weeks
303-.0107 .01293 (303*2π)/3561 weeks
304-.00697 .01198 (304*2π)/3561 weeks
305-.00664 .01277 (305*2π)/3561 weeks
306-.01117 .01036 (306*2π)/3561 weeks
307-.00465 .01191 (307*2π)/3561 weeks
308-.01029 .01342 (308*2π)/3561 weeks
309-.00337 .00512 (309*2π)/3561 weeks
310-.00409 .01272 (310*2π)/3561 weeks
311-.00339 .006 (311*2π)/3561 weeks
312-.00722 .0004 (312*2π)/3561 weeks
313.00772 .00653 (313*2π)/3561 weeks
314-.01378 .01353 (314*2π)/3561 weeks
315-.00762 .01118 (315*2π)/3561 weeks
316.00062 .01416 (316*2π)/3561 weeks
317-.00185 .02002 (317*2π)/3561 weeks
318-.01003 .02662 (318*2π)/3561 weeks
319-.01477 .0108 (319*2π)/3561 weeks
320.00297 .03536 (320*2π)/3561 weeks
321-.00828 .01978 (321*2π)/3561 weeks
322-.01363 .01181 (322*2π)/3561 weeks
323-.00464 .02947 (323*2π)/3561 weeks
324.0054 .04467 (324*2π)/3561 weeks
325-.03167 .02672 (325*2π)/3561 weeks
326.00825 .03593 (326*2π)/3561 weeks
327-.0167 .02151 (327*2π)/3561 weeks
328-.01189 .04209 (328*2π)/3561 weeks
329-.00309 .01357 (329*2π)/3561 weeks
330.00374 .02791 (330*2π)/3561 weeks
331-.00807 .03461 (331*2π)/3561 weeks
332-.00984 .02198 (332*2π)/3561 weeks
333.01458 .02639 (333*2π)/3561 weeks
334.01396 .01683 (334*2π)/3561 weeks
335-.01679 .0371 (335*2π)/3561 weeks
336.01509 .03834 (336*2π)/3561 weeks
337-.0148 .00615 (337*2π)/3561 weeks
338-.01278 .05928 (338*2π)/3561 weeks
339.01512 .06386 (339*2π)/3561 weeks
340-.00698 .01687 (340*2π)/3561 weeks
341-.03913 .05017 (341*2π)/3561 weeks
342-.00565 .05989 (342*2π)/3561 weeks
343-.02464 .03223 (343*2π)/3561 weeks
344.01619 .05429 (344*2π)/3561 weeks
345.03334 .07473 (345*2π)/3561 weeks
346-.04449 .09306 (346*2π)/3561 weeks
347.00505 .10923 (347*2π)/3561 weeks
348.0109 .15845 (348*2π)/3561 weeks
349.03944 .12645 (349*2π)/3561 weeks
350-.09417 .15866 (350*2π)/3561 weeks
351.02965 .24468 (351*2π)/3561 weeks
352.08427 .22508 (352*2π)/3561 weeks
353-.11827 .40981 (353*2π)/3561 weeks
354.19001 .55197 (354*2π)/3561 weeks