Back to list of Stocks    See Also: Seasonal Analysis of HYMBGenetic Algorithms Stock Portfolio Generator, and Fourier Calculator

Fourier Analysis of HYMB (SPDR® Nuveen S&P High Yield Municipal Bond ETF)


HYMB (SPDR® Nuveen S&P High Yield Municipal Bond ETF) appears to have interesting cyclic behaviour every 30 weeks (.6232*sine), 27 weeks (.5945*sine), and 33 weeks (.4631*sine).

HYMB (SPDR® Nuveen S&P High Yield Municipal Bond ETF) has an average price of 48.88 (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 4/14/2011 to 7/10/2017 for HYMB (SPDR® Nuveen S&P High Yield Municipal Bond ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
048.88452   0 
1-.12943 -5.70031 (1*2π)/327327 weeks
2-1.59972 -2.63585 (2*2π)/327164 weeks
3-.6814 -3.46259 (3*2π)/327109 weeks
4.19338 -.72841 (4*2π)/32782 weeks
5-.29039 -.99012 (5*2π)/32765 weeks
6.39284 -1.48357 (6*2π)/32755 weeks
7.19766 -.65345 (7*2π)/32747 weeks
8-.10374 -1.17479 (8*2π)/32741 weeks
9-.10082 -1.0107 (9*2π)/32736 weeks
10-.11918 -.46308 (10*2π)/32733 weeks
11-.25914 -.6232 (11*2π)/32730 weeks
12.0826 -.59448 (12*2π)/32727 weeks
13-.09586 -.26378 (13*2π)/32725 weeks
14-.07737 -.56274 (14*2π)/32723 weeks
15.14757 -.38397 (15*2π)/32722 weeks
16-.07454 -.31546 (16*2π)/32720 weeks
17-.04239 -.44678 (17*2π)/32719 weeks
18-.00804 -.38269 (18*2π)/32718 weeks
19-.26147 -.32392 (19*2π)/32717 weeks
20-.07397 -.31332 (20*2π)/32716 weeks
21-.14822 -.28558 (21*2π)/32716 weeks
22-.05685 -.22273 (22*2π)/32715 weeks
23-.08884 -.26224 (23*2π)/32714 weeks
24.06687 -.2479 (24*2π)/32714 weeks
25.00071 -.16516 (25*2π)/32713 weeks
26-.13339 -.34448 (26*2π)/32713 weeks
27-.02751 -.30795 (27*2π)/32712 weeks
28-.05404 -.22169 (28*2π)/32712 weeks
29-.13598 -.2252 (29*2π)/32711 weeks
30.01094 -.20123 (30*2π)/32711 weeks
31-.1288 -.13999 (31*2π)/32711 weeks
32-.07076 -.16079 (32*2π)/32710 weeks
33-.03679 -.13519 (33*2π)/32710 weeks
34-.09478 -.16289 (34*2π)/32710 weeks
35-.02158 -.18017 (35*2π)/3279 weeks
36-.00602 -.14266 (36*2π)/3279 weeks
37-.19248 -.2101 (37*2π)/3279 weeks
38-.03733 -.21209 (38*2π)/3279 weeks
39-.08778 -.11393 (39*2π)/3278 weeks
40-.12276 -.12969 (40*2π)/3278 weeks
41-.03569 -.12709 (41*2π)/3278 weeks
42-.07237 -.11153 (42*2π)/3278 weeks
43-.00191 -.11172 (43*2π)/3278 weeks
44-.06229 -.10539 (44*2π)/3277 weeks
45-.03574 -.13576 (45*2π)/3277 weeks
46-.04446 -.12952 (46*2π)/3277 weeks
47-.04146 -.13295 (47*2π)/3277 weeks
48-.04387 -.10384 (48*2π)/3277 weeks
49-.10133 -.14535 (49*2π)/3277 weeks
50-.00607 -.13369 (50*2π)/3277 weeks
51-.0618 -.07459 (51*2π)/3276 weeks
52-.07883 -.10146 (52*2π)/3276 weeks
53-.02642 -.14917 (53*2π)/3276 weeks
54-.01224 -.11498 (54*2π)/3276 weeks
55-.09899 -.1078 (55*2π)/3276 weeks
56-.07382 -.13077 (56*2π)/3276 weeks
57-.04955 -.07105 (57*2π)/3276 weeks
58-.08063 -.09901 (58*2π)/3276 weeks
59-.04428 -.05461 (59*2π)/3276 weeks
60-.09113 -.06486 (60*2π)/3275 weeks
61-.02135 -.09527 (61*2π)/3275 weeks
62-.05462 -.07542 (62*2π)/3275 weeks
63-.05538 -.1192 (63*2π)/3275 weeks
64-.05041 -.11708 (64*2π)/3275 weeks
65-.06103 -.09159 (65*2π)/3275 weeks
66-.07751 -.08544 (66*2π)/3275 weeks
67-.08546 -.0757 (67*2π)/3275 weeks
68-.09613 -.07701 (68*2π)/3275 weeks
69-.02326 -.05942 (69*2π)/3275 weeks
70-.03864 -.08552 (70*2π)/3275 weeks
71-.06025 -.07056 (71*2π)/3275 weeks
72-.02732 -.05152 (72*2π)/3275 weeks
73-.05095 -.07738 (73*2π)/3274 weeks
74-.07738 -.07321 (74*2π)/3274 weeks
75-.08925 -.04854 (75*2π)/3274 weeks
76-.07508 -.12585 (76*2π)/3274 weeks
77-.03245 -.03632 (77*2π)/3274 weeks
78-.08607 -.06723 (78*2π)/3274 weeks
79-.03588 -.08263 (79*2π)/3274 weeks
80-.0535 -.05139 (80*2π)/3274 weeks
81-.04831 -.09693 (81*2π)/3274 weeks
82-.05369 -.06811 (82*2π)/3274 weeks
83-.07275 -.03852 (83*2π)/3274 weeks
84-.02766 -.08358 (84*2π)/3274 weeks
85-.0654 -.01666 (85*2π)/3274 weeks
86-.07072 -.05731 (86*2π)/3274 weeks
87-.05315 -.05428 (87*2π)/3274 weeks
88-.06883 -.0284 (88*2π)/3274 weeks
89-.06799 -.05954 (89*2π)/3274 weeks
90-.05073 -.05177 (90*2π)/3274 weeks
91-.05244 -.05515 (91*2π)/3274 weeks
92-.06777 -.06252 (92*2π)/3274 weeks
93-.08994 -.01572 (93*2π)/3274 weeks
94-.0384 -.07413 (94*2π)/3273 weeks
95-.07557 -.05434 (95*2π)/3273 weeks
96-.02878 -.02499 (96*2π)/3273 weeks
97-.04768 -.05636 (97*2π)/3273 weeks
98-.06311 -.06343 (98*2π)/3273 weeks
99-.04972 -.03928 (99*2π)/3273 weeks
100-.03809 -.04695 (100*2π)/3273 weeks
101-.08938 -.03537 (101*2π)/3273 weeks
102-.06088 -.05071 (102*2π)/3273 weeks
103-.07434 -.04271 (103*2π)/3273 weeks
104-.05841 -.03559 (104*2π)/3273 weeks
105-.06152 -.03669 (105*2π)/3273 weeks
106-.08265 -.03218 (106*2π)/3273 weeks
107-.04425 -.03852 (107*2π)/3273 weeks
108-.06349 -.00762 (108*2π)/3273 weeks
109-.07654 -.06345 (109*2π)/3273 weeks
110-.05412 -.05033 (110*2π)/3273 weeks
111-.05168 -.03559 (111*2π)/3273 weeks
112-.0613 -.02191 (112*2π)/3273 weeks
113-.06653 -.04721 (113*2π)/3273 weeks
114-.03932 -.02416 (114*2π)/3273 weeks
115-.0671 -.04217 (115*2π)/3273 weeks
116-.07358 -.02716 (116*2π)/3273 weeks
117-.06098 -.02428 (117*2π)/3273 weeks
118-.07819 -.04755 (118*2π)/3273 weeks
119-.06565 -.01107 (119*2π)/3273 weeks
120-.05567 -.01922 (120*2π)/3273 weeks
121-.077 -.05856 (121*2π)/3273 weeks
122-.04849 -.01347 (122*2π)/3273 weeks
123-.05544 -.01341 (123*2π)/3273 weeks
124-.05585 -.03363 (124*2π)/3273 weeks
125-.05913 -.01894 (125*2π)/3273 weeks
126-.05084 -.00946 (126*2π)/3273 weeks
127-.06927 -.01971 (127*2π)/3273 weeks
128-.06318 -.01005 (128*2π)/3273 weeks
129-.08623 -.03197 (129*2π)/3273 weeks
130-.05603 -.028 (130*2π)/3273 weeks
131-.05314 -.00107 (131*2π)/3272 weeks
132-.08692 -.0221 (132*2π)/3272 weeks
133-.04 -.03604 (133*2π)/3272 weeks
134-.04003 -.00195 (134*2π)/3272 weeks
135-.0841 -.03016 (135*2π)/3272 weeks
136-.06352 -.0258 (136*2π)/3272 weeks
137-.05367 -.01653 (137*2π)/3272 weeks
138-.09017 -.02173 (138*2π)/3272 weeks
139-.05268 .00487 (139*2π)/3272 weeks
140-.06022 .00463 (140*2π)/3272 weeks
141-.06651 .00002 (141*2π)/3272 weeks
142-.04177 .00137 (142*2π)/3272 weeks
143-.06268 -.01432 (143*2π)/3272 weeks
144-.06004 -.0197 (144*2π)/3272 weeks
145-.0488 -.01059 (145*2π)/3272 weeks
146-.07456 -.00416 (146*2π)/3272 weeks
147-.07386 -.01292 (147*2π)/3272 weeks
148-.04334 -.02692 (148*2π)/3272 weeks
149-.06926 .01522 (149*2π)/3272 weeks
150-.07203 -.03535 (150*2π)/3272 weeks
151-.03238 .01083 (151*2π)/3272 weeks
152-.07855 -.01718 (152*2π)/3272 weeks
153-.0446 -.01225 (153*2π)/3272 weeks
154-.05344 .00938 (154*2π)/3272 weeks
155-.07891 -.0277 (155*2π)/3272 weeks
156-.03923 -.00559 (156*2π)/3272 weeks
157-.04113 .01879 (157*2π)/3272 weeks
158-.09021 -.01408 (158*2π)/3272 weeks
159-.04762 -.00875 (159*2π)/3272 weeks
160-.04751 .0248 (160*2π)/3272 weeks
161-.08315 -.02037 (161*2π)/3272 weeks
162-.05841 -.01131 (162*2π)/3272 weeks
163-.06801 .01136 (163*2π)/3272 weeks
164-.06801 -.01136 (164*2π)/3272 weeks
165-.05841 .01131 (165*2π)/3272 weeks
166-.08315 .02037 (166*2π)/3272 weeks
167-.04751 -.0248 (167*2π)/3272 weeks
168-.04762 .00875 (168*2π)/3272 weeks
169-.09021 .01408 (169*2π)/3272 weeks
170-.04113 -.01879 (170*2π)/3272 weeks
171-.03923 .00559 (171*2π)/3272 weeks
172-.07891 .0277 (172*2π)/3272 weeks
173-.05344 -.00938 (173*2π)/3272 weeks
174-.0446 .01225 (174*2π)/3272 weeks
175-.07855 .01718 (175*2π)/3272 weeks
176-.03238 -.01083 (176*2π)/3272 weeks
177-.07203 .03535 (177*2π)/3272 weeks
178-.06926 -.01522 (178*2π)/3272 weeks
179-.04334 .02692 (179*2π)/3272 weeks
180-.07386 .01292 (180*2π)/3272 weeks
181-.07456 .00416 (181*2π)/3272 weeks
182-.0488 .01059 (182*2π)/3272 weeks
183-.06004 .0197 (183*2π)/3272 weeks
184-.06268 .01432 (184*2π)/3272 weeks
185-.04177 -.00137 (185*2π)/3272 weeks
186-.06651 -.00002 (186*2π)/3272 weeks
187-.06022 -.00463 (187*2π)/3272 weeks
188-.05268 -.00487 (188*2π)/3272 weeks
189-.09017 .02173 (189*2π)/3272 weeks
190-.05367 .01653 (190*2π)/3272 weeks
191-.06352 .0258 (191*2π)/3272 weeks
192-.0841 .03016 (192*2π)/3272 weeks
193-.04003 .00195 (193*2π)/3272 weeks
194-.04 .03604 (194*2π)/3272 weeks
195-.08692 .0221 (195*2π)/3272 weeks
196-.05314 .00107 (196*2π)/3272 weeks
197-.05603 .028 (197*2π)/3272 weeks
198-.08623 .03197 (198*2π)/3272 weeks
199-.06318 .01005 (199*2π)/3272 weeks
200-.06927 .01971 (200*2π)/3272 weeks
201-.05084 .00946 (201*2π)/3272 weeks
202-.05913 .01894 (202*2π)/3272 weeks
203-.05585 .03363 (203*2π)/3272 weeks
204-.05544 .01341 (204*2π)/3272 weeks
205-.04849 .01347 (205*2π)/3272 weeks
206-.077 .05856 (206*2π)/3272 weeks
207-.05567 .01922 (207*2π)/3272 weeks
208-.06565 .01107 (208*2π)/3272 weeks
209-.07819 .04755 (209*2π)/3272 weeks
210-.06098 .02428 (210*2π)/3272 weeks
211-.07358 .02716 (211*2π)/3272 weeks
212-.0671 .04217 (212*2π)/3272 weeks
213-.03932 .02416 (213*2π)/3272 weeks
214-.06653 .04721 (214*2π)/3272 weeks
215-.0613 .02191 (215*2π)/3272 weeks
216-.05168 .03559 (216*2π)/3272 weeks
217-.05412 .05033 (217*2π)/3272 weeks
218-.07654 .06345 (218*2π)/3272 weeks
219-.06349 .00762 (219*2π)/3271 weeks
220-.04425 .03852 (220*2π)/3271 weeks
221-.08265 .03218 (221*2π)/3271 weeks
222-.06152 .03669 (222*2π)/3271 weeks
223-.05841 .03559 (223*2π)/3271 weeks
224-.07434 .04271 (224*2π)/3271 weeks
225-.06088 .05071 (225*2π)/3271 weeks
226-.08938 .03537 (226*2π)/3271 weeks
227-.03809 .04695 (227*2π)/3271 weeks
228-.04972 .03928 (228*2π)/3271 weeks
229-.06311 .06343 (229*2π)/3271 weeks
230-.04768 .05636 (230*2π)/3271 weeks
231-.02878 .02499 (231*2π)/3271 weeks
232-.07557 .05434 (232*2π)/3271 weeks
233-.0384 .07413 (233*2π)/3271 weeks
234-.08994 .01572 (234*2π)/3271 weeks
235-.06777 .06252 (235*2π)/3271 weeks
236-.05244 .05515 (236*2π)/3271 weeks
237-.05073 .05177 (237*2π)/3271 weeks
238-.06799 .05954 (238*2π)/3271 weeks
239-.06883 .0284 (239*2π)/3271 weeks
240-.05315 .05428 (240*2π)/3271 weeks
241-.07072 .05731 (241*2π)/3271 weeks
242-.0654 .01666 (242*2π)/3271 weeks
243-.02766 .08358 (243*2π)/3271 weeks
244-.07275 .03852 (244*2π)/3271 weeks
245-.05369 .06811 (245*2π)/3271 weeks
246-.04831 .09693 (246*2π)/3271 weeks
247-.0535 .05139 (247*2π)/3271 weeks
248-.03588 .08263 (248*2π)/3271 weeks
249-.08607 .06723 (249*2π)/3271 weeks
250-.03245 .03632 (250*2π)/3271 weeks
251-.07508 .12585 (251*2π)/3271 weeks
252-.08925 .04854 (252*2π)/3271 weeks
253-.07738 .07321 (253*2π)/3271 weeks
254-.05095 .07738 (254*2π)/3271 weeks
255-.02732 .05152 (255*2π)/3271 weeks
256-.06025 .07056 (256*2π)/3271 weeks
257-.03864 .08552 (257*2π)/3271 weeks
258-.02326 .05942 (258*2π)/3271 weeks
259-.09613 .07701 (259*2π)/3271 weeks
260-.08546 .0757 (260*2π)/3271 weeks
261-.07751 .08544 (261*2π)/3271 weeks
262-.06103 .09159 (262*2π)/3271 weeks
263-.05041 .11708 (263*2π)/3271 weeks
264-.05538 .1192 (264*2π)/3271 weeks
265-.05462 .07542 (265*2π)/3271 weeks
266-.02135 .09527 (266*2π)/3271 weeks
267-.09113 .06486 (267*2π)/3271 weeks
268-.04428 .05461 (268*2π)/3271 weeks
269-.08063 .09901 (269*2π)/3271 weeks
270-.04955 .07105 (270*2π)/3271 weeks
271-.07382 .13077 (271*2π)/3271 weeks
272-.09899 .1078 (272*2π)/3271 weeks
273-.01224 .11498 (273*2π)/3271 weeks
274-.02642 .14917 (274*2π)/3271 weeks
275-.07883 .10146 (275*2π)/3271 weeks
276-.0618 .07459 (276*2π)/3271 weeks
277-.00607 .13369 (277*2π)/3271 weeks
278-.10133 .14535 (278*2π)/3271 weeks
279-.04387 .10384 (279*2π)/3271 weeks
280-.04146 .13295 (280*2π)/3271 weeks
281-.04446 .12952 (281*2π)/3271 weeks
282-.03574 .13576 (282*2π)/3271 weeks
283-.06229 .10539 (283*2π)/3271 weeks
284-.00191 .11172 (284*2π)/3271 weeks
285-.07237 .11153 (285*2π)/3271 weeks
286-.03569 .12709 (286*2π)/3271 weeks
287-.12276 .12969 (287*2π)/3271 weeks
288-.08778 .11393 (288*2π)/3271 weeks
289-.03733 .21209 (289*2π)/3271 weeks
290-.19248 .2101 (290*2π)/3271 weeks
291-.00602 .14266 (291*2π)/3271 weeks
292-.02158 .18017 (292*2π)/3271 weeks
293-.09478 .16289 (293*2π)/3271 weeks
294-.03679 .13519 (294*2π)/3271 weeks
295-.07076 .16079 (295*2π)/3271 weeks
296-.1288 .13999 (296*2π)/3271 weeks
297.01094 .20123 (297*2π)/3271 weeks
298-.13598 .2252 (298*2π)/3271 weeks
299-.05404 .22169 (299*2π)/3271 weeks
300-.02751 .30795 (300*2π)/3271 weeks
301-.13339 .34448 (301*2π)/3271 weeks
302.00071 .16516 (302*2π)/3271 weeks
303.06687 .2479 (303*2π)/3271 weeks
304-.08884 .26224 (304*2π)/3271 weeks
305-.05685 .22273 (305*2π)/3271 weeks
306-.14822 .28558 (306*2π)/3271 weeks
307-.07397 .31332 (307*2π)/3271 weeks
308-.26147 .32392 (308*2π)/3271 weeks
309-.00804 .38269 (309*2π)/3271 weeks
310-.04239 .44678 (310*2π)/3271 weeks
311-.07454 .31546 (311*2π)/3271 weeks
312.14757 .38397 (312*2π)/3271 weeks
313-.07737 .56274 (313*2π)/3271 weeks
314-.09586 .26378 (314*2π)/3271 weeks
315.0826 .59448 (315*2π)/3271 weeks
316-.25914 .6232 (316*2π)/3271 weeks
317-.11918 .46308 (317*2π)/3271 weeks
318-.10082 1.0107 (318*2π)/3271 weeks
319-.10374 1.17479 (319*2π)/3271 weeks
320.19766 .65345 (320*2π)/3271 weeks
321.39284 1.48357 (321*2π)/3271 weeks
322-.29039 .99012 (322*2π)/3271 weeks
323.19338 .72841 (323*2π)/3271 weeks
324-.6814 3.46259 (324*2π)/3271 weeks
325-1.59972 2.63585 (325*2π)/3271 weeks



Back to list of Stocks