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Fourier Analysis of BOND (PIMCO Total Return Active Excha)


BOND (PIMCO Total Return Active Excha) appears to have interesting cyclic behaviour every 24 weeks (.7216*sine), 22 weeks (.7146*sine), and 26 weeks (.4744*sine).

BOND (PIMCO Total Return Active Excha) has an average price of 98.24 (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 3/1/2012 to 3/13/2017 for BOND (PIMCO Total Return Active Excha), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
098.24448   0 
1-.50424 -5.01488 (1*2π)/264264 weeks
2-.3105 -1.42024 (2*2π)/264132 weeks
3-1.33302 -2.37882 (3*2π)/26488 weeks
4-.91215 -1.60906 (4*2π)/26466 weeks
5.0486 -.89823 (5*2π)/26453 weeks
6-.33071 -.61562 (6*2π)/26444 weeks
7-.06469 -.5387 (7*2π)/26438 weeks
8.00183 -1.13113 (8*2π)/26433 weeks
9.13331 -.52691 (9*2π)/26429 weeks
10.00859 -.47438 (10*2π)/26426 weeks
11-.31023 -.72156 (11*2π)/26424 weeks
12-.04965 -.71465 (12*2π)/26422 weeks
13.06617 -.59658 (13*2π)/26420 weeks
14-.21686 -.4694 (14*2π)/26419 weeks
15-.13346 -.44244 (15*2π)/26418 weeks
16-.05985 -.45699 (16*2π)/26417 weeks
17-.21974 -.47408 (17*2π)/26416 weeks
18-.06835 -.3043 (18*2π)/26415 weeks
19-.22491 -.22805 (19*2π)/26414 weeks
20-.29487 -.26157 (20*2π)/26413 weeks
21.08973 -.24177 (21*2π)/26413 weeks
22-.06727 -.26439 (22*2π)/26412 weeks
23-.10094 -.18147 (23*2π)/26411 weeks
24-.07072 -.36369 (24*2π)/26411 weeks
25.0073 -.2136 (25*2π)/26411 weeks
26-.00752 -.24124 (26*2π)/26410 weeks
27-.11361 -.18399 (27*2π)/26410 weeks
28.01422 -.24496 (28*2π)/2649 weeks
29-.07586 -.2477 (29*2π)/2649 weeks
30-.1893 -.09877 (30*2π)/2649 weeks
31-.08471 -.24271 (31*2π)/2649 weeks
32-.09621 -.20028 (32*2π)/2648 weeks
33-.09169 -.11672 (33*2π)/2648 weeks
34-.16067 -.18601 (34*2π)/2648 weeks
35-.031 -.12846 (35*2π)/2648 weeks
36-.05782 -.16409 (36*2π)/2647 weeks
37-.0799 -.13528 (37*2π)/2647 weeks
38-.11365 -.15521 (38*2π)/2647 weeks
39-.02703 -.09054 (39*2π)/2647 weeks
40-.03235 -.18115 (40*2π)/2647 weeks
41-.08877 -.05875 (41*2π)/2646 weeks
42-.03177 -.11329 (42*2π)/2646 weeks
43-.05625 -.12663 (43*2π)/2646 weeks
44-.06742 -.0925 (44*2π)/2646 weeks
45-.09006 -.11612 (45*2π)/2646 weeks
46-.07469 -.10174 (46*2π)/2646 weeks
47-.07875 -.08807 (47*2π)/2646 weeks
48-.09312 -.09794 (48*2π)/2646 weeks
49-.0682 -.04761 (49*2π)/2645 weeks
50-.03583 -.12511 (50*2π)/2645 weeks
51-.01784 -.11376 (51*2π)/2645 weeks
52-.00696 -.09548 (52*2π)/2645 weeks
53-.05748 -.09257 (53*2π)/2645 weeks
54-.09853 -.14133 (54*2π)/2645 weeks
55-.05581 -.10328 (55*2π)/2645 weeks
56-.10238 -.09546 (56*2π)/2645 weeks
57-.0902 -.09346 (57*2π)/2645 weeks
58-.05201 -.12103 (58*2π)/2645 weeks
59-.11851 -.08643 (59*2π)/2644 weeks
60-.10588 -.0265 (60*2π)/2644 weeks
61-.06488 -.07371 (61*2π)/2644 weeks
62-.07235 -.02856 (62*2π)/2644 weeks
63-.01843 -.01302 (63*2π)/2644 weeks
64-.02893 -.1276 (64*2π)/2644 weeks
65-.07236 -.07831 (65*2π)/2644 weeks
66-.07185 -.05882 (66*2π)/2644 weeks
67-.0804 -.12329 (67*2π)/2644 weeks
68-.05974 -.02603 (68*2π)/2644 weeks
69-.09868 -.0752 (69*2π)/2644 weeks
70-.02878 -.05984 (70*2π)/2644 weeks
71-.01255 -.07858 (71*2π)/2644 weeks
72-.09295 -.08152 (72*2π)/2644 weeks
73-.07717 -.0846 (73*2π)/2644 weeks
74-.07414 -.05193 (74*2π)/2644 weeks
75-.04894 .00212 (75*2π)/2644 weeks
76-.08877 -.09509 (76*2π)/2643 weeks
77-.09322 -.06673 (77*2π)/2643 weeks
78-.07501 -.06679 (78*2π)/2643 weeks
79-.08238 -.08795 (79*2π)/2643 weeks
80-.05435 -.05116 (80*2π)/2643 weeks
81-.05416 -.08386 (81*2π)/2643 weeks
82-.08171 .02256 (82*2π)/2643 weeks
83-.03316 -.02795 (83*2π)/2643 weeks
84-.05986 -.04937 (84*2π)/2643 weeks
85-.0571 -.04239 (85*2π)/2643 weeks
86-.09292 -.07825 (86*2π)/2643 weeks
87-.06929 -.07638 (87*2π)/2643 weeks
88-.10843 -.00472 (88*2π)/2643 weeks
89-.06579 -.00363 (89*2π)/2643 weeks
90-.1047 -.07384 (90*2π)/2643 weeks
91-.07672 -.06823 (91*2π)/2643 weeks
92-.03439 -.02487 (92*2π)/2643 weeks
93-.06826 -.0064 (93*2π)/2643 weeks
94-.08358 -.06955 (94*2π)/2643 weeks
95-.06291 -.06179 (95*2π)/2643 weeks
96-.10926 -.02121 (96*2π)/2643 weeks
97-.10704 -.0278 (97*2π)/2643 weeks
98-.09368 -.06299 (98*2π)/2643 weeks
99-.08199 -.00347 (99*2π)/2643 weeks
100-.07985 .00179 (100*2π)/2643 weeks
101-.08811 -.05175 (101*2π)/2643 weeks
102-.0768 -.00246 (102*2π)/2643 weeks
103-.05012 -.02812 (103*2π)/2643 weeks
104-.12094 .00657 (104*2π)/2643 weeks
105-.05857 .00856 (105*2π)/2643 weeks
106-.04152 -.03478 (106*2π)/2642 weeks
107-.06602 -.03306 (107*2π)/2642 weeks
108-.09671 .00347 (108*2π)/2642 weeks
109-.10991 -.04599 (109*2π)/2642 weeks
110-.10416 -.01736 (110*2π)/2642 weeks
111-.06826 -.0389 (111*2π)/2642 weeks
112-.142 -.0262 (112*2π)/2642 weeks
113-.11251 .00046 (113*2π)/2642 weeks
114-.09822 -.02804 (114*2π)/2642 weeks
115-.05794 -.04022 (115*2π)/2642 weeks
116-.11349 -.00978 (116*2π)/2642 weeks
117-.08049 .00581 (117*2π)/2642 weeks
118-.0551 -.01324 (118*2π)/2642 weeks
119-.0815 .01559 (119*2π)/2642 weeks
120-.04696 .01749 (120*2π)/2642 weeks
121-.11133 -.04315 (121*2π)/2642 weeks
122-.03778 .01072 (122*2π)/2642 weeks
123-.06017 .00529 (123*2π)/2642 weeks
124-.07941 -.00781 (124*2π)/2642 weeks
125-.08972 -.01601 (125*2π)/2642 weeks
126-.10295 -.00166 (126*2π)/2642 weeks
127-.04314 .02588 (127*2π)/2642 weeks
128-.09433 -.00929 (128*2π)/2642 weeks
129-.07789 .01764 (129*2π)/2642 weeks
130-.02976 .00294 (130*2π)/2642 weeks
131-.08636 .00223 (131*2π)/2642 weeks
132-.0808   (132*2π)/2642 weeks
133-.08636 -.00223 (133*2π)/2642 weeks
134-.02976 -.00294 (134*2π)/2642 weeks
135-.07789 -.01764 (135*2π)/2642 weeks
136-.09433 .00929 (136*2π)/2642 weeks
137-.04314 -.02588 (137*2π)/2642 weeks
138-.10295 .00166 (138*2π)/2642 weeks
139-.08972 .01601 (139*2π)/2642 weeks
140-.07941 .00781 (140*2π)/2642 weeks
141-.06017 -.00529 (141*2π)/2642 weeks
142-.03778 -.01072 (142*2π)/2642 weeks
143-.11133 .04315 (143*2π)/2642 weeks
144-.04696 -.01749 (144*2π)/2642 weeks
145-.0815 -.01559 (145*2π)/2642 weeks
146-.0551 .01324 (146*2π)/2642 weeks
147-.08049 -.00581 (147*2π)/2642 weeks
148-.11349 .00978 (148*2π)/2642 weeks
149-.05794 .04022 (149*2π)/2642 weeks
150-.09822 .02804 (150*2π)/2642 weeks
151-.11251 -.00046 (151*2π)/2642 weeks
152-.142 .0262 (152*2π)/2642 weeks
153-.06826 .0389 (153*2π)/2642 weeks
154-.10416 .01736 (154*2π)/2642 weeks
155-.10991 .04599 (155*2π)/2642 weeks
156-.09671 -.00347 (156*2π)/2642 weeks
157-.06602 .03306 (157*2π)/2642 weeks
158-.04152 .03478 (158*2π)/2642 weeks
159-.05857 -.00856 (159*2π)/2642 weeks
160-.12094 -.00657 (160*2π)/2642 weeks
161-.05012 .02812 (161*2π)/2642 weeks
162-.0768 .00246 (162*2π)/2642 weeks
163-.08811 .05175 (163*2π)/2642 weeks
164-.07985 -.00179 (164*2π)/2642 weeks
165-.08199 .00347 (165*2π)/2642 weeks
166-.09368 .06299 (166*2π)/2642 weeks
167-.10704 .0278 (167*2π)/2642 weeks
168-.10926 .02121 (168*2π)/2642 weeks
169-.06291 .06179 (169*2π)/2642 weeks
170-.08358 .06955 (170*2π)/2642 weeks
171-.06826 .0064 (171*2π)/2642 weeks
172-.03439 .02487 (172*2π)/2642 weeks
173-.07672 .06823 (173*2π)/2642 weeks
174-.1047 .07384 (174*2π)/2642 weeks
175-.06579 .00363 (175*2π)/2642 weeks
176-.10843 .00472 (176*2π)/2642 weeks
177-.06929 .07638 (177*2π)/2641 weeks
178-.09292 .07825 (178*2π)/2641 weeks
179-.0571 .04239 (179*2π)/2641 weeks
180-.05986 .04937 (180*2π)/2641 weeks
181-.03316 .02795 (181*2π)/2641 weeks
182-.08171 -.02256 (182*2π)/2641 weeks
183-.05416 .08386 (183*2π)/2641 weeks
184-.05435 .05116 (184*2π)/2641 weeks
185-.08238 .08795 (185*2π)/2641 weeks
186-.07501 .06679 (186*2π)/2641 weeks
187-.09322 .06673 (187*2π)/2641 weeks
188-.08877 .09509 (188*2π)/2641 weeks
189-.04894 -.00212 (189*2π)/2641 weeks
190-.07414 .05193 (190*2π)/2641 weeks
191-.07717 .0846 (191*2π)/2641 weeks
192-.09295 .08152 (192*2π)/2641 weeks
193-.01255 .07858 (193*2π)/2641 weeks
194-.02878 .05984 (194*2π)/2641 weeks
195-.09868 .0752 (195*2π)/2641 weeks
196-.05974 .02603 (196*2π)/2641 weeks
197-.0804 .12329 (197*2π)/2641 weeks
198-.07185 .05882 (198*2π)/2641 weeks
199-.07236 .07831 (199*2π)/2641 weeks
200-.02893 .1276 (200*2π)/2641 weeks
201-.01843 .01302 (201*2π)/2641 weeks
202-.07235 .02856 (202*2π)/2641 weeks
203-.06488 .07371 (203*2π)/2641 weeks
204-.10588 .0265 (204*2π)/2641 weeks
205-.11851 .08643 (205*2π)/2641 weeks
206-.05201 .12103 (206*2π)/2641 weeks
207-.0902 .09346 (207*2π)/2641 weeks
208-.10238 .09546 (208*2π)/2641 weeks
209-.05581 .10328 (209*2π)/2641 weeks
210-.09853 .14133 (210*2π)/2641 weeks
211-.05748 .09257 (211*2π)/2641 weeks
212-.00696 .09548 (212*2π)/2641 weeks
213-.01784 .11376 (213*2π)/2641 weeks
214-.03583 .12511 (214*2π)/2641 weeks
215-.0682 .04761 (215*2π)/2641 weeks
216-.09312 .09794 (216*2π)/2641 weeks
217-.07875 .08807 (217*2π)/2641 weeks
218-.07469 .10174 (218*2π)/2641 weeks
219-.09006 .11612 (219*2π)/2641 weeks
220-.06742 .0925 (220*2π)/2641 weeks
221-.05625 .12663 (221*2π)/2641 weeks
222-.03177 .11329 (222*2π)/2641 weeks
223-.08877 .05875 (223*2π)/2641 weeks
224-.03235 .18115 (224*2π)/2641 weeks
225-.02703 .09054 (225*2π)/2641 weeks
226-.11365 .15521 (226*2π)/2641 weeks
227-.0799 .13528 (227*2π)/2641 weeks
228-.05782 .16409 (228*2π)/2641 weeks
229-.031 .12846 (229*2π)/2641 weeks
230-.16067 .18601 (230*2π)/2641 weeks
231-.09169 .11672 (231*2π)/2641 weeks
232-.09621 .20028 (232*2π)/2641 weeks
233-.08471 .24271 (233*2π)/2641 weeks
234-.1893 .09877 (234*2π)/2641 weeks
235-.07586 .2477 (235*2π)/2641 weeks
236.01422 .24496 (236*2π)/2641 weeks
237-.11361 .18399 (237*2π)/2641 weeks
238-.00752 .24124 (238*2π)/2641 weeks
239.0073 .2136 (239*2π)/2641 weeks
240-.07072 .36369 (240*2π)/2641 weeks
241-.10094 .18147 (241*2π)/2641 weeks
242-.06727 .26439 (242*2π)/2641 weeks
243.08973 .24177 (243*2π)/2641 weeks
244-.29487 .26157 (244*2π)/2641 weeks
245-.22491 .22805 (245*2π)/2641 weeks
246-.06835 .3043 (246*2π)/2641 weeks
247-.21974 .47408 (247*2π)/2641 weeks
248-.05985 .45699 (248*2π)/2641 weeks
249-.13346 .44244 (249*2π)/2641 weeks
250-.21686 .4694 (250*2π)/2641 weeks
251.06617 .59658 (251*2π)/2641 weeks
252-.04965 .71465 (252*2π)/2641 weeks
253-.31023 .72156 (253*2π)/2641 weeks
254.00859 .47438 (254*2π)/2641 weeks
255.13331 .52691 (255*2π)/2641 weeks
256.00183 1.13113 (256*2π)/2641 weeks
257-.06469 .5387 (257*2π)/2641 weeks
258-.33071 .61562 (258*2π)/2641 weeks
259.0486 .89823 (259*2π)/2641 weeks
260-.91215 1.60906 (260*2π)/2641 weeks
261-1.33302 2.37882 (261*2π)/2641 weeks
262-.3105 1.42024 (262*2π)/2641 weeks

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