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# Fourier Analysis of UUSTX (ULTRA SHORT-TERM BOND FUND ULTRA SHORT-TERM BOND FUND SHARES)

UUSTX (ULTRA SHORT-TERM BOND FUND ULTRA SHORT-TERM BOND FUND SHARES) appears to have interesting cyclic behaviour every 40 weeks (.0331*sine), 36 weeks (.0273*sine), and 33 weeks (.0058*cosine).

UUSTX (ULTRA SHORT-TERM BOND FUND ULTRA SHORT-TERM BOND FUND SHARES) has an average price of 9.49 (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 10/25/2010 to 6/4/2018 for UUSTX (ULTRA SHORT-TERM BOND FUND ULTRA SHORT-TERM BOND FUND SHARES), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
09.48672   0
1-.06684 -.27322 (1*2π)/398398 weeks
2.00712 -.18439 (2*2π)/398199 weeks
3-.00944 -.12482 (3*2π)/398133 weeks
4.00045 -.06293 (4*2π)/398100 weeks
5-.00366 -.05949 (5*2π)/39880 weeks
6-.0145 -.0651 (6*2π)/39866 weeks
7-.00643 -.03508 (7*2π)/39857 weeks
8.00253 -.04073 (8*2π)/39850 weeks
9-.00135 -.04491 (9*2π)/39844 weeks
10-.00014 -.03311 (10*2π)/39840 weeks
11.00058 -.02733 (11*2π)/39836 weeks
12.00576 -.02681 (12*2π)/39833 weeks
13-.00206 -.02209 (13*2π)/39831 weeks
14-.00281 -.02056 (14*2π)/39828 weeks
15.00169 -.02481 (15*2π)/39827 weeks
16-.00378 -.01849 (16*2π)/39825 weeks
17-.00167 -.0164 (17*2π)/39823 weeks
18-.00046 -.01844 (18*2π)/39822 weeks
19-.00286 -.0178 (19*2π)/39821 weeks
20-.00318 -.01612 (20*2π)/39820 weeks
21.00023 -.01538 (21*2π)/39819 weeks
22-.00232 -.01526 (22*2π)/39818 weeks
23-.00118 -.01375 (23*2π)/39817 weeks
24-.00205 -.01321 (24*2π)/39817 weeks
25-.00332 -.01234 (25*2π)/39816 weeks
26-.00421 -.0114 (26*2π)/39815 weeks
27-.00176 -.01157 (27*2π)/39815 weeks
28-.0013 -.01119 (28*2π)/39814 weeks
29-.00279 -.01133 (29*2π)/39814 weeks
30-.00182 -.01068 (30*2π)/39813 weeks
31-.00337 -.00685 (31*2π)/39813 weeks
32-.00166 -.00935 (32*2π)/39812 weeks
33-.00357 -.00842 (33*2π)/39812 weeks
34-.00265 -.00883 (34*2π)/39812 weeks
35-.00255 -.00945 (35*2π)/39811 weeks
36-.0013 -.00842 (36*2π)/39811 weeks
37-.00258 -.00754 (37*2π)/39811 weeks
38-.00184 -.00818 (38*2π)/39810 weeks
39-.00169 -.0081 (39*2π)/39810 weeks
40-.00236 -.00748 (40*2π)/39810 weeks
41-.00156 -.00776 (41*2π)/39810 weeks
42-.00195 -.00672 (42*2π)/3989 weeks
43-.00317 -.00693 (43*2π)/3989 weeks
44-.00156 -.00681 (44*2π)/3989 weeks
45-.0016 -.00581 (45*2π)/3989 weeks
46-.00277 -.00588 (46*2π)/3989 weeks
47-.0015 -.00592 (47*2π)/3988 weeks
48-.0031 -.00587 (48*2π)/3988 weeks
49-.00362 -.00594 (49*2π)/3988 weeks
50-.00158 -.00551 (50*2π)/3988 weeks
51-.00261 -.00592 (51*2π)/3988 weeks
52-.00195 -.00586 (52*2π)/3988 weeks
53-.00265 -.00566 (53*2π)/3988 weeks
54-.00278 -.00569 (54*2π)/3987 weeks
55-.00317 -.00517 (55*2π)/3987 weeks
56-.00327 -.00459 (56*2π)/3987 weeks
57-.00334 -.00519 (57*2π)/3987 weeks
58-.00201 -.00542 (58*2π)/3987 weeks
59-.00293 -.00588 (59*2π)/3987 weeks
60-.00207 -.0044 (60*2π)/3987 weeks
61-.00185 -.00539 (61*2π)/3987 weeks
62-.00206 -.00381 (62*2π)/3986 weeks
63-.00314 -.00421 (63*2π)/3986 weeks
64-.00239 -.00359 (64*2π)/3986 weeks
65-.00246 -.00417 (65*2π)/3986 weeks
66-.00222 -.00414 (66*2π)/3986 weeks
67-.0026 -.00408 (67*2π)/3986 weeks
68-.00246 -.00405 (68*2π)/3986 weeks
69-.0016 -.00393 (69*2π)/3986 weeks
70-.00249 -.00418 (70*2π)/3986 weeks
71-.00228 -.00329 (71*2π)/3986 weeks
72-.0023 -.00403 (72*2π)/3986 weeks
73-.00296 -.00372 (73*2π)/3985 weeks
74-.00278 -.00298 (74*2π)/3985 weeks
75-.00155 -.004 (75*2π)/3985 weeks
76-.0024 -.00336 (76*2π)/3985 weeks
77-.00254 -.00241 (77*2π)/3985 weeks
78-.00226 -.00361 (78*2π)/3985 weeks
79-.00212 -.00334 (79*2π)/3985 weeks
80-.00218 -.00311 (80*2π)/3985 weeks
81-.00143 -.00378 (81*2π)/3985 weeks
82-.00245 -.00346 (82*2π)/3985 weeks
83-.00216 -.00241 (83*2π)/3985 weeks
84-.00187 -.00337 (84*2π)/3985 weeks
85-.0024 -.00315 (85*2π)/3985 weeks
86-.00226 -.00304 (86*2π)/3985 weeks
87-.00177 -.00316 (87*2π)/3985 weeks
88-.0027 -.00299 (88*2π)/3985 weeks
89-.00192 -.00329 (89*2π)/3984 weeks
90-.00063 -.00278 (90*2π)/3984 weeks
91-.0002 -.00319 (91*2π)/3984 weeks
92-.00514 -.00249 (92*2π)/3984 weeks
93-.00405 -.00257 (93*2π)/3984 weeks
94-.0028 -.00313 (94*2π)/3984 weeks
95-.00265 -.00317 (95*2π)/3984 weeks
96-.00315 -.00235 (96*2π)/3984 weeks
97-.00184 -.00207 (97*2π)/3984 weeks
98-.00302 -.00201 (98*2π)/3984 weeks
99-.00243 -.00184 (99*2π)/3984 weeks
100-.00134 -.00234 (100*2π)/3984 weeks
101-.00224 -.0022 (101*2π)/3984 weeks
102-.00262 -.00195 (102*2π)/3984 weeks
103-.00237 -.00167 (103*2π)/3984 weeks
104-.00237 -.00212 (104*2π)/3984 weeks
105-.00257 -.00125 (105*2π)/3984 weeks
106-.00236 -.00176 (106*2π)/3984 weeks
107-.0027 -.00255 (107*2π)/3984 weeks
108-.00238 -.0011 (108*2π)/3984 weeks
109-.00242 -.00151 (109*2π)/3984 weeks
110-.0027 -.00226 (110*2π)/3984 weeks
111-.00222 -.00156 (111*2π)/3984 weeks
112-.00285 -.00199 (112*2π)/3984 weeks
113-.00218 -.00208 (113*2π)/3984 weeks
114-.00221 -.00231 (114*2π)/3983 weeks
115-.00221 -.00174 (115*2π)/3983 weeks
116-.00263 -.00204 (116*2π)/3983 weeks
117-.00228 -.0022 (117*2π)/3983 weeks
118-.0022 -.00201 (118*2π)/3983 weeks
119-.00227 -.0022 (119*2π)/3983 weeks
120-.00189 -.00177 (120*2π)/3983 weeks
121-.00237 -.00179 (121*2π)/3983 weeks
122-.00258 -.00126 (122*2π)/3983 weeks
123-.00307 -.00304 (123*2π)/3983 weeks
124-.00243 -.00095 (124*2π)/3983 weeks
125-.00152 -.00083 (125*2π)/3983 weeks
126-.00256 -.00157 (126*2π)/3983 weeks
127-.00285 -.00107 (127*2π)/3983 weeks
128-.00255 -.00155 (128*2π)/3983 weeks
129-.00181 -.00123 (129*2π)/3983 weeks
130-.00295 -.00129 (130*2π)/3983 weeks
131-.00257 -.00128 (131*2π)/3983 weeks
132-.0026 -.00076 (132*2π)/3983 weeks
133-.00237 -.00133 (133*2π)/3983 weeks
134-.00232 -.00162 (134*2π)/3983 weeks
135-.0022 -.00107 (135*2π)/3983 weeks
136-.0026 -.00089 (136*2π)/3983 weeks
137-.00232 -.00148 (137*2π)/3983 weeks
138-.00207 -.00104 (138*2π)/3983 weeks
139-.00249 -.00172 (139*2π)/3983 weeks
140-.00181 -.00132 (140*2π)/3983 weeks
141-.00233 -.00139 (141*2π)/3983 weeks
142-.00189 -.00125 (142*2π)/3983 weeks
143-.00225 -.00146 (143*2π)/3983 weeks
144-.00281 -.00104 (144*2π)/3983 weeks
145-.00247 -.00101 (145*2π)/3983 weeks
146-.00194 -.00102 (146*2π)/3983 weeks
147-.00261 -.001 (147*2π)/3983 weeks
148-.00227 -.00127 (148*2π)/3983 weeks
149-.00249 -.00101 (149*2π)/3983 weeks
150-.00239 -.00087 (150*2π)/3983 weeks
151-.00126 -.00142 (151*2π)/3983 weeks
152-.00253 -.001 (152*2π)/3983 weeks
153-.00215 -.00127 (153*2π)/3983 weeks
154-.00241 -.00132 (154*2π)/3983 weeks
155-.00201 -.00101 (155*2π)/3983 weeks
156-.0027 -.00056 (156*2π)/3983 weeks
157-.00226 -.00048 (157*2π)/3983 weeks
158-.00248 -.00091 (158*2π)/3983 weeks
159-.00253 -.00068 (159*2π)/3983 weeks
160-.00249 -.00102 (160*2π)/3982 weeks
161-.00236 -.00062 (161*2π)/3982 weeks
162-.00277 -.0008 (162*2π)/3982 weeks
163-.00202 -.00141 (163*2π)/3982 weeks
164-.00277 -.00058 (164*2π)/3982 weeks
165-.00227 -.0005 (165*2π)/3982 weeks
166-.00282 -.00036 (166*2π)/3982 weeks
167-.00224 -.00041 (167*2π)/3982 weeks
168-.00249 -.00077 (168*2π)/3982 weeks
169-.00287 -.00038 (169*2π)/3982 weeks
170-.00207 -.00042 (170*2π)/3982 weeks
171-.00248 -.00074 (171*2π)/3982 weeks
172-.00263 -.00037 (172*2π)/3982 weeks
173-.00283 -.00068 (173*2π)/3982 weeks
174-.0025 -.00061 (174*2π)/3982 weeks
175-.00197 .00012 (175*2π)/3982 weeks
176-.00249 -.00036 (176*2π)/3982 weeks
177-.00264 -.00092 (177*2π)/3982 weeks
178-.00248 .00029 (178*2π)/3982 weeks
179-.0024 -.00075 (179*2π)/3982 weeks
180-.0027 .00002 (180*2π)/3982 weeks
181-.00212 -.00055 (181*2π)/3982 weeks
182-.00231 -.00001 (182*2π)/3982 weeks
183-.00109 .00085 (183*2π)/3982 weeks
184-.00268 .0001 (184*2π)/3982 weeks
185-.00237 -.00065 (185*2π)/3982 weeks
186-.00321 -.00006 (186*2π)/3982 weeks
187-.00252 -.00009 (187*2π)/3982 weeks
188-.00279 -.00025 (188*2π)/3982 weeks
189-.00273 -.00023 (189*2π)/3982 weeks
190-.00236 -.00013 (190*2π)/3982 weeks
191-.00244 -.0004 (191*2π)/3982 weeks
192-.00219 -.00006 (192*2π)/3982 weeks
193-.00313 .00044 (193*2π)/3982 weeks
194-.00279 -.0004 (194*2π)/3982 weeks
195-.00254 -.00035 (195*2π)/3982 weeks
196-.00275 -.00034 (196*2π)/3982 weeks
197-.00264 -.0004 (197*2π)/3982 weeks
198-.00252 -.00018 (198*2π)/3982 weeks
199-.00225   (199*2π)/3982 weeks
200-.00252 .00018 (200*2π)/3982 weeks
201-.00264 .0004 (201*2π)/3982 weeks
202-.00275 .00034 (202*2π)/3982 weeks
203-.00254 .00035 (203*2π)/3982 weeks
204-.00279 .0004 (204*2π)/3982 weeks
205-.00313 -.00044 (205*2π)/3982 weeks
206-.00219 .00006 (206*2π)/3982 weeks
207-.00244 .0004 (207*2π)/3982 weeks
208-.00236 .00013 (208*2π)/3982 weeks
209-.00273 .00023 (209*2π)/3982 weeks
210-.00279 .00025 (210*2π)/3982 weeks
211-.00252 .00009 (211*2π)/3982 weeks
212-.00321 .00006 (212*2π)/3982 weeks
213-.00237 .00065 (213*2π)/3982 weeks
214-.00268 -.0001 (214*2π)/3982 weeks
215-.00109 -.00085 (215*2π)/3982 weeks
216-.00231 .00001 (216*2π)/3982 weeks
217-.00212 .00055 (217*2π)/3982 weeks
218-.0027 -.00002 (218*2π)/3982 weeks
219-.0024 .00075 (219*2π)/3982 weeks
220-.00248 -.00029 (220*2π)/3982 weeks
221-.00264 .00092 (221*2π)/3982 weeks
222-.00249 .00036 (222*2π)/3982 weeks
223-.00197 -.00012 (223*2π)/3982 weeks
224-.0025 .00061 (224*2π)/3982 weeks
225-.00283 .00068 (225*2π)/3982 weeks
226-.00263 .00037 (226*2π)/3982 weeks
227-.00248 .00074 (227*2π)/3982 weeks
228-.00207 .00042 (228*2π)/3982 weeks
229-.00287 .00038 (229*2π)/3982 weeks
230-.00249 .00077 (230*2π)/3982 weeks
231-.00224 .00041 (231*2π)/3982 weeks
232-.00282 .00036 (232*2π)/3982 weeks
233-.00227 .0005 (233*2π)/3982 weeks
234-.00277 .00058 (234*2π)/3982 weeks
235-.00202 .00141 (235*2π)/3982 weeks
236-.00277 .0008 (236*2π)/3982 weeks
237-.00236 .00062 (237*2π)/3982 weeks
238-.00249 .00102 (238*2π)/3982 weeks
239-.00253 .00068 (239*2π)/3982 weeks
240-.00248 .00091 (240*2π)/3982 weeks
241-.00226 .00048 (241*2π)/3982 weeks
242-.0027 .00056 (242*2π)/3982 weeks
243-.00201 .00101 (243*2π)/3982 weeks
244-.00241 .00132 (244*2π)/3982 weeks
245-.00215 .00127 (245*2π)/3982 weeks
246-.00253 .001 (246*2π)/3982 weeks
247-.00126 .00142 (247*2π)/3982 weeks
248-.00239 .00087 (248*2π)/3982 weeks
249-.00249 .00101 (249*2π)/3982 weeks
250-.00227 .00127 (250*2π)/3982 weeks
251-.00261 .001 (251*2π)/3982 weeks
252-.00194 .00102 (252*2π)/3982 weeks
253-.00247 .00101 (253*2π)/3982 weeks
254-.00281 .00104 (254*2π)/3982 weeks
255-.00225 .00146 (255*2π)/3982 weeks
256-.00189 .00125 (256*2π)/3982 weeks
257-.00233 .00139 (257*2π)/3982 weeks
258-.00181 .00132 (258*2π)/3982 weeks
259-.00249 .00172 (259*2π)/3982 weeks
260-.00207 .00104 (260*2π)/3982 weeks
261-.00232 .00148 (261*2π)/3982 weeks
262-.0026 .00089 (262*2π)/3982 weeks
263-.0022 .00107 (263*2π)/3982 weeks
264-.00232 .00162 (264*2π)/3982 weeks
265-.00237 .00133 (265*2π)/3982 weeks
266-.0026 .00076 (266*2π)/3981 weeks
267-.00257 .00128 (267*2π)/3981 weeks
268-.00295 .00129 (268*2π)/3981 weeks
269-.00181 .00123 (269*2π)/3981 weeks
270-.00255 .00155 (270*2π)/3981 weeks
271-.00285 .00107 (271*2π)/3981 weeks
272-.00256 .00157 (272*2π)/3981 weeks
273-.00152 .00083 (273*2π)/3981 weeks
274-.00243 .00095 (274*2π)/3981 weeks
275-.00307 .00304 (275*2π)/3981 weeks
276-.00258 .00126 (276*2π)/3981 weeks
277-.00237 .00179 (277*2π)/3981 weeks
278-.00189 .00177 (278*2π)/3981 weeks
279-.00227 .0022 (279*2π)/3981 weeks
280-.0022 .00201 (280*2π)/3981 weeks
281-.00228 .0022 (281*2π)/3981 weeks
282-.00263 .00204 (282*2π)/3981 weeks
283-.00221 .00174 (283*2π)/3981 weeks
284-.00221 .00231 (284*2π)/3981 weeks
285-.00218 .00208 (285*2π)/3981 weeks
286-.00285 .00199 (286*2π)/3981 weeks
287-.00222 .00156 (287*2π)/3981 weeks
288-.0027 .00226 (288*2π)/3981 weeks
289-.00242 .00151 (289*2π)/3981 weeks
290-.00238 .0011 (290*2π)/3981 weeks
291-.0027 .00255 (291*2π)/3981 weeks
292-.00236 .00176 (292*2π)/3981 weeks
293-.00257 .00125 (293*2π)/3981 weeks
294-.00237 .00212 (294*2π)/3981 weeks
295-.00237 .00167 (295*2π)/3981 weeks
296-.00262 .00195 (296*2π)/3981 weeks
297-.00224 .0022 (297*2π)/3981 weeks
298-.00134 .00234 (298*2π)/3981 weeks
299-.00243 .00184 (299*2π)/3981 weeks
300-.00302 .00201 (300*2π)/3981 weeks
301-.00184 .00207 (301*2π)/3981 weeks
302-.00315 .00235 (302*2π)/3981 weeks
303-.00265 .00317 (303*2π)/3981 weeks
304-.0028 .00313 (304*2π)/3981 weeks
305-.00405 .00257 (305*2π)/3981 weeks
306-.00514 .00249 (306*2π)/3981 weeks
307-.0002 .00319 (307*2π)/3981 weeks
308-.00063 .00278 (308*2π)/3981 weeks
309-.00192 .00329 (309*2π)/3981 weeks
310-.0027 .00299 (310*2π)/3981 weeks
311-.00177 .00316 (311*2π)/3981 weeks
312-.00226 .00304 (312*2π)/3981 weeks
313-.0024 .00315 (313*2π)/3981 weeks
314-.00187 .00337 (314*2π)/3981 weeks
315-.00216 .00241 (315*2π)/3981 weeks
316-.00245 .00346 (316*2π)/3981 weeks
317-.00143 .00378 (317*2π)/3981 weeks
318-.00218 .00311 (318*2π)/3981 weeks
319-.00212 .00334 (319*2π)/3981 weeks
320-.00226 .00361 (320*2π)/3981 weeks
321-.00254 .00241 (321*2π)/3981 weeks
322-.0024 .00336 (322*2π)/3981 weeks
323-.00155 .004 (323*2π)/3981 weeks
324-.00278 .00298 (324*2π)/3981 weeks
325-.00296 .00372 (325*2π)/3981 weeks
326-.0023 .00403 (326*2π)/3981 weeks
327-.00228 .00329 (327*2π)/3981 weeks
328-.00249 .00418 (328*2π)/3981 weeks
329-.0016 .00393 (329*2π)/3981 weeks
330-.00246 .00405 (330*2π)/3981 weeks
331-.0026 .00408 (331*2π)/3981 weeks
332-.00222 .00414 (332*2π)/3981 weeks
333-.00246 .00417 (333*2π)/3981 weeks
334-.00239 .00359 (334*2π)/3981 weeks
335-.00314 .00421 (335*2π)/3981 weeks
336-.00206 .00381 (336*2π)/3981 weeks
337-.00185 .00539 (337*2π)/3981 weeks
338-.00207 .0044 (338*2π)/3981 weeks
339-.00293 .00588 (339*2π)/3981 weeks
340-.00201 .00542 (340*2π)/3981 weeks
341-.00334 .00519 (341*2π)/3981 weeks
342-.00327 .00459 (342*2π)/3981 weeks
343-.00317 .00517 (343*2π)/3981 weeks
344-.00278 .00569 (344*2π)/3981 weeks
345-.00265 .00566 (345*2π)/3981 weeks
346-.00195 .00586 (346*2π)/3981 weeks
347-.00261 .00592 (347*2π)/3981 weeks
348-.00158 .00551 (348*2π)/3981 weeks
349-.00362 .00594 (349*2π)/3981 weeks
350-.0031 .00587 (350*2π)/3981 weeks
351-.0015 .00592 (351*2π)/3981 weeks
352-.00277 .00588 (352*2π)/3981 weeks
353-.0016 .00581 (353*2π)/3981 weeks
354-.00156 .00681 (354*2π)/3981 weeks
355-.00317 .00693 (355*2π)/3981 weeks
356-.00195 .00672 (356*2π)/3981 weeks
357-.00156 .00776 (357*2π)/3981 weeks
358-.00236 .00748 (358*2π)/3981 weeks
359-.00169 .0081 (359*2π)/3981 weeks
360-.00184 .00818 (360*2π)/3981 weeks
361-.00258 .00754 (361*2π)/3981 weeks
362-.0013 .00842 (362*2π)/3981 weeks
363-.00255 .00945 (363*2π)/3981 weeks
364-.00265 .00883 (364*2π)/3981 weeks
365-.00357 .00842 (365*2π)/3981 weeks
366-.00166 .00935 (366*2π)/3981 weeks
367-.00337 .00685 (367*2π)/3981 weeks
368-.00182 .01068 (368*2π)/3981 weeks
369-.00279 .01133 (369*2π)/3981 weeks
370-.0013 .01119 (370*2π)/3981 weeks
371-.00176 .01157 (371*2π)/3981 weeks
372-.00421 .0114 (372*2π)/3981 weeks
373-.00332 .01234 (373*2π)/3981 weeks
374-.00205 .01321 (374*2π)/3981 weeks
375-.00118 .01375 (375*2π)/3981 weeks
376-.00232 .01526 (376*2π)/3981 weeks
377.00023 .01538 (377*2π)/3981 weeks
378-.00318 .01612 (378*2π)/3981 weeks
379-.00286 .0178 (379*2π)/3981 weeks
380-.00046 .01844 (380*2π)/3981 weeks
381-.00167 .0164 (381*2π)/3981 weeks
382-.00378 .01849 (382*2π)/3981 weeks
383.00169 .02481 (383*2π)/3981 weeks
384-.00281 .02056 (384*2π)/3981 weeks
385-.00206 .02209 (385*2π)/3981 weeks
386.00576 .02681 (386*2π)/3981 weeks
387.00058 .02733 (387*2π)/3981 weeks
388-.00014 .03311 (388*2π)/3981 weeks
389-.00135 .04491 (389*2π)/3981 weeks
390.00253 .04073 (390*2π)/3981 weeks
391-.00643 .03508 (391*2π)/3981 weeks
392-.0145 .0651 (392*2π)/3981 weeks
393-.00366 .05949 (393*2π)/3981 weeks
394.00045 .06293 (394*2π)/3981 weeks
395-.00944 .12482 (395*2π)/3981 weeks
396.00712 .18439 (396*2π)/3981 weeks