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Fourier Analysis of VNQI (Vanguard Global ex-US Real Estate ETF)


VNQI (Vanguard Global ex-US Real Estate ETF) appears to have interesting cyclic behaviour every 35 weeks (.9217*sine), 27 weeks (.73*sine), and 21 weeks (.474*cosine).

VNQI (Vanguard Global ex-US Real Estate ETF) has an average price of 46.72 (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 11/1/2010 to 7/17/2017 for VNQI (Vanguard Global ex-US Real Estate ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
046.72221   0 
1-2.58357 -5.83051 (1*2π)/351351 weeks
21.76084 -3.2285 (2*2π)/351176 weeks
32.00872 -1.46925 (3*2π)/351117 weeks
4-.70032 -.29722 (4*2π)/35188 weeks
5-.23766 -.53005 (5*2π)/35170 weeks
6.70282 -.18018 (6*2π)/35159 weeks
7-.04424 -1.45736 (7*2π)/35150 weeks
8-.45775 -1.31983 (8*2π)/35144 weeks
9.51694 -1.23962 (9*2π)/35139 weeks
10-.45348 -.92173 (10*2π)/35135 weeks
11.4583 -.28148 (11*2π)/35132 weeks
12-.29111 -.05694 (12*2π)/35129 weeks
13-.29861 -.73003 (13*2π)/35127 weeks
14-.10565 -.17514 (14*2π)/35125 weeks
15.1767 -.12651 (15*2π)/35123 weeks
16.4521 -.52772 (16*2π)/35122 weeks
17-.47401 -.51319 (17*2π)/35121 weeks
18-.37458 -.71354 (18*2π)/35120 weeks
19.02508 -.289 (19*2π)/35118 weeks
20.0892 -.11825 (20*2π)/35118 weeks
21.02216 -.40453 (21*2π)/35117 weeks
22-.13181 -.16596 (22*2π)/35116 weeks
23-.31537 -.12128 (23*2π)/35115 weeks
24-.12616 -.43699 (24*2π)/35115 weeks
25.0341 -.23573 (25*2π)/35114 weeks
26-.24982 -.37454 (26*2π)/35114 weeks
27.36425 -.33217 (27*2π)/35113 weeks
28.00471 -.19068 (28*2π)/35113 weeks
29-.19121 -.0715 (29*2π)/35112 weeks
30.20328 -.10602 (30*2π)/35112 weeks
31-.27079 -.42821 (31*2π)/35111 weeks
32.02596 -.09034 (32*2π)/35111 weeks
33-.02152 .04343 (33*2π)/35111 weeks
34-.01133 -.20887 (34*2π)/35110 weeks
35.05732 -.21876 (35*2π)/35110 weeks
36-.21382 -.18295 (36*2π)/35110 weeks
37.05527 -.0792 (37*2π)/3519 weeks
38-.04445 -.15673 (38*2π)/3519 weeks
39-.10921 -.23365 (39*2π)/3519 weeks
40.06243 -.16152 (40*2π)/3519 weeks
41.0904 -.00106 (41*2π)/3519 weeks
42.12231 -.10832 (42*2π)/3518 weeks
43-.10609 -.05584 (43*2π)/3518 weeks
44-.07796 -.1054 (44*2π)/3518 weeks
45-.0221 -.1793 (45*2π)/3518 weeks
46-.0356 -.15385 (46*2π)/3518 weeks
47.09788 -.13455 (47*2π)/3517 weeks
48.01932 -.17918 (48*2π)/3517 weeks
49.18164 -.07257 (49*2π)/3517 weeks
50-.06108 -.02884 (50*2π)/3517 weeks
51-.03117 .0497 (51*2π)/3517 weeks
52-.2169 -.05441 (52*2π)/3517 weeks
53-.08861 -.20529 (53*2π)/3517 weeks
54-.03922 -.21932 (54*2π)/3517 weeks
55.10685 -.12929 (55*2π)/3516 weeks
56-.08072 -.15977 (56*2π)/3516 weeks
57-.04624 -.03708 (57*2π)/3516 weeks
58.01792 -.04486 (58*2π)/3516 weeks
59-.0063 -.12092 (59*2π)/3516 weeks
60-.12485 -.13147 (60*2π)/3516 weeks
61.04107 -.15372 (61*2π)/3516 weeks
62-.08957 -.07097 (62*2π)/3516 weeks
63.02676 -.04837 (63*2π)/3516 weeks
64.10459 -.08639 (64*2π)/3515 weeks
65-.00692 -.23016 (65*2π)/3515 weeks
66-.10166 -.12275 (66*2π)/3515 weeks
67-.13209 -.10629 (67*2π)/3515 weeks
68-.01838 -.046 (68*2π)/3515 weeks
69-.05038 -.08542 (69*2π)/3515 weeks
70-.11416 -.08205 (70*2π)/3515 weeks
71-.05907 .01623 (71*2π)/3515 weeks
72.08085 -.10353 (72*2π)/3515 weeks
73.08488 -.02697 (73*2π)/3515 weeks
74-.09239 -.12505 (74*2π)/3515 weeks
75-.00426 -.03 (75*2π)/3515 weeks
76-.0507 -.02663 (76*2π)/3515 weeks
77-.04268 -.19968 (77*2π)/3515 weeks
78-.07941 -.07772 (78*2π)/3515 weeks
79-.18938 -.08488 (79*2π)/3514 weeks
80.03137 -.0626 (80*2π)/3514 weeks
81.03859 -.08932 (81*2π)/3514 weeks
82-.00629 -.05302 (82*2π)/3514 weeks
83.03519 -.05983 (83*2π)/3514 weeks
84-.06139 -.08275 (84*2π)/3514 weeks
85-.04255 .02393 (85*2π)/3514 weeks
86.00428 -.08892 (86*2π)/3514 weeks
87-.11166 -.01218 (87*2π)/3514 weeks
88-.03809 .00377 (88*2π)/3514 weeks
89-.00225 .01435 (89*2π)/3514 weeks
90-.09791 -.09641 (90*2π)/3514 weeks
91-.08188 -.08932 (91*2π)/3514 weeks
92-.10708 -.05823 (92*2π)/3514 weeks
93.02102 -.03201 (93*2π)/3514 weeks
94.01183 -.04447 (94*2π)/3514 weeks
95-.05472 .01421 (95*2π)/3514 weeks
96-.05035 -.03254 (96*2π)/3514 weeks
97-.07735 -.05748 (97*2π)/3514 weeks
98-.0158 -.10895 (98*2π)/3514 weeks
99-.01047 -.10061 (99*2π)/3514 weeks
100-.05636 -.09655 (100*2π)/3514 weeks
101-.00314 -.06149 (101*2π)/3513 weeks
102-.08703 .01059 (102*2π)/3513 weeks
103-.06626 -.0271 (103*2π)/3513 weeks
104-.07601 -.03682 (104*2π)/3513 weeks
105-.02125 .00358 (105*2π)/3513 weeks
106-.0839 .00915 (106*2π)/3513 weeks
107-.03614 -.01721 (107*2π)/3513 weeks
108-.10319 -.06854 (108*2π)/3513 weeks
109-.02892 -.04072 (109*2π)/3513 weeks
110-.14188 -.03948 (110*2π)/3513 weeks
111-.05143 -.00305 (111*2π)/3513 weeks
112-.00112 .01624 (112*2π)/3513 weeks
113-.02685 -.02722 (113*2π)/3513 weeks
114-.0164 -.01113 (114*2π)/3513 weeks
115-.07386 -.04617 (115*2π)/3513 weeks
116-.1086 -.02279 (116*2π)/3513 weeks
117-.03613 -.03669 (117*2π)/3513 weeks
118-.10327 -.02093 (118*2π)/3513 weeks
119-.038 .01032 (119*2π)/3513 weeks
120-.04986 -.02495 (120*2π)/3513 weeks
121-.12617 -.07259 (121*2π)/3513 weeks
122-.03005 -.01675 (122*2π)/3513 weeks
123-.02183 -.07955 (123*2π)/3513 weeks
124-.07514 -.07228 (124*2π)/3513 weeks
125-.05546 .09 (125*2π)/3513 weeks
126-.06481 -.01353 (126*2π)/3513 weeks
127-.07493 .00422 (127*2π)/3513 weeks
128-.11678 -.05494 (128*2π)/3513 weeks
129-.05591 -.086 (129*2π)/3513 weeks
130.01973 -.04855 (130*2π)/3513 weeks
131-.02492 -.02755 (131*2π)/3513 weeks
132-.02631 -.0338 (132*2π)/3513 weeks
133-.04461 -.03353 (133*2π)/3513 weeks
134-.09866 -.01219 (134*2π)/3513 weeks
135-.02757 -.03494 (135*2π)/3513 weeks
136-.11143 -.02564 (136*2π)/3513 weeks
137.00107 -.08003 (137*2π)/3513 weeks
138-.02573 -.04222 (138*2π)/3513 weeks
139-.0273 .0106 (139*2π)/3513 weeks
140.00346 -.0429 (140*2π)/3513 weeks
141-.08661 -.03517 (141*2π)/3512 weeks
142-.04582 -.01665 (142*2π)/3512 weeks
143-.03727 .01812 (143*2π)/3512 weeks
144-.03006 .01821 (144*2π)/3512 weeks
145-.04385 .00795 (145*2π)/3512 weeks
146-.11118 -.0045 (146*2π)/3512 weeks
147-.04846 -.00369 (147*2π)/3512 weeks
148-.04006 -.02966 (148*2π)/3512 weeks
149-.03643 .00671 (149*2π)/3512 weeks
150-.05354 -.05309 (150*2π)/3512 weeks
151-.02383 -.01358 (151*2π)/3512 weeks
152-.04888 -.01288 (152*2π)/3512 weeks
153-.13097 -.02235 (153*2π)/3512 weeks
154-.10366 -.0092 (154*2π)/3512 weeks
155-.01604 -.04906 (155*2π)/3512 weeks
156-.03881 -.02606 (156*2π)/3512 weeks
157-.0391 .02678 (157*2π)/3512 weeks
158.02051 .02736 (158*2π)/3512 weeks
159-.02155 -.02455 (159*2π)/3512 weeks
160-.06395 -.01011 (160*2π)/3512 weeks
161-.1248 -.02142 (161*2π)/3512 weeks
162-.00981 -.01532 (162*2π)/3512 weeks
163-.01901 -.03009 (163*2π)/3512 weeks
164.01002 -.02172 (164*2π)/3512 weeks
165-.01401 -.03037 (165*2π)/3512 weeks
166-.08433 .05927 (166*2π)/3512 weeks
167-.03452 .03868 (167*2π)/3512 weeks
168.01762 .06288 (168*2π)/3512 weeks
169-.03213 -.01016 (169*2π)/3512 weeks
170-.09264 -.03692 (170*2π)/3512 weeks
171-.02211 .02802 (171*2π)/3512 weeks
172.0035 -.02224 (172*2π)/3512 weeks
173-.00934 -.04576 (173*2π)/3512 weeks
174-.06267 .10242 (174*2π)/3512 weeks
175-.03997 .02242 (175*2π)/3512 weeks
176-.03997 -.02242 (176*2π)/3512 weeks
177-.06267 -.10242 (177*2π)/3512 weeks
178-.00934 .04576 (178*2π)/3512 weeks
179.0035 .02224 (179*2π)/3512 weeks
180-.02211 -.02802 (180*2π)/3512 weeks
181-.09264 .03692 (181*2π)/3512 weeks
182-.03213 .01016 (182*2π)/3512 weeks
183.01762 -.06288 (183*2π)/3512 weeks
184-.03452 -.03868 (184*2π)/3512 weeks
185-.08433 -.05927 (185*2π)/3512 weeks
186-.01401 .03037 (186*2π)/3512 weeks
187.01002 .02172 (187*2π)/3512 weeks
188-.01901 .03009 (188*2π)/3512 weeks
189-.00981 .01532 (189*2π)/3512 weeks
190-.1248 .02142 (190*2π)/3512 weeks
191-.06395 .01011 (191*2π)/3512 weeks
192-.02155 .02455 (192*2π)/3512 weeks
193.02051 -.02736 (193*2π)/3512 weeks
194-.0391 -.02678 (194*2π)/3512 weeks
195-.03881 .02606 (195*2π)/3512 weeks
196-.01604 .04906 (196*2π)/3512 weeks
197-.10366 .0092 (197*2π)/3512 weeks
198-.13097 .02235 (198*2π)/3512 weeks
199-.04888 .01288 (199*2π)/3512 weeks
200-.02383 .01358 (200*2π)/3512 weeks
201-.05354 .05309 (201*2π)/3512 weeks
202-.03643 -.00671 (202*2π)/3512 weeks
203-.04006 .02966 (203*2π)/3512 weeks
204-.04846 .00369 (204*2π)/3512 weeks
205-.11118 .0045 (205*2π)/3512 weeks
206-.04385 -.00795 (206*2π)/3512 weeks
207-.03006 -.01821 (207*2π)/3512 weeks
208-.03727 -.01812 (208*2π)/3512 weeks
209-.04582 .01665 (209*2π)/3512 weeks
210-.08661 .03517 (210*2π)/3512 weeks
211.00346 .0429 (211*2π)/3512 weeks
212-.0273 -.0106 (212*2π)/3512 weeks
213-.02573 .04222 (213*2π)/3512 weeks
214.00107 .08003 (214*2π)/3512 weeks
215-.11143 .02564 (215*2π)/3512 weeks
216-.02757 .03494 (216*2π)/3512 weeks
217-.09866 .01219 (217*2π)/3512 weeks
218-.04461 .03353 (218*2π)/3512 weeks
219-.02631 .0338 (219*2π)/3512 weeks
220-.02492 .02755 (220*2π)/3512 weeks
221.01973 .04855 (221*2π)/3512 weeks
222-.05591 .086 (222*2π)/3512 weeks
223-.11678 .05494 (223*2π)/3512 weeks
224-.07493 -.00422 (224*2π)/3512 weeks
225-.06481 .01353 (225*2π)/3512 weeks
226-.05546 -.09 (226*2π)/3512 weeks
227-.07514 .07228 (227*2π)/3512 weeks
228-.02183 .07955 (228*2π)/3512 weeks
229-.03005 .01675 (229*2π)/3512 weeks
230-.12617 .07259 (230*2π)/3512 weeks
231-.04986 .02495 (231*2π)/3512 weeks
232-.038 -.01032 (232*2π)/3512 weeks
233-.10327 .02093 (233*2π)/3512 weeks
234-.03613 .03669 (234*2π)/3512 weeks
235-.1086 .02279 (235*2π)/3511 weeks
236-.07386 .04617 (236*2π)/3511 weeks
237-.0164 .01113 (237*2π)/3511 weeks
238-.02685 .02722 (238*2π)/3511 weeks
239-.00112 -.01624 (239*2π)/3511 weeks
240-.05143 .00305 (240*2π)/3511 weeks
241-.14188 .03948 (241*2π)/3511 weeks
242-.02892 .04072 (242*2π)/3511 weeks
243-.10319 .06854 (243*2π)/3511 weeks
244-.03614 .01721 (244*2π)/3511 weeks
245-.0839 -.00915 (245*2π)/3511 weeks
246-.02125 -.00358 (246*2π)/3511 weeks
247-.07601 .03682 (247*2π)/3511 weeks
248-.06626 .0271 (248*2π)/3511 weeks
249-.08703 -.01059 (249*2π)/3511 weeks
250-.00314 .06149 (250*2π)/3511 weeks
251-.05636 .09655 (251*2π)/3511 weeks
252-.01047 .10061 (252*2π)/3511 weeks
253-.0158 .10895 (253*2π)/3511 weeks
254-.07735 .05748 (254*2π)/3511 weeks
255-.05035 .03254 (255*2π)/3511 weeks
256-.05472 -.01421 (256*2π)/3511 weeks
257.01183 .04447 (257*2π)/3511 weeks
258.02102 .03201 (258*2π)/3511 weeks
259-.10708 .05823 (259*2π)/3511 weeks
260-.08188 .08932 (260*2π)/3511 weeks
261-.09791 .09641 (261*2π)/3511 weeks
262-.00225 -.01435 (262*2π)/3511 weeks
263-.03809 -.00377 (263*2π)/3511 weeks
264-.11166 .01218 (264*2π)/3511 weeks
265.00428 .08892 (265*2π)/3511 weeks
266-.04255 -.02393 (266*2π)/3511 weeks
267-.06139 .08275 (267*2π)/3511 weeks
268.03519 .05983 (268*2π)/3511 weeks
269-.00629 .05302 (269*2π)/3511 weeks
270.03859 .08932 (270*2π)/3511 weeks
271.03137 .0626 (271*2π)/3511 weeks
272-.18938 .08488 (272*2π)/3511 weeks
273-.07941 .07772 (273*2π)/3511 weeks
274-.04268 .19968 (274*2π)/3511 weeks
275-.0507 .02663 (275*2π)/3511 weeks
276-.00426 .03 (276*2π)/3511 weeks
277-.09239 .12505 (277*2π)/3511 weeks
278.08488 .02697 (278*2π)/3511 weeks
279.08085 .10353 (279*2π)/3511 weeks
280-.05907 -.01623 (280*2π)/3511 weeks
281-.11416 .08205 (281*2π)/3511 weeks
282-.05038 .08542 (282*2π)/3511 weeks
283-.01838 .046 (283*2π)/3511 weeks
284-.13209 .10629 (284*2π)/3511 weeks
285-.10166 .12275 (285*2π)/3511 weeks
286-.00692 .23016 (286*2π)/3511 weeks
287.10459 .08639 (287*2π)/3511 weeks
288.02676 .04837 (288*2π)/3511 weeks
289-.08957 .07097 (289*2π)/3511 weeks
290.04107 .15372 (290*2π)/3511 weeks
291-.12485 .13147 (291*2π)/3511 weeks
292-.0063 .12092 (292*2π)/3511 weeks
293.01792 .04486 (293*2π)/3511 weeks
294-.04624 .03708 (294*2π)/3511 weeks
295-.08072 .15977 (295*2π)/3511 weeks
296.10685 .12929 (296*2π)/3511 weeks
297-.03922 .21932 (297*2π)/3511 weeks
298-.08861 .20529 (298*2π)/3511 weeks
299-.2169 .05441 (299*2π)/3511 weeks
300-.03117 -.0497 (300*2π)/3511 weeks
301-.06108 .02884 (301*2π)/3511 weeks
302.18164 .07257 (302*2π)/3511 weeks
303.01932 .17918 (303*2π)/3511 weeks
304.09788 .13455 (304*2π)/3511 weeks
305-.0356 .15385 (305*2π)/3511 weeks
306-.0221 .1793 (306*2π)/3511 weeks
307-.07796 .1054 (307*2π)/3511 weeks
308-.10609 .05584 (308*2π)/3511 weeks
309.12231 .10832 (309*2π)/3511 weeks
310.0904 .00106 (310*2π)/3511 weeks
311.06243 .16152 (311*2π)/3511 weeks
312-.10921 .23365 (312*2π)/3511 weeks
313-.04445 .15673 (313*2π)/3511 weeks
314.05527 .0792 (314*2π)/3511 weeks
315-.21382 .18295 (315*2π)/3511 weeks
316.05732 .21876 (316*2π)/3511 weeks
317-.01133 .20887 (317*2π)/3511 weeks
318-.02152 -.04343 (318*2π)/3511 weeks
319.02596 .09034 (319*2π)/3511 weeks
320-.27079 .42821 (320*2π)/3511 weeks
321.20328 .10602 (321*2π)/3511 weeks
322-.19121 .0715 (322*2π)/3511 weeks
323.00471 .19068 (323*2π)/3511 weeks
324.36425 .33217 (324*2π)/3511 weeks
325-.24982 .37454 (325*2π)/3511 weeks
326.0341 .23573 (326*2π)/3511 weeks
327-.12616 .43699 (327*2π)/3511 weeks
328-.31537 .12128 (328*2π)/3511 weeks
329-.13181 .16596 (329*2π)/3511 weeks
330.02216 .40453 (330*2π)/3511 weeks
331.0892 .11825 (331*2π)/3511 weeks
332.02508 .289 (332*2π)/3511 weeks
333-.37458 .71354 (333*2π)/3511 weeks
334-.47401 .51319 (334*2π)/3511 weeks
335.4521 .52772 (335*2π)/3511 weeks
336.1767 .12651 (336*2π)/3511 weeks
337-.10565 .17514 (337*2π)/3511 weeks
338-.29861 .73003 (338*2π)/3511 weeks
339-.29111 .05694 (339*2π)/3511 weeks
340.4583 .28148 (340*2π)/3511 weeks
341-.45348 .92173 (341*2π)/3511 weeks
342.51694 1.23962 (342*2π)/3511 weeks
343-.45775 1.31983 (343*2π)/3511 weeks
344-.04424 1.45736 (344*2π)/3511 weeks
345.70282 .18018 (345*2π)/3511 weeks
346-.23766 .53005 (346*2π)/3511 weeks
347-.70032 .29722 (347*2π)/3511 weeks
3482.00872 1.46925 (348*2π)/3511 weeks
3491.76084 3.2285 (349*2π)/3511 weeks



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