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# Fourier Analysis of VFWAX (VANGUARD FTSE ALL-WORLD EX-US INDEX FUND ADMIRAL SHARES)

VFWAX (VANGUARD FTSE ALL-WORLD EX-US INDEX FUND ADMIRAL SHARES) appears to have interesting cyclic behaviour every 29 weeks (.536*sine), 31 weeks (.518*sine), and 34 weeks (.2896*sine).

VFWAX (VANGUARD FTSE ALL-WORLD EX-US INDEX FUND ADMIRAL SHARES) has an average price of 26.78 (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 9/27/2011 to 4/16/2018 for VFWAX (VANGUARD FTSE ALL-WORLD EX-US INDEX FUND ADMIRAL SHARES), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
026.77913   0
1-.21349 -1.57242 (1*2π)/343343 weeks
21.25437 -3.10682 (2*2π)/343172 weeks
3-.00417 -1.8206 (3*2π)/343114 weeks
4.0971 -1.05346 (4*2π)/34386 weeks
5.23768 -1.11138 (5*2π)/34369 weeks
6-.41918 -.31824 (6*2π)/34357 weeks
7.13147 -.52914 (7*2π)/34349 weeks
8-.41415 -.58765 (8*2π)/34343 weeks
9-.00587 -.78743 (9*2π)/34338 weeks
10-.25895 -.28959 (10*2π)/34334 weeks
11-.10557 -.51805 (11*2π)/34331 weeks
12-.0704 -.53603 (12*2π)/34329 weeks
13.12902 -.29469 (13*2π)/34326 weeks
14.01064 -.422 (14*2π)/34325 weeks
15-.07316 -.04027 (15*2π)/34323 weeks
16.22084 -.06652 (16*2π)/34321 weeks
17-.09126 -.18713 (17*2π)/34320 weeks
18-.2594 -.04356 (18*2π)/34319 weeks
19-.00031 -.08221 (19*2π)/34318 weeks
20-.04207 -.16526 (20*2π)/34317 weeks
21-.00249 .00206 (21*2π)/34316 weeks
22-.01887 -.11333 (22*2π)/34316 weeks
23-.08879 -.11987 (23*2π)/34315 weeks
24-.02727 -.18983 (24*2π)/34314 weeks
25.03171 -.1227 (25*2π)/34314 weeks
26-.03122 -.0517 (26*2π)/34313 weeks
27-.01989 -.18091 (27*2π)/34313 weeks
28-.09667 -.11383 (28*2π)/34312 weeks
29.04599 -.19884 (29*2π)/34312 weeks
30-.21404 -.08353 (30*2π)/34311 weeks
31-.01942 -.27479 (31*2π)/34311 weeks
32-.10626 -.20726 (32*2π)/34311 weeks
33-.03413 -.07178 (33*2π)/34310 weeks
34-.05132 -.07489 (34*2π)/34310 weeks
35-.05941 -.20679 (35*2π)/34310 weeks
36-.00013 -.05707 (36*2π)/34310 weeks
37-.08516 -.08315 (37*2π)/3439 weeks
38-.09645 -.05896 (38*2π)/3439 weeks
39-.11429 -.0748 (39*2π)/3439 weeks
40-.07196 -.09445 (40*2π)/3439 weeks
41-.08005 .03198 (41*2π)/3438 weeks
42-.05064 -.09352 (42*2π)/3438 weeks
43-.0228 -.09647 (43*2π)/3438 weeks
44.00703 -.10446 (44*2π)/3438 weeks
45-.04829 -.04357 (45*2π)/3438 weeks
46-.01845 -.08719 (46*2π)/3437 weeks
47-.02791 -.01714 (47*2π)/3437 weeks
48-.09554 -.08024 (48*2π)/3437 weeks
49-.00767 -.09804 (49*2π)/3437 weeks
50-.08128 -.09 (50*2π)/3437 weeks
51-.09882 -.09771 (51*2π)/3437 weeks
52-.0241 -.13197 (52*2π)/3437 weeks
53-.03059 -.16639 (53*2π)/3436 weeks
54-.04498 -.17987 (54*2π)/3436 weeks
55-.00836 -.07231 (55*2π)/3436 weeks
56-.03912 -.13735 (56*2π)/3436 weeks
57-.10144 -.12079 (57*2π)/3436 weeks
58-.05254 -.04905 (58*2π)/3436 weeks
59-.0778 -.09645 (59*2π)/3436 weeks
60-.02293 -.14282 (60*2π)/3436 weeks
61-.06569 -.05312 (61*2π)/3436 weeks
62.01067 -.06974 (62*2π)/3436 weeks
63-.04312 -.16401 (63*2π)/3435 weeks
64-.11259 -.02204 (64*2π)/3435 weeks
65-.0281 -.06486 (65*2π)/3435 weeks
66-.024 -.12332 (66*2π)/3435 weeks
67-.02767 -.02651 (67*2π)/3435 weeks
68.01274 -.07791 (68*2π)/3435 weeks
69-.07768 -.04594 (69*2π)/3435 weeks
70-.00913 -.00294 (70*2π)/3435 weeks
71-.03154 -.01181 (71*2π)/3435 weeks
72-.08873 -.06076 (72*2π)/3435 weeks
73.01301 -.05535 (73*2π)/3435 weeks
74-.03212 -.04142 (74*2π)/3435 weeks
75-.05944 -.00953 (75*2π)/3435 weeks
76-.01098 -.06555 (76*2π)/3435 weeks
77.00507 -.06145 (77*2π)/3434 weeks
78-.06585 .00562 (78*2π)/3434 weeks
79.01031 -.05518 (79*2π)/3434 weeks
80-.04457 -.04018 (80*2π)/3434 weeks
81-.01749 -.06382 (81*2π)/3434 weeks
82-.0404 -.00686 (82*2π)/3434 weeks
83-.03288 -.08019 (83*2π)/3434 weeks
84-.08271 .00909 (84*2π)/3434 weeks
85-.02934 -.0528 (85*2π)/3434 weeks
86-.09196 -.03646 (86*2π)/3434 weeks
87-.0507 -.0139 (87*2π)/3434 weeks
88-.06621 -.07163 (88*2π)/3434 weeks
89-.08507 -.06001 (89*2π)/3434 weeks
90-.07133 -.01141 (90*2π)/3434 weeks
91-.06 -.05689 (91*2π)/3434 weeks
92-.08792 -.01583 (92*2π)/3434 weeks
93-.07277 -.04583 (93*2π)/3434 weeks
94-.07109 -.04807 (94*2π)/3434 weeks
95-.05635 -.01356 (95*2π)/3434 weeks
96-.03387 -.02979 (96*2π)/3434 weeks
97-.04032 -.05032 (97*2π)/3434 weeks
98-.05803 .00554 (98*2π)/3434 weeks
99-.06388 -.0198 (99*2π)/3433 weeks
100-.02049 -.02399 (100*2π)/3433 weeks
101-.02711 -.02984 (101*2π)/3433 weeks
102-.02877 -.07481 (102*2π)/3433 weeks
103-.01593 -.01281 (103*2π)/3433 weeks
104-.02691 .00756 (104*2π)/3433 weeks
105-.01393 -.01538 (105*2π)/3433 weeks
106-.02805 .00599 (106*2π)/3433 weeks
107-.04366 -.03239 (107*2π)/3433 weeks
108.02779 -.01113 (108*2π)/3433 weeks
109.00223 -.04717 (109*2π)/3433 weeks
110-.0331 -.01869 (110*2π)/3433 weeks
111-.00468 -.04957 (111*2π)/3433 weeks
112-.00796 -.04817 (112*2π)/3433 weeks
113-.03924 -.04331 (113*2π)/3433 weeks
114-.01795 -.0457 (114*2π)/3433 weeks
115-.06206 -.02504 (115*2π)/3433 weeks
116-.03363 -.02346 (116*2π)/3433 weeks
117-.05564 -.04611 (117*2π)/3433 weeks
118-.05516 -.0085 (118*2π)/3433 weeks
119-.05784 -.0465 (119*2π)/3433 weeks
120-.07665 .00403 (120*2π)/3433 weeks
121-.05487 -.04856 (121*2π)/3433 weeks
122-.11632 .00272 (122*2π)/3433 weeks
123-.06658 -.02014 (123*2π)/3433 weeks
124-.05412 -.02073 (124*2π)/3433 weeks
125-.07741 -.00031 (125*2π)/3433 weeks
126-.07079 -.01457 (126*2π)/3433 weeks
127-.0821 -.03279 (127*2π)/3433 weeks
128-.06703 -.04918 (128*2π)/3433 weeks
129-.05838 -.02316 (129*2π)/3433 weeks
130-.06994 -.02302 (130*2π)/3433 weeks
131-.06694 -.01022 (131*2π)/3433 weeks
132-.04474 -.01797 (132*2π)/3433 weeks
133-.04797 .0215 (133*2π)/3433 weeks
134-.08089 -.0302 (134*2π)/3433 weeks
135-.05986 -.01258 (135*2π)/3433 weeks
136-.04307 -.04226 (136*2π)/3433 weeks
137-.04956 -.01418 (137*2π)/3433 weeks
138-.0451 -.03993 (138*2π)/3432 weeks
139-.05796 -.02662 (139*2π)/3432 weeks
140-.04719 -.03082 (140*2π)/3432 weeks
141-.03399 -.03165 (141*2π)/3432 weeks
142-.04139 -.03999 (142*2π)/3432 weeks
143-.03415 .01324 (143*2π)/3432 weeks
144-.02656 -.02991 (144*2π)/3432 weeks
145-.05217 -.03346 (145*2π)/3432 weeks
146-.05405 -.01911 (146*2π)/3432 weeks
147-.04415 -.01826 (147*2π)/3432 weeks
148-.0293 -.01602 (148*2π)/3432 weeks
149-.02159 -.06332 (149*2π)/3432 weeks
150-.03576 -.00238 (150*2π)/3432 weeks
151-.0116 .00487 (151*2π)/3432 weeks
152-.03958 .00236 (152*2π)/3432 weeks
153-.00494 -.00652 (153*2π)/3432 weeks
154-.03678 -.03806 (154*2π)/3432 weeks
155-.01465 .00489 (155*2π)/3432 weeks
156-.04237 -.00867 (156*2π)/3432 weeks
157-.03176 -.01677 (157*2π)/3432 weeks
158-.03741 .01039 (158*2π)/3432 weeks
159-.0095 -.02045 (159*2π)/3432 weeks
160-.02576 -.00352 (160*2π)/3432 weeks
161-.04297 -.00216 (161*2π)/3432 weeks
162-.0003 .01305 (162*2π)/3432 weeks
163-.03182 -.02072 (163*2π)/3432 weeks
164-.08528 .0159 (164*2π)/3432 weeks
165-.02479 .01801 (165*2π)/3432 weeks
166-.02523 -.03729 (166*2π)/3432 weeks
167-.02181 .01292 (167*2π)/3432 weeks
168-.01591 -.01042 (168*2π)/3432 weeks
169-.03782 -.00721 (169*2π)/3432 weeks
170.01048 .00384 (170*2π)/3432 weeks
171-.01812 -.01417 (171*2π)/3432 weeks
172-.01812 .01417 (172*2π)/3432 weeks
173.01048 -.00384 (173*2π)/3432 weeks
174-.03782 .00721 (174*2π)/3432 weeks
175-.01591 .01042 (175*2π)/3432 weeks
176-.02181 -.01292 (176*2π)/3432 weeks
177-.02523 .03729 (177*2π)/3432 weeks
178-.02479 -.01801 (178*2π)/3432 weeks
179-.08528 -.0159 (179*2π)/3432 weeks
180-.03182 .02072 (180*2π)/3432 weeks
181-.0003 -.01305 (181*2π)/3432 weeks
182-.04297 .00216 (182*2π)/3432 weeks
183-.02576 .00352 (183*2π)/3432 weeks
184-.0095 .02045 (184*2π)/3432 weeks
185-.03741 -.01039 (185*2π)/3432 weeks
186-.03176 .01677 (186*2π)/3432 weeks
187-.04237 .00867 (187*2π)/3432 weeks
188-.01465 -.00489 (188*2π)/3432 weeks
189-.03678 .03806 (189*2π)/3432 weeks
190-.00494 .00652 (190*2π)/3432 weeks
191-.03958 -.00236 (191*2π)/3432 weeks
192-.0116 -.00487 (192*2π)/3432 weeks
193-.03576 .00238 (193*2π)/3432 weeks
194-.02159 .06332 (194*2π)/3432 weeks
195-.0293 .01602 (195*2π)/3432 weeks
196-.04415 .01826 (196*2π)/3432 weeks
197-.05405 .01911 (197*2π)/3432 weeks
198-.05217 .03346 (198*2π)/3432 weeks
199-.02656 .02991 (199*2π)/3432 weeks
200-.03415 -.01324 (200*2π)/3432 weeks
201-.04139 .03999 (201*2π)/3432 weeks
202-.03399 .03165 (202*2π)/3432 weeks
203-.04719 .03082 (203*2π)/3432 weeks
204-.05796 .02662 (204*2π)/3432 weeks
205-.0451 .03993 (205*2π)/3432 weeks
206-.04956 .01418 (206*2π)/3432 weeks
207-.04307 .04226 (207*2π)/3432 weeks
208-.05986 .01258 (208*2π)/3432 weeks
209-.08089 .0302 (209*2π)/3432 weeks
210-.04797 -.0215 (210*2π)/3432 weeks
211-.04474 .01797 (211*2π)/3432 weeks
212-.06694 .01022 (212*2π)/3432 weeks
213-.06994 .02302 (213*2π)/3432 weeks
214-.05838 .02316 (214*2π)/3432 weeks
215-.06703 .04918 (215*2π)/3432 weeks
216-.0821 .03279 (216*2π)/3432 weeks
217-.07079 .01457 (217*2π)/3432 weeks
218-.07741 .00031 (218*2π)/3432 weeks
219-.05412 .02073 (219*2π)/3432 weeks
220-.06658 .02014 (220*2π)/3432 weeks
221-.11632 -.00272 (221*2π)/3432 weeks
222-.05487 .04856 (222*2π)/3432 weeks
223-.07665 -.00403 (223*2π)/3432 weeks
224-.05784 .0465 (224*2π)/3432 weeks
225-.05516 .0085 (225*2π)/3432 weeks
226-.05564 .04611 (226*2π)/3432 weeks
227-.03363 .02346 (227*2π)/3432 weeks
228-.06206 .02504 (228*2π)/3432 weeks
229-.01795 .0457 (229*2π)/3431 weeks
230-.03924 .04331 (230*2π)/3431 weeks
231-.00796 .04817 (231*2π)/3431 weeks
232-.00468 .04957 (232*2π)/3431 weeks
233-.0331 .01869 (233*2π)/3431 weeks
234.00223 .04717 (234*2π)/3431 weeks
235.02779 .01113 (235*2π)/3431 weeks
236-.04366 .03239 (236*2π)/3431 weeks
237-.02805 -.00599 (237*2π)/3431 weeks
238-.01393 .01538 (238*2π)/3431 weeks
239-.02691 -.00756 (239*2π)/3431 weeks
240-.01593 .01281 (240*2π)/3431 weeks
241-.02877 .07481 (241*2π)/3431 weeks
242-.02711 .02984 (242*2π)/3431 weeks
243-.02049 .02399 (243*2π)/3431 weeks
244-.06388 .0198 (244*2π)/3431 weeks
245-.05803 -.00554 (245*2π)/3431 weeks
246-.04032 .05032 (246*2π)/3431 weeks
247-.03387 .02979 (247*2π)/3431 weeks
248-.05635 .01356 (248*2π)/3431 weeks
249-.07109 .04807 (249*2π)/3431 weeks
250-.07277 .04583 (250*2π)/3431 weeks
251-.08792 .01583 (251*2π)/3431 weeks
252-.06 .05689 (252*2π)/3431 weeks
253-.07133 .01141 (253*2π)/3431 weeks
254-.08507 .06001 (254*2π)/3431 weeks
255-.06621 .07163 (255*2π)/3431 weeks
256-.0507 .0139 (256*2π)/3431 weeks
257-.09196 .03646 (257*2π)/3431 weeks
258-.02934 .0528 (258*2π)/3431 weeks
259-.08271 -.00909 (259*2π)/3431 weeks
260-.03288 .08019 (260*2π)/3431 weeks
261-.0404 .00686 (261*2π)/3431 weeks
262-.01749 .06382 (262*2π)/3431 weeks
263-.04457 .04018 (263*2π)/3431 weeks
264.01031 .05518 (264*2π)/3431 weeks
265-.06585 -.00562 (265*2π)/3431 weeks
266.00507 .06145 (266*2π)/3431 weeks
267-.01098 .06555 (267*2π)/3431 weeks
268-.05944 .00953 (268*2π)/3431 weeks
269-.03212 .04142 (269*2π)/3431 weeks
270.01301 .05535 (270*2π)/3431 weeks
271-.08873 .06076 (271*2π)/3431 weeks
272-.03154 .01181 (272*2π)/3431 weeks
273-.00913 .00294 (273*2π)/3431 weeks
274-.07768 .04594 (274*2π)/3431 weeks
275.01274 .07791 (275*2π)/3431 weeks
276-.02767 .02651 (276*2π)/3431 weeks
277-.024 .12332 (277*2π)/3431 weeks
278-.0281 .06486 (278*2π)/3431 weeks
279-.11259 .02204 (279*2π)/3431 weeks
280-.04312 .16401 (280*2π)/3431 weeks
281.01067 .06974 (281*2π)/3431 weeks
282-.06569 .05312 (282*2π)/3431 weeks
283-.02293 .14282 (283*2π)/3431 weeks
284-.0778 .09645 (284*2π)/3431 weeks
285-.05254 .04905 (285*2π)/3431 weeks
286-.10144 .12079 (286*2π)/3431 weeks
287-.03912 .13735 (287*2π)/3431 weeks
288-.00836 .07231 (288*2π)/3431 weeks
289-.04498 .17987 (289*2π)/3431 weeks
290-.03059 .16639 (290*2π)/3431 weeks
291-.0241 .13197 (291*2π)/3431 weeks
292-.09882 .09771 (292*2π)/3431 weeks
293-.08128 .09 (293*2π)/3431 weeks
294-.00767 .09804 (294*2π)/3431 weeks
295-.09554 .08024 (295*2π)/3431 weeks
296-.02791 .01714 (296*2π)/3431 weeks
297-.01845 .08719 (297*2π)/3431 weeks
298-.04829 .04357 (298*2π)/3431 weeks
299.00703 .10446 (299*2π)/3431 weeks
300-.0228 .09647 (300*2π)/3431 weeks
301-.05064 .09352 (301*2π)/3431 weeks
302-.08005 -.03198 (302*2π)/3431 weeks
303-.07196 .09445 (303*2π)/3431 weeks
304-.11429 .0748 (304*2π)/3431 weeks
305-.09645 .05896 (305*2π)/3431 weeks
306-.08516 .08315 (306*2π)/3431 weeks
307-.00013 .05707 (307*2π)/3431 weeks
308-.05941 .20679 (308*2π)/3431 weeks
309-.05132 .07489 (309*2π)/3431 weeks
310-.03413 .07178 (310*2π)/3431 weeks
311-.10626 .20726 (311*2π)/3431 weeks
312-.01942 .27479 (312*2π)/3431 weeks
313-.21404 .08353 (313*2π)/3431 weeks
314.04599 .19884 (314*2π)/3431 weeks
315-.09667 .11383 (315*2π)/3431 weeks
316-.01989 .18091 (316*2π)/3431 weeks
317-.03122 .0517 (317*2π)/3431 weeks
318.03171 .1227 (318*2π)/3431 weeks
319-.02727 .18983 (319*2π)/3431 weeks
320-.08879 .11987 (320*2π)/3431 weeks
321-.01887 .11333 (321*2π)/3431 weeks
322-.00249 -.00206 (322*2π)/3431 weeks
323-.04207 .16526 (323*2π)/3431 weeks
324-.00031 .08221 (324*2π)/3431 weeks
325-.2594 .04356 (325*2π)/3431 weeks
326-.09126 .18713 (326*2π)/3431 weeks
327.22084 .06652 (327*2π)/3431 weeks
328-.07316 .04027 (328*2π)/3431 weeks
329.01064 .422 (329*2π)/3431 weeks
330.12902 .29469 (330*2π)/3431 weeks
331-.0704 .53603 (331*2π)/3431 weeks
332-.10557 .51805 (332*2π)/3431 weeks
333-.25895 .28959 (333*2π)/3431 weeks
334-.00587 .78743 (334*2π)/3431 weeks
335-.41415 .58765 (335*2π)/3431 weeks
336.13147 .52914 (336*2π)/3431 weeks
337-.41918 .31824 (337*2π)/3431 weeks
338.23768 1.11138 (338*2π)/3431 weeks
339.0971 1.05346 (339*2π)/3431 weeks
340-.00417 1.8206 (340*2π)/3431 weeks
3411.25437 3.10682 (341*2π)/3431 weeks