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Fourier Analysis of HYS (PIMCO 0-5 Year High Yield Corpo)


HYS (PIMCO 0-5 Year High Yield Corpo) appears to have interesting cyclic behaviour every 27 weeks (.8062*sine), 29 weeks (.7719*sine), and 8 weeks (.2735*cosine).

HYS (PIMCO 0-5 Year High Yield Corpo) has an average price of 87.8 (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 6/17/2011 to 1/9/2017 for HYS (PIMCO 0-5 Year High Yield Corpo), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
087.80433   0 
1-3.78709 -5.22607 (1*2π)/292292 weeks
21.28629 -3.04722 (2*2π)/292146 weeks
31.05733 -3.20165 (3*2π)/29297 weeks
4.66428 -2.97098 (4*2π)/29273 weeks
5-.80158 -2.29012 (5*2π)/29258 weeks
6-.22177 -1.32817 (6*2π)/29249 weeks
7.21264 -.95203 (7*2π)/29242 weeks
8.16398 -.86888 (8*2π)/29237 weeks
9.55095 -.85597 (9*2π)/29232 weeks
10.21642 -.77187 (10*2π)/29229 weeks
11-.24078 -.8062 (11*2π)/29227 weeks
12-.10707 -.45161 (12*2π)/29224 weeks
13.1182 -.40515 (13*2π)/29222 weeks
14.23227 -.46052 (14*2π)/29221 weeks
15.2043 -.48541 (15*2π)/29219 weeks
16-.13796 -.46595 (16*2π)/29218 weeks
17-.11898 -.39706 (17*2π)/29217 weeks
18.00431 -.3353 (18*2π)/29216 weeks
19-.14699 -.26307 (19*2π)/29215 weeks
20-.10183 -.42025 (20*2π)/29215 weeks
21.05333 -.36129 (21*2π)/29214 weeks
22-.15119 -.29261 (22*2π)/29213 weeks
23-.14184 -.4109 (23*2π)/29213 weeks
24-.14028 -.44738 (24*2π)/29212 weeks
25-.22128 -.29068 (25*2π)/29212 weeks
26.01505 -.37461 (26*2π)/29211 weeks
27-.09559 -.24514 (27*2π)/29211 weeks
28-.14084 -.36399 (28*2π)/29210 weeks
29-.14498 -.40232 (29*2π)/29210 weeks
30-.21597 -.13371 (30*2π)/29210 weeks
31-.1492 -.22183 (31*2π)/2929 weeks
32-.00533 -.08565 (32*2π)/2929 weeks
33-.02409 -.15774 (33*2π)/2929 weeks
34-.24431 -.23303 (34*2π)/2929 weeks
35-.16625 -.10625 (35*2π)/2928 weeks
36-.2735 -.14691 (36*2π)/2928 weeks
37-.13531 -.17197 (37*2π)/2928 weeks
38-.07283 -.16169 (38*2π)/2928 weeks
39-.14788 -.2118 (39*2π)/2927 weeks
40-.08188 -.2184 (40*2π)/2927 weeks
41-.05802 -.29906 (41*2π)/2927 weeks
42-.12312 -.32429 (42*2π)/2927 weeks
43-.06783 -.2027 (43*2π)/2927 weeks
44.08248 -.1753 (44*2π)/2927 weeks
45.0868 -.27009 (45*2π)/2926 weeks
46.04349 -.20173 (46*2π)/2926 weeks
47-.12458 -.24453 (47*2π)/2926 weeks
48-.10779 -.16575 (48*2π)/2926 weeks
49-.06796 -.10594 (49*2π)/2926 weeks
50-.05961 -.09642 (50*2π)/2926 weeks
51-.10728 -.06928 (51*2π)/2926 weeks
52-.07534 -.09407 (52*2π)/2926 weeks
53-.01983 -.122 (53*2π)/2926 weeks
54-.03804 -.21811 (54*2π)/2925 weeks
55-.16339 -.19521 (55*2π)/2925 weeks
56-.17699 -.15034 (56*2π)/2925 weeks
57-.07296 -.05882 (57*2π)/2925 weeks
58-.04057 -.1346 (58*2π)/2925 weeks
59-.08776 -.13385 (59*2π)/2925 weeks
60-.12221 -.10265 (60*2π)/2925 weeks
61-.14694 -.09805 (61*2π)/2925 weeks
62-.06069 -.02155 (62*2π)/2925 weeks
63-.05273 -.07957 (63*2π)/2925 weeks
64-.09771 -.08321 (64*2π)/2925 weeks
65-.09494 -.07669 (65*2π)/2924 weeks
66-.16038 -.11399 (66*2π)/2924 weeks
67-.14494 -.0453 (67*2π)/2924 weeks
68-.08302 -.05306 (68*2π)/2924 weeks
69-.05709 -.07945 (69*2π)/2924 weeks
70-.04046 -.10332 (70*2π)/2924 weeks
71-.08142 -.11793 (71*2π)/2924 weeks
72-.13196 -.04495 (72*2π)/2924 weeks
73-.08273 -.05051 (73*2π)/2924 weeks
74-.04535 -.10098 (74*2π)/2924 weeks
75-.08721 -.14103 (75*2π)/2924 weeks
76-.11001 -.16156 (76*2π)/2924 weeks
77-.15519 -.09604 (77*2π)/2924 weeks
78-.0888 -.08439 (78*2π)/2924 weeks
79-.08248 -.13182 (79*2π)/2924 weeks
80-.08065 -.11855 (80*2π)/2924 weeks
81-.07944 -.107 (81*2π)/2924 weeks
82-.11883 -.05982 (82*2π)/2924 weeks
83-.05695 -.03565 (83*2π)/2924 weeks
84-.0612 -.07521 (84*2π)/2923 weeks
85-.09746 -.05282 (85*2π)/2923 weeks
86-.10686 -.07321 (86*2π)/2923 weeks
87-.10847 -.03882 (87*2π)/2923 weeks
88-.08975 -.07525 (88*2π)/2923 weeks
89-.06654 -.05566 (89*2π)/2923 weeks
90-.11183 -.06535 (90*2π)/2923 weeks
91-.08731 -.04663 (91*2π)/2923 weeks
92-.04329 -.10271 (92*2π)/2923 weeks
93-.06713 -.13182 (93*2π)/2923 weeks
94-.07409 -.05706 (94*2π)/2923 weeks
95-.08571 -.05428 (95*2π)/2923 weeks
96-.08718 -.00589 (96*2π)/2923 weeks
97-.05066 -.02052 (97*2π)/2923 weeks
98-.07808 -.033 (98*2π)/2923 weeks
99-.06312 -.02713 (99*2π)/2923 weeks
100-.07528 -.03756 (100*2π)/2923 weeks
101-.10603 -.05843 (101*2π)/2923 weeks
102-.08014 -.01324 (102*2π)/2923 weeks
103-.07853 -.04847 (103*2π)/2923 weeks
104-.05989 -.06375 (104*2π)/2923 weeks
105-.06274 -.04712 (105*2π)/2923 weeks
106-.09185 -.08819 (106*2π)/2923 weeks
107-.07519 -.03445 (107*2π)/2923 weeks
108-.09118 -.01517 (108*2π)/2923 weeks
109-.12034 -.0165 (109*2π)/2923 weeks
110-.0811 -.03741 (110*2π)/2923 weeks
111-.15412 -.06511 (111*2π)/2923 weeks
112-.08365 -.01768 (112*2π)/2923 weeks
113-.08002 -.0345 (113*2π)/2923 weeks
114-.11847 -.0394 (114*2π)/2923 weeks
115-.08845 -.07977 (115*2π)/2923 weeks
116-.11653 -.05329 (116*2π)/2923 weeks
117-.08794 -.0406 (117*2π)/2922 weeks
118-.05584 -.04862 (118*2π)/2922 weeks
119-.07109 -.05205 (119*2π)/2922 weeks
120-.10062 -.0361 (120*2π)/2922 weeks
121-.09045 .01587 (121*2π)/2922 weeks
122-.11314 -.01805 (122*2π)/2922 weeks
123-.10491 -.02888 (123*2π)/2922 weeks
124-.06406 -.02822 (124*2π)/2922 weeks
125-.099 -.0178 (125*2π)/2922 weeks
126-.06274 -.00336 (126*2π)/2922 weeks
127-.09221 -.01134 (127*2π)/2922 weeks
128-.11158 .00595 (128*2π)/2922 weeks
129-.04531 -.01884 (129*2π)/2922 weeks
130-.08336 -.0118 (130*2π)/2922 weeks
131-.08283 .00747 (131*2π)/2922 weeks
132-.03546 -.01081 (132*2π)/2922 weeks
133-.09166 .0123 (133*2π)/2922 weeks
134-.06187 .00609 (134*2π)/2922 weeks
135-.05182 -.01569 (135*2π)/2922 weeks
136-.06719 -.00565 (136*2π)/2922 weeks
137-.05323 -.01984 (137*2π)/2922 weeks
138-.07502 .02451 (138*2π)/2922 weeks
139-.04399 .02417 (139*2π)/2922 weeks
140-.06352 -.03696 (140*2π)/2922 weeks
141-.09865 -.01799 (141*2π)/2922 weeks
142-.14181 -.00083 (142*2π)/2922 weeks
143-.10199 .05161 (143*2π)/2922 weeks
144-.06137 .04184 (144*2π)/2922 weeks
145-.09858 -.01164 (145*2π)/2922 weeks
146-.1039   (146*2π)/2922 weeks
147-.09858 .01164 (147*2π)/2922 weeks
148-.06137 -.04184 (148*2π)/2922 weeks
149-.10199 -.05161 (149*2π)/2922 weeks
150-.14181 .00083 (150*2π)/2922 weeks
151-.09865 .01799 (151*2π)/2922 weeks
152-.06352 .03696 (152*2π)/2922 weeks
153-.04399 -.02417 (153*2π)/2922 weeks
154-.07502 -.02451 (154*2π)/2922 weeks
155-.05323 .01984 (155*2π)/2922 weeks
156-.06719 .00565 (156*2π)/2922 weeks
157-.05182 .01569 (157*2π)/2922 weeks
158-.06187 -.00609 (158*2π)/2922 weeks
159-.09166 -.0123 (159*2π)/2922 weeks
160-.03546 .01081 (160*2π)/2922 weeks
161-.08283 -.00747 (161*2π)/2922 weeks
162-.08336 .0118 (162*2π)/2922 weeks
163-.04531 .01884 (163*2π)/2922 weeks
164-.11158 -.00595 (164*2π)/2922 weeks
165-.09221 .01134 (165*2π)/2922 weeks
166-.06274 .00336 (166*2π)/2922 weeks
167-.099 .0178 (167*2π)/2922 weeks
168-.06406 .02822 (168*2π)/2922 weeks
169-.10491 .02888 (169*2π)/2922 weeks
170-.11314 .01805 (170*2π)/2922 weeks
171-.09045 -.01587 (171*2π)/2922 weeks
172-.10062 .0361 (172*2π)/2922 weeks
173-.07109 .05205 (173*2π)/2922 weeks
174-.05584 .04862 (174*2π)/2922 weeks
175-.08794 .0406 (175*2π)/2922 weeks
176-.11653 .05329 (176*2π)/2922 weeks
177-.08845 .07977 (177*2π)/2922 weeks
178-.11847 .0394 (178*2π)/2922 weeks
179-.08002 .0345 (179*2π)/2922 weeks
180-.08365 .01768 (180*2π)/2922 weeks
181-.15412 .06511 (181*2π)/2922 weeks
182-.0811 .03741 (182*2π)/2922 weeks
183-.12034 .0165 (183*2π)/2922 weeks
184-.09118 .01517 (184*2π)/2922 weeks
185-.07519 .03445 (185*2π)/2922 weeks
186-.09185 .08819 (186*2π)/2922 weeks
187-.06274 .04712 (187*2π)/2922 weeks
188-.05989 .06375 (188*2π)/2922 weeks
189-.07853 .04847 (189*2π)/2922 weeks
190-.08014 .01324 (190*2π)/2922 weeks
191-.10603 .05843 (191*2π)/2922 weeks
192-.07528 .03756 (192*2π)/2922 weeks
193-.06312 .02713 (193*2π)/2922 weeks
194-.07808 .033 (194*2π)/2922 weeks
195-.05066 .02052 (195*2π)/2921 weeks
196-.08718 .00589 (196*2π)/2921 weeks
197-.08571 .05428 (197*2π)/2921 weeks
198-.07409 .05706 (198*2π)/2921 weeks
199-.06713 .13182 (199*2π)/2921 weeks
200-.04329 .10271 (200*2π)/2921 weeks
201-.08731 .04663 (201*2π)/2921 weeks
202-.11183 .06535 (202*2π)/2921 weeks
203-.06654 .05566 (203*2π)/2921 weeks
204-.08975 .07525 (204*2π)/2921 weeks
205-.10847 .03882 (205*2π)/2921 weeks
206-.10686 .07321 (206*2π)/2921 weeks
207-.09746 .05282 (207*2π)/2921 weeks
208-.0612 .07521 (208*2π)/2921 weeks
209-.05695 .03565 (209*2π)/2921 weeks
210-.11883 .05982 (210*2π)/2921 weeks
211-.07944 .107 (211*2π)/2921 weeks
212-.08065 .11855 (212*2π)/2921 weeks
213-.08248 .13182 (213*2π)/2921 weeks
214-.0888 .08439 (214*2π)/2921 weeks
215-.15519 .09604 (215*2π)/2921 weeks
216-.11001 .16156 (216*2π)/2921 weeks
217-.08721 .14103 (217*2π)/2921 weeks
218-.04535 .10098 (218*2π)/2921 weeks
219-.08273 .05051 (219*2π)/2921 weeks
220-.13196 .04495 (220*2π)/2921 weeks
221-.08142 .11793 (221*2π)/2921 weeks
222-.04046 .10332 (222*2π)/2921 weeks
223-.05709 .07945 (223*2π)/2921 weeks
224-.08302 .05306 (224*2π)/2921 weeks
225-.14494 .0453 (225*2π)/2921 weeks
226-.16038 .11399 (226*2π)/2921 weeks
227-.09494 .07669 (227*2π)/2921 weeks
228-.09771 .08321 (228*2π)/2921 weeks
229-.05273 .07957 (229*2π)/2921 weeks
230-.06069 .02155 (230*2π)/2921 weeks
231-.14694 .09805 (231*2π)/2921 weeks
232-.12221 .10265 (232*2π)/2921 weeks
233-.08776 .13385 (233*2π)/2921 weeks
234-.04057 .1346 (234*2π)/2921 weeks
235-.07296 .05882 (235*2π)/2921 weeks
236-.17699 .15034 (236*2π)/2921 weeks
237-.16339 .19521 (237*2π)/2921 weeks
238-.03804 .21811 (238*2π)/2921 weeks
239-.01983 .122 (239*2π)/2921 weeks
240-.07534 .09407 (240*2π)/2921 weeks
241-.10728 .06928 (241*2π)/2921 weeks
242-.05961 .09642 (242*2π)/2921 weeks
243-.06796 .10594 (243*2π)/2921 weeks
244-.10779 .16575 (244*2π)/2921 weeks
245-.12458 .24453 (245*2π)/2921 weeks
246.04349 .20173 (246*2π)/2921 weeks
247.0868 .27009 (247*2π)/2921 weeks
248.08248 .1753 (248*2π)/2921 weeks
249-.06783 .2027 (249*2π)/2921 weeks
250-.12312 .32429 (250*2π)/2921 weeks
251-.05802 .29906 (251*2π)/2921 weeks
252-.08188 .2184 (252*2π)/2921 weeks
253-.14788 .2118 (253*2π)/2921 weeks
254-.07283 .16169 (254*2π)/2921 weeks
255-.13531 .17197 (255*2π)/2921 weeks
256-.2735 .14691 (256*2π)/2921 weeks
257-.16625 .10625 (257*2π)/2921 weeks
258-.24431 .23303 (258*2π)/2921 weeks
259-.02409 .15774 (259*2π)/2921 weeks
260-.00533 .08565 (260*2π)/2921 weeks
261-.1492 .22183 (261*2π)/2921 weeks
262-.21597 .13371 (262*2π)/2921 weeks
263-.14498 .40232 (263*2π)/2921 weeks
264-.14084 .36399 (264*2π)/2921 weeks
265-.09559 .24514 (265*2π)/2921 weeks
266.01505 .37461 (266*2π)/2921 weeks
267-.22128 .29068 (267*2π)/2921 weeks
268-.14028 .44738 (268*2π)/2921 weeks
269-.14184 .4109 (269*2π)/2921 weeks
270-.15119 .29261 (270*2π)/2921 weeks
271.05333 .36129 (271*2π)/2921 weeks
272-.10183 .42025 (272*2π)/2921 weeks
273-.14699 .26307 (273*2π)/2921 weeks
274.00431 .3353 (274*2π)/2921 weeks
275-.11898 .39706 (275*2π)/2921 weeks
276-.13796 .46595 (276*2π)/2921 weeks
277.2043 .48541 (277*2π)/2921 weeks
278.23227 .46052 (278*2π)/2921 weeks
279.1182 .40515 (279*2π)/2921 weeks
280-.10707 .45161 (280*2π)/2921 weeks
281-.24078 .8062 (281*2π)/2921 weeks
282.21642 .77187 (282*2π)/2921 weeks
283.55095 .85597 (283*2π)/2921 weeks
284.16398 .86888 (284*2π)/2921 weeks
285.21264 .95203 (285*2π)/2921 weeks
286-.22177 1.32817 (286*2π)/2921 weeks
287-.80158 2.29012 (287*2π)/2921 weeks
288.66428 2.97098 (288*2π)/2921 weeks
2891.05733 3.20165 (289*2π)/2921 weeks
2901.28629 3.04722 (290*2π)/2921 weeks

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