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# Fourier Analysis of VGRLX (VANGUARD GLOBAL EX-U.S. REAL ESTATE INDEX FUND ADMIRAL)

VGRLX (VANGUARD GLOBAL EX-U.S. REAL ESTATE INDEX FUND ADMIRAL) appears to have interesting cyclic behaviour every 39 weeks (.737*sine), 36 weeks (.4117*sine), and 36 weeks (.3183*cosine).

VGRLX (VANGUARD GLOBAL EX-U.S. REAL ESTATE INDEX FUND ADMIRAL) has an average price of 28.18 (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 11/1/2010 to 4/23/2018 for VGRLX (VANGUARD GLOBAL EX-U.S. REAL ESTATE INDEX FUND ADMIRAL), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
028.18497   0
1-.37763 -3.5543 (1*2π)/391391 weeks
21.56 -2.90184 (2*2π)/391196 weeks
31.08552 -1.78079 (3*2π)/391130 weeks
4.32319 -.33833 (4*2π)/39198 weeks
5-.20933 -1.08711 (5*2π)/39178 weeks
6-.41927 -1.00547 (6*2π)/39165 weeks
7-.37972 -.07696 (7*2π)/39156 weeks
8.04164 -.66669 (8*2π)/39149 weeks
9-.20836 -.82447 (9*2π)/39143 weeks
10.19791 -.73697 (10*2π)/39139 weeks
11-.31831 -.41167 (11*2π)/39136 weeks
12.24669 -.35441 (12*2π)/39133 weeks
13-.05352 -.08543 (13*2π)/39130 weeks
14-.25179 -.31925 (14*2π)/39128 weeks
15.05036 -.40093 (15*2π)/39126 weeks
16-.18063 -.31275 (16*2π)/39124 weeks
17-.18396 -.05615 (17*2π)/39123 weeks
18.19164 -.06618 (18*2π)/39122 weeks
19-.24277 -.27945 (19*2π)/39121 weeks
20-.21401 -.32404 (20*2π)/39120 weeks
21.07829 -.13714 (21*2π)/39119 weeks
22.13489 -.1369 (22*2π)/39118 weeks
23-.0256 -.17853 (23*2π)/39117 weeks
24.06123 -.06952 (24*2π)/39116 weeks
25.0164 -.12907 (25*2π)/39116 weeks
26-.12832 -.24202 (26*2π)/39115 weeks
27.00044 -.30251 (27*2π)/39114 weeks
28.01847 -.17385 (28*2π)/39114 weeks
29-.10531 -.27368 (29*2π)/39113 weeks
30.18553 -.27166 (30*2π)/39113 weeks
31-.01779 -.1354 (31*2π)/39113 weeks
32-.02363 -.06977 (32*2π)/39112 weeks
33.00739 -.26867 (33*2π)/39112 weeks
34-.14573 -.04746 (34*2π)/39112 weeks
35.0604 -.2598 (35*2π)/39111 weeks
36-.03526 -.14594 (36*2π)/39111 weeks
37-.12835 -.03823 (37*2π)/39111 weeks
38-.05335 -.11668 (38*2π)/39110 weeks
39-.00369 -.13916 (39*2π)/39110 weeks
40-.14183 -.0946 (40*2π)/39110 weeks
41.01704 -.09371 (41*2π)/39110 weeks
42-.05701 -.10194 (42*2π)/3919 weeks
43-.07315 -.0807 (43*2π)/3919 weeks
44-.00953 -.13968 (44*2π)/3919 weeks
45.01515 -.09052 (45*2π)/3919 weeks
46-.04308 -.0071 (46*2π)/3919 weeks
47.05513 .00388 (47*2π)/3918 weeks
48-.03445 -.02449 (48*2π)/3918 weeks
49-.02031 -.05985 (49*2π)/3918 weeks
50-.00063 -.10796 (50*2π)/3918 weeks
51.00002 -.11618 (51*2π)/3918 weeks
52.02673 -.15705 (52*2π)/3918 weeks
53-.02637 -.09629 (53*2π)/3917 weeks
54.02975 -.10786 (54*2π)/3917 weeks
55.04753 .01488 (55*2π)/3917 weeks
56-.0067 -.03632 (56*2π)/3917 weeks
57-.04529 .00925 (57*2π)/3917 weeks
58-.11409 -.07076 (58*2π)/3917 weeks
59-.04903 -.14731 (59*2π)/3917 weeks
60-.04652 -.16135 (60*2π)/3917 weeks
61.00794 -.14911 (61*2π)/3916 weeks
62-.07188 -.0611 (62*2π)/3916 weeks
63-.01476 -.06814 (63*2π)/3916 weeks
64-.06137 -.08639 (64*2π)/3916 weeks
65-.08197 -.02323 (65*2π)/3916 weeks
66-.04637 -.02862 (66*2π)/3916 weeks
67-.07209 -.08055 (67*2π)/3916 weeks
68.00943 -.06869 (68*2π)/3916 weeks
69-.0607 -.03276 (69*2π)/3916 weeks
70.0101 -.05382 (70*2π)/3916 weeks
71-.01802 -.10333 (71*2π)/3916 weeks
72-.11975 -.05031 (72*2π)/3915 weeks
73-.02117 .01903 (73*2π)/3915 weeks
74-.01422 -.03149 (74*2π)/3915 weeks
75-.0293 -.07954 (75*2π)/3915 weeks
76-.03615 -.01217 (76*2π)/3915 weeks
77-.03295 -.01966 (77*2π)/3915 weeks
78-.07328 -.03085 (78*2π)/3915 weeks
79-.01221 .01553 (79*2π)/3915 weeks
80.03069 -.08647 (80*2π)/3915 weeks
81.03041 -.05523 (81*2π)/3915 weeks
82-.06887 .00536 (82*2π)/3915 weeks
83.01048 -.04195 (83*2π)/3915 weeks
84-.02456 -.01351 (84*2π)/3915 weeks
85-.05854 -.00801 (85*2π)/3915 weeks
86.01515 -.07997 (86*2π)/3915 weeks
87-.03907 -.06584 (87*2π)/3914 weeks
88-.08999 -.05914 (88*2π)/3914 weeks
89.02266 -.05635 (89*2π)/3914 weeks
90.00044 -.07279 (90*2π)/3914 weeks
91-.01884 -.03483 (91*2π)/3914 weeks
92-.02025 -.05034 (92*2π)/3914 weeks
93-.02873 .00366 (93*2π)/3914 weeks
94-.00102 -.04466 (94*2π)/3914 weeks
95-.05107 -.0253 (95*2π)/3914 weeks
96-.00023 -.03198 (96*2π)/3914 weeks
97-.06337 -.02674 (97*2π)/3914 weeks
98-.04149 -.00082 (98*2π)/3914 weeks
99-.02214 -.00958 (99*2π)/3914 weeks
100-.0941 -.03543 (100*2π)/3914 weeks
101-.05825 -.02568 (101*2π)/3914 weeks
102-.03601 -.00613 (102*2π)/3914 weeks
103-.03611 -.05488 (103*2π)/3914 weeks
104-.03228 -.00542 (104*2π)/3914 weeks
105-.0038 .02464 (105*2π)/3914 weeks
106-.03109 .01992 (106*2π)/3914 weeks
107-.02394 -.00203 (107*2π)/3914 weeks
108-.03119 -.01497 (108*2π)/3914 weeks
109-.01437 -.05351 (109*2π)/3914 weeks
110-.01088 -.03898 (110*2π)/3914 weeks
111-.02189 -.01204 (111*2π)/3914 weeks
112.00642 -.02417 (112*2π)/3913 weeks
113.03194 .00279 (113*2π)/3913 weeks
114-.01539 -.03581 (114*2π)/3913 weeks
115-.02366 -.02079 (115*2π)/3913 weeks
116-.02902 -.04431 (116*2π)/3913 weeks
117-.00322 -.00853 (117*2π)/3913 weeks
118-.03333 -.00335 (118*2π)/3913 weeks
119-.02176 -.03386 (119*2π)/3913 weeks
120-.05112 -.04068 (120*2π)/3913 weeks
121-.01625 -.05591 (121*2π)/3913 weeks
122-.02317 -.01408 (122*2π)/3913 weeks
123-.02575 -.08182 (123*2π)/3913 weeks
124-.05814 -.0592 (124*2π)/3913 weeks
125-.04828 -.00386 (125*2π)/3913 weeks
126-.03772 -.01911 (126*2π)/3913 weeks
127-.03714 -.0223 (127*2π)/3913 weeks
128-.075 -.02436 (128*2π)/3913 weeks
129-.06781 -.00622 (129*2π)/3913 weeks
130-.04586 -.01468 (130*2π)/3913 weeks
131-.05725 .01171 (131*2π)/3913 weeks
132-.04159 -.01993 (132*2π)/3913 weeks
133-.05778 .0044 (133*2π)/3913 weeks
134-.0418 .01832 (134*2π)/3913 weeks
135-.05252 -.03083 (135*2π)/3913 weeks
136-.03508 .00943 (136*2π)/3913 weeks
137-.01312 -.02631 (137*2π)/3913 weeks
138-.04437 -.00442 (138*2π)/3913 weeks
139.01201 .04199 (139*2π)/3913 weeks
140-.03418 -.01155 (140*2π)/3913 weeks
141-.03297 -.00776 (141*2π)/3913 weeks
142-.04935 -.00925 (142*2π)/3913 weeks
143-.04979 -.04231 (143*2π)/3913 weeks
144-.03123 -.03998 (144*2π)/3913 weeks
145.00078 -.0123 (145*2π)/3913 weeks
146-.00536 -.01234 (146*2π)/3913 weeks
147-.018 -.01259 (147*2π)/3913 weeks
148-.03761 -.01345 (148*2π)/3913 weeks
149-.02494 .00852 (149*2π)/3913 weeks
150-.0172 -.02979 (150*2π)/3913 weeks
151-.0278 -.0081 (151*2π)/3913 weeks
152-.04627 -.05129 (152*2π)/3913 weeks
153-.0015 -.02801 (153*2π)/3913 weeks
154-.00642 -.03331 (154*2π)/3913 weeks
155-.01876 .00281 (155*2π)/3913 weeks
156.00013 -.02877 (156*2π)/3913 weeks
157-.04957 -.0136 (157*2π)/3912 weeks
158-.01923 -.01332 (158*2π)/3912 weeks
159-.0078 -.00185 (159*2π)/3912 weeks
160-.01785 -.01274 (160*2π)/3912 weeks
161-.03095 -.00341 (161*2π)/3912 weeks
162-.03028 .00334 (162*2π)/3912 weeks
163-.04902 -.02413 (163*2π)/3912 weeks
164-.04136 -.00911 (164*2π)/3912 weeks
165-.04079 -.01536 (165*2π)/3912 weeks
166-.01908 -.00245 (166*2π)/3912 weeks
167-.03197 -.03198 (167*2π)/3912 weeks
168-.02009 -.00641 (168*2π)/3912 weeks
169-.03202 .00048 (169*2π)/3912 weeks
170-.0368 .01893 (170*2π)/3912 weeks
171-.0233 -.02721 (171*2π)/3912 weeks
172-.04892 -.04791 (172*2π)/3912 weeks
173-.0208 -.03225 (173*2π)/3912 weeks
174-.02508 -.03735 (174*2π)/3912 weeks
175-.0307 -.00519 (175*2π)/3912 weeks
176-.00503 .01051 (176*2π)/3912 weeks
177-.02077 -.0185 (177*2π)/3912 weeks
178-.03839 -.0045 (178*2π)/3912 weeks
179-.04376 .00159 (179*2π)/3912 weeks
180-.02154 -.05194 (180*2π)/3912 weeks
181-.03343 -.02475 (181*2π)/3912 weeks
182-.01792 -.02148 (182*2π)/3912 weeks
183-.00099 -.00213 (183*2π)/3912 weeks
184-.00441 -.01862 (184*2π)/3912 weeks
185-.06005 .0198 (185*2π)/3912 weeks
186-.02696 .00907 (186*2π)/3912 weeks
187.00592 -.00192 (187*2π)/3912 weeks
188-.0513 -.01901 (188*2π)/3912 weeks
189-.06106 .00514 (189*2π)/3912 weeks
190-.01299 -.01956 (190*2π)/3912 weeks
191-.04835 -.0145 (191*2π)/3912 weeks
192-.02728 .00515 (192*2π)/3912 weeks
193-.00998 -.00418 (193*2π)/3912 weeks
194-.05905 .03332 (194*2π)/3912 weeks
195-.03498 .01287 (195*2π)/3912 weeks
196-.03498 -.01287 (196*2π)/3912 weeks
197-.05905 -.03332 (197*2π)/3912 weeks
198-.00998 .00418 (198*2π)/3912 weeks
199-.02728 -.00515 (199*2π)/3912 weeks
200-.04835 .0145 (200*2π)/3912 weeks
201-.01299 .01956 (201*2π)/3912 weeks
202-.06106 -.00514 (202*2π)/3912 weeks
203-.0513 .01901 (203*2π)/3912 weeks
204.00592 .00192 (204*2π)/3912 weeks
205-.02696 -.00907 (205*2π)/3912 weeks
206-.06005 -.0198 (206*2π)/3912 weeks
207-.00441 .01862 (207*2π)/3912 weeks
208-.00099 .00213 (208*2π)/3912 weeks
209-.01792 .02148 (209*2π)/3912 weeks
210-.03343 .02475 (210*2π)/3912 weeks
211-.02154 .05194 (211*2π)/3912 weeks
212-.04376 -.00159 (212*2π)/3912 weeks
213-.03839 .0045 (213*2π)/3912 weeks
214-.02077 .0185 (214*2π)/3912 weeks
215-.00503 -.01051 (215*2π)/3912 weeks
216-.0307 .00519 (216*2π)/3912 weeks
217-.02508 .03735 (217*2π)/3912 weeks
218-.0208 .03225 (218*2π)/3912 weeks
219-.04892 .04791 (219*2π)/3912 weeks
220-.0233 .02721 (220*2π)/3912 weeks
221-.0368 -.01893 (221*2π)/3912 weeks
222-.03202 -.00048 (222*2π)/3912 weeks
223-.02009 .00641 (223*2π)/3912 weeks
224-.03197 .03198 (224*2π)/3912 weeks
225-.01908 .00245 (225*2π)/3912 weeks
226-.04079 .01536 (226*2π)/3912 weeks
227-.04136 .00911 (227*2π)/3912 weeks
228-.04902 .02413 (228*2π)/3912 weeks
229-.03028 -.00334 (229*2π)/3912 weeks
230-.03095 .00341 (230*2π)/3912 weeks
231-.01785 .01274 (231*2π)/3912 weeks
232-.0078 .00185 (232*2π)/3912 weeks
233-.01923 .01332 (233*2π)/3912 weeks
234-.04957 .0136 (234*2π)/3912 weeks
235.00013 .02877 (235*2π)/3912 weeks
236-.01876 -.00281 (236*2π)/3912 weeks
237-.00642 .03331 (237*2π)/3912 weeks
238-.0015 .02801 (238*2π)/3912 weeks
239-.04627 .05129 (239*2π)/3912 weeks
240-.0278 .0081 (240*2π)/3912 weeks
241-.0172 .02979 (241*2π)/3912 weeks
242-.02494 -.00852 (242*2π)/3912 weeks
243-.03761 .01345 (243*2π)/3912 weeks
244-.018 .01259 (244*2π)/3912 weeks
245-.00536 .01234 (245*2π)/3912 weeks
246.00078 .0123 (246*2π)/3912 weeks
247-.03123 .03998 (247*2π)/3912 weeks
248-.04979 .04231 (248*2π)/3912 weeks
249-.04935 .00925 (249*2π)/3912 weeks
250-.03297 .00776 (250*2π)/3912 weeks
251-.03418 .01155 (251*2π)/3912 weeks
252.01201 -.04199 (252*2π)/3912 weeks
253-.04437 .00442 (253*2π)/3912 weeks
254-.01312 .02631 (254*2π)/3912 weeks
255-.03508 -.00943 (255*2π)/3912 weeks
256-.05252 .03083 (256*2π)/3912 weeks
257-.0418 -.01832 (257*2π)/3912 weeks
258-.05778 -.0044 (258*2π)/3912 weeks
259-.04159 .01993 (259*2π)/3912 weeks
260-.05725 -.01171 (260*2π)/3912 weeks
261-.04586 .01468 (261*2π)/3911 weeks
262-.06781 .00622 (262*2π)/3911 weeks
263-.075 .02436 (263*2π)/3911 weeks
264-.03714 .0223 (264*2π)/3911 weeks
265-.03772 .01911 (265*2π)/3911 weeks
266-.04828 .00386 (266*2π)/3911 weeks
267-.05814 .0592 (267*2π)/3911 weeks
268-.02575 .08182 (268*2π)/3911 weeks
269-.02317 .01408 (269*2π)/3911 weeks
270-.01625 .05591 (270*2π)/3911 weeks
271-.05112 .04068 (271*2π)/3911 weeks
272-.02176 .03386 (272*2π)/3911 weeks
273-.03333 .00335 (273*2π)/3911 weeks
274-.00322 .00853 (274*2π)/3911 weeks
275-.02902 .04431 (275*2π)/3911 weeks
276-.02366 .02079 (276*2π)/3911 weeks
277-.01539 .03581 (277*2π)/3911 weeks
278.03194 -.00279 (278*2π)/3911 weeks
279.00642 .02417 (279*2π)/3911 weeks
280-.02189 .01204 (280*2π)/3911 weeks
281-.01088 .03898 (281*2π)/3911 weeks
282-.01437 .05351 (282*2π)/3911 weeks
283-.03119 .01497 (283*2π)/3911 weeks
284-.02394 .00203 (284*2π)/3911 weeks
285-.03109 -.01992 (285*2π)/3911 weeks
286-.0038 -.02464 (286*2π)/3911 weeks
287-.03228 .00542 (287*2π)/3911 weeks
288-.03611 .05488 (288*2π)/3911 weeks
289-.03601 .00613 (289*2π)/3911 weeks
290-.05825 .02568 (290*2π)/3911 weeks
291-.0941 .03543 (291*2π)/3911 weeks
292-.02214 .00958 (292*2π)/3911 weeks
293-.04149 .00082 (293*2π)/3911 weeks
294-.06337 .02674 (294*2π)/3911 weeks
295-.00023 .03198 (295*2π)/3911 weeks
296-.05107 .0253 (296*2π)/3911 weeks
297-.00102 .04466 (297*2π)/3911 weeks
298-.02873 -.00366 (298*2π)/3911 weeks
299-.02025 .05034 (299*2π)/3911 weeks
300-.01884 .03483 (300*2π)/3911 weeks
301.00044 .07279 (301*2π)/3911 weeks
302.02266 .05635 (302*2π)/3911 weeks
303-.08999 .05914 (303*2π)/3911 weeks
304-.03907 .06584 (304*2π)/3911 weeks
305.01515 .07997 (305*2π)/3911 weeks
306-.05854 .00801 (306*2π)/3911 weeks
307-.02456 .01351 (307*2π)/3911 weeks
308.01048 .04195 (308*2π)/3911 weeks
309-.06887 -.00536 (309*2π)/3911 weeks
310.03041 .05523 (310*2π)/3911 weeks
311.03069 .08647 (311*2π)/3911 weeks
312-.01221 -.01553 (312*2π)/3911 weeks
313-.07328 .03085 (313*2π)/3911 weeks
314-.03295 .01966 (314*2π)/3911 weeks
315-.03615 .01217 (315*2π)/3911 weeks
316-.0293 .07954 (316*2π)/3911 weeks
317-.01422 .03149 (317*2π)/3911 weeks
318-.02117 -.01903 (318*2π)/3911 weeks
319-.11975 .05031 (319*2π)/3911 weeks
320-.01802 .10333 (320*2π)/3911 weeks
321.0101 .05382 (321*2π)/3911 weeks
322-.0607 .03276 (322*2π)/3911 weeks
323.00943 .06869 (323*2π)/3911 weeks
324-.07209 .08055 (324*2π)/3911 weeks
325-.04637 .02862 (325*2π)/3911 weeks
326-.08197 .02323 (326*2π)/3911 weeks
327-.06137 .08639 (327*2π)/3911 weeks
328-.01476 .06814 (328*2π)/3911 weeks
329-.07188 .0611 (329*2π)/3911 weeks
330.00794 .14911 (330*2π)/3911 weeks
331-.04652 .16135 (331*2π)/3911 weeks
332-.04903 .14731 (332*2π)/3911 weeks
333-.11409 .07076 (333*2π)/3911 weeks
334-.04529 -.00925 (334*2π)/3911 weeks
335-.0067 .03632 (335*2π)/3911 weeks
336.04753 -.01488 (336*2π)/3911 weeks
337.02975 .10786 (337*2π)/3911 weeks
338-.02637 .09629 (338*2π)/3911 weeks
339.02673 .15705 (339*2π)/3911 weeks
340.00002 .11618 (340*2π)/3911 weeks
341-.00063 .10796 (341*2π)/3911 weeks
342-.02031 .05985 (342*2π)/3911 weeks
343-.03445 .02449 (343*2π)/3911 weeks
344.05513 -.00388 (344*2π)/3911 weeks
345-.04308 .0071 (345*2π)/3911 weeks
346.01515 .09052 (346*2π)/3911 weeks
347-.00953 .13968 (347*2π)/3911 weeks
348-.07315 .0807 (348*2π)/3911 weeks
349-.05701 .10194 (349*2π)/3911 weeks
350.01704 .09371 (350*2π)/3911 weeks
351-.14183 .0946 (351*2π)/3911 weeks
352-.00369 .13916 (352*2π)/3911 weeks
353-.05335 .11668 (353*2π)/3911 weeks
354-.12835 .03823 (354*2π)/3911 weeks
355-.03526 .14594 (355*2π)/3911 weeks
356.0604 .2598 (356*2π)/3911 weeks
357-.14573 .04746 (357*2π)/3911 weeks
358.00739 .26867 (358*2π)/3911 weeks
359-.02363 .06977 (359*2π)/3911 weeks
360-.01779 .1354 (360*2π)/3911 weeks
361.18553 .27166 (361*2π)/3911 weeks
362-.10531 .27368 (362*2π)/3911 weeks
363.01847 .17385 (363*2π)/3911 weeks
364.00044 .30251 (364*2π)/3911 weeks
365-.12832 .24202 (365*2π)/3911 weeks
366.0164 .12907 (366*2π)/3911 weeks
367.06123 .06952 (367*2π)/3911 weeks
368-.0256 .17853 (368*2π)/3911 weeks
369.13489 .1369 (369*2π)/3911 weeks
370.07829 .13714 (370*2π)/3911 weeks
371-.21401 .32404 (371*2π)/3911 weeks
372-.24277 .27945 (372*2π)/3911 weeks
373.19164 .06618 (373*2π)/3911 weeks
374-.18396 .05615 (374*2π)/3911 weeks
375-.18063 .31275 (375*2π)/3911 weeks
376.05036 .40093 (376*2π)/3911 weeks
377-.25179 .31925 (377*2π)/3911 weeks
378-.05352 .08543 (378*2π)/3911 weeks
379.24669 .35441 (379*2π)/3911 weeks
380-.31831 .41167 (380*2π)/3911 weeks
381.19791 .73697 (381*2π)/3911 weeks
382-.20836 .82447 (382*2π)/3911 weeks
383.04164 .66669 (383*2π)/3911 weeks
384-.37972 .07696 (384*2π)/3911 weeks
385-.41927 1.00547 (385*2π)/3911 weeks
386-.20933 1.08711 (386*2π)/3911 weeks
387.32319 .33833 (387*2π)/3911 weeks
3881.08552 1.78079 (388*2π)/3911 weeks
3891.56 2.90184 (389*2π)/3911 weeks