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Fourier Analysis of VNQI (Vanguard Global ex-U.S. Real Es)


VNQI (Vanguard Global ex-U.S. Real Es) appears to have interesting cyclic behaviour every 19 weeks (.73*sine), 33 weeks (.698*cosine), and 27 weeks (.5662*sine).

VNQI (Vanguard Global ex-U.S. Real Es) has an average price of 46.14 (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 1/17/2017 for VNQI (Vanguard Global ex-U.S. Real Es), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
046.1436   0 
1-2.71383 -6.25273 (1*2π)/325325 weeks
21.41371 -2.72784 (2*2π)/325163 weeks
31.80041 -.34082 (3*2π)/325108 weeks
4-.6648 -1.07033 (4*2π)/32581 weeks
5-.58068 -1.2636 (5*2π)/32565 weeks
6-1.29511 -.10484 (6*2π)/32554 weeks
7-.49538 -.35464 (7*2π)/32546 weeks
8.03415 -1.15072 (8*2π)/32541 weeks
9-.26267 -.03515 (9*2π)/32536 weeks
10.698 -.29714 (10*2π)/32533 weeks
11-.15848 .21545 (11*2π)/32530 weeks
12-.3156 -.56621 (12*2π)/32527 weeks
13-.13999 -.0353 (13*2π)/32525 weeks
14.00905 .12036 (14*2π)/32523 weeks
15.50163 .11158 (15*2π)/32522 weeks
16-.15769 -.40958 (16*2π)/32520 weeks
17.14959 -.73 (17*2π)/32519 weeks
18.10252 -.36237 (18*2π)/32518 weeks
19-.17902 -.18057 (19*2π)/32517 weeks
20.04809 -.02423 (20*2π)/32516 weeks
21-.10704 -.00917 (21*2π)/32515 weeks
22-.17219 -.41409 (22*2π)/32515 weeks
23.09453 -.25394 (23*2π)/32514 weeks
24-.23072 -.29546 (24*2π)/32514 weeks
25.43183 -.30371 (25*2π)/32513 weeks
26.06463 -.16498 (26*2π)/32513 weeks
27-.21241 -.14766 (27*2π)/32512 weeks
28.09274 .14357 (28*2π)/32512 weeks
29.10772 -.45632 (29*2π)/32511 weeks
30.06087 -.15507 (30*2π)/32511 weeks
31-.19974 -.13628 (31*2π)/32510 weeks
32-.0723 -.16804 (32*2π)/32510 weeks
33-.0945 .03885 (33*2π)/32510 weeks
34.11451 -.18015 (34*2π)/32510 weeks
35-.0615 -.13835 (35*2π)/3259 weeks
36-.12261 -.18426 (36*2π)/3259 weeks
37.08006 -.15776 (37*2π)/3259 weeks
38.07885 .02552 (38*2π)/3259 weeks
39.14022 -.03855 (39*2π)/3258 weeks
40-.09847 -.07522 (40*2π)/3258 weeks
41-.09325 -.12027 (41*2π)/3258 weeks
42-.00107 -.1393 (42*2π)/3258 weeks
43.00127 -.20892 (43*2π)/3258 weeks
44-.00308 -.07221 (44*2π)/3257 weeks
45.12434 -.14412 (45*2π)/3257 weeks
46-.01432 .11564 (46*2π)/3257 weeks
47.02307 .06263 (47*2π)/3257 weeks
48-.20248 .02837 (48*2π)/3257 weeks
49-.09778 -.18711 (49*2π)/3257 weeks
50-.03225 -.19424 (50*2π)/3257 weeks
51.12177 -.07051 (51*2π)/3256 weeks
52-.01858 -.16362 (52*2π)/3256 weeks
53-.07213 -.07103 (53*2π)/3256 weeks
54-.05738 -.0052 (54*2π)/3256 weeks
55-.0183 -.01015 (55*2π)/3256 weeks
56-.02853 -.17849 (56*2π)/3256 weeks
57.03612 -.01209 (57*2π)/3256 weeks
58.05812 -.14061 (58*2π)/3256 weeks
59.03136 -.16544 (59*2π)/3256 weeks
60-.11473 -.15985 (60*2π)/3255 weeks
61-.10246 -.03364 (61*2π)/3255 weeks
62-.11159 -.05342 (62*2π)/3255 weeks
63-.00138 -.0084 (63*2π)/3255 weeks
64-.01648 -.0603 (64*2π)/3255 weeks
65-.07387 -.12175 (65*2π)/3255 weeks
66-.14173 -.06178 (66*2π)/3255 weeks
67.0207 -.01943 (67*2π)/3255 weeks
68-.05129 .10659 (68*2π)/3255 weeks
69.03106 -.05241 (69*2π)/3255 weeks
70-.03908 -.00014 (70*2π)/3255 weeks
71-.14792 -.09051 (71*2π)/3255 weeks
72-.03899 .01721 (72*2π)/3255 weeks
73-.1332 .0257 (73*2π)/3254 weeks
74.08078 -.05009 (74*2π)/3254 weeks
75.06673 -.05379 (75*2π)/3254 weeks
76.01454 -.0159 (76*2π)/3254 weeks
77.06602 .01429 (77*2π)/3254 weeks
78.01869 -.06697 (78*2π)/3254 weeks
79-.07363 .01315 (79*2π)/3254 weeks
80.05001 .03951 (80*2π)/3254 weeks
81-.01101 -.05528 (81*2π)/3254 weeks
82-.03152 -.03764 (82*2π)/3254 weeks
83-.14341 .00934 (83*2π)/3254 weeks
84-.07623 -.02667 (84*2π)/3254 weeks
85-.05932 .00101 (85*2π)/3254 weeks
86.05163 -.03545 (86*2π)/3254 weeks
87.02616 -.02574 (87*2π)/3254 weeks
88-.05334 .04171 (88*2π)/3254 weeks
89-.04537 .00158 (89*2π)/3254 weeks
90-.08136 -.0362 (90*2π)/3254 weeks
91-.00052 -.04079 (91*2π)/3254 weeks
92.01598 -.0106 (92*2π)/3254 weeks
93.03064 -.05308 (93*2π)/3253 weeks
94.04439 .04466 (94*2π)/3253 weeks
95-.02234 -.01953 (95*2π)/3253 weeks
96-.02723 -.01194 (96*2π)/3253 weeks
97.03005 -.02015 (97*2π)/3253 weeks
98-.04052 .02331 (98*2π)/3253 weeks
99-.00354 -.0251 (99*2π)/3253 weeks
100-.07489 -.06356 (100*2π)/3253 weeks
101.01218 -.03152 (101*2π)/3253 weeks
102-.09576 -.08512 (102*2π)/3253 weeks
103-.05295 -.03842 (103*2π)/3253 weeks
104-.04711 .02998 (104*2π)/3253 weeks
105-.02787 .00139 (105*2π)/3253 weeks
106-.0533 .04925 (106*2π)/3253 weeks
107-.03111 .02491 (107*2π)/3253 weeks
108-.02383 -.04637 (108*2π)/3253 weeks
109-.05168 .02136 (109*2π)/3253 weeks
110.01161 -.00728 (110*2π)/3253 weeks
111-.03278 -.02869 (111*2π)/3253 weeks
112-.10629 -.05729 (112*2π)/3253 weeks
113-.00712 -.00488 (113*2π)/3253 weeks
114.02979 -.05573 (114*2π)/3253 weeks
115.00655 -.09398 (115*2π)/3253 weeks
116-.09664 .04698 (116*2π)/3253 weeks
117-.05363 -.00184 (117*2π)/3253 weeks
118-.09168 .00269 (118*2π)/3253 weeks
119-.06883 -.08751 (119*2π)/3253 weeks
120.01027 -.09552 (120*2π)/3253 weeks
121-.01505 -.01385 (121*2π)/3253 weeks
122-.02077 -.02336 (122*2π)/3253 weeks
123-.03782 -.01083 (123*2π)/3253 weeks
124-.07415 .01426 (124*2π)/3253 weeks
125-.00657 -.02168 (125*2π)/3253 weeks
126-.09924 -.02997 (126*2π)/3253 weeks
127.02782 -.04589 (127*2π)/3253 weeks
128.01011 -.03338 (128*2π)/3253 weeks
129-.04406 .01008 (129*2π)/3253 weeks
130.0139 .04643 (130*2π)/3253 weeks
131.00572 -.02668 (131*2π)/3252 weeks
132.0182 -.01097 (132*2π)/3252 weeks
133-.00669 -.00131 (133*2π)/3252 weeks
134-.03314 .00635 (134*2π)/3252 weeks
135-.08154 .03125 (135*2π)/3252 weeks
136-.0183 -.01125 (136*2π)/3252 weeks
137-.01835 -.02843 (137*2π)/3252 weeks
138-.01863 .01331 (138*2π)/3252 weeks
139-.01743 -.04501 (139*2π)/3252 weeks
140-.00082 .00773 (140*2π)/3252 weeks
141-.00572 .02307 (141*2π)/3252 weeks
142-.04677 -.06129 (142*2π)/3252 weeks
143-.06143 -.09188 (143*2π)/3252 weeks
144-.00403 -.02745 (144*2π)/3252 weeks
145.02921 -.01619 (145*2π)/3252 weeks
146.01866 -.05201 (146*2π)/3252 weeks
147-.04829 -.03085 (147*2π)/3252 weeks
148-.06305 .001 (148*2π)/3252 weeks
149-.10835 -.00838 (149*2π)/3252 weeks
150.00757 -.02187 (150*2π)/3252 weeks
151.00278 -.03475 (151*2π)/3252 weeks
152.0348 -.00766 (152*2π)/3252 weeks
153.05756 -.02278 (153*2π)/3252 weeks
154-.05749 -.02709 (154*2π)/3252 weeks
155-.03522 -.02839 (155*2π)/3252 weeks
156-.08876 .04857 (156*2π)/3252 weeks
157-.06785 .04169 (157*2π)/3252 weeks
158.01874 -.01963 (158*2π)/3252 weeks
159-.02487 -.04754 (159*2π)/3252 weeks
160-.03621 -.026 (160*2π)/3252 weeks
161-.02081 .11746 (161*2π)/3252 weeks
162-.03426 .02109 (162*2π)/3252 weeks
163-.03426 -.02109 (163*2π)/3252 weeks
164-.02081 -.11746 (164*2π)/3252 weeks
165-.03621 .026 (165*2π)/3252 weeks
166-.02487 .04754 (166*2π)/3252 weeks
167.01874 .01963 (167*2π)/3252 weeks
168-.06785 -.04169 (168*2π)/3252 weeks
169-.08876 -.04857 (169*2π)/3252 weeks
170-.03522 .02839 (170*2π)/3252 weeks
171-.05749 .02709 (171*2π)/3252 weeks
172.05756 .02278 (172*2π)/3252 weeks
173.0348 .00766 (173*2π)/3252 weeks
174.00278 .03475 (174*2π)/3252 weeks
175.00757 .02187 (175*2π)/3252 weeks
176-.10835 .00838 (176*2π)/3252 weeks
177-.06305 -.001 (177*2π)/3252 weeks
178-.04829 .03085 (178*2π)/3252 weeks
179.01866 .05201 (179*2π)/3252 weeks
180.02921 .01619 (180*2π)/3252 weeks
181-.00403 .02745 (181*2π)/3252 weeks
182-.06143 .09188 (182*2π)/3252 weeks
183-.04677 .06129 (183*2π)/3252 weeks
184-.00572 -.02307 (184*2π)/3252 weeks
185-.00082 -.00773 (185*2π)/3252 weeks
186-.01743 .04501 (186*2π)/3252 weeks
187-.01863 -.01331 (187*2π)/3252 weeks
188-.01835 .02843 (188*2π)/3252 weeks
189-.0183 .01125 (189*2π)/3252 weeks
190-.08154 -.03125 (190*2π)/3252 weeks
191-.03314 -.00635 (191*2π)/3252 weeks
192-.00669 .00131 (192*2π)/3252 weeks
193.0182 .01097 (193*2π)/3252 weeks
194.00572 .02668 (194*2π)/3252 weeks
195.0139 -.04643 (195*2π)/3252 weeks
196-.04406 -.01008 (196*2π)/3252 weeks
197.01011 .03338 (197*2π)/3252 weeks
198.02782 .04589 (198*2π)/3252 weeks
199-.09924 .02997 (199*2π)/3252 weeks
200-.00657 .02168 (200*2π)/3252 weeks
201-.07415 -.01426 (201*2π)/3252 weeks
202-.03782 .01083 (202*2π)/3252 weeks
203-.02077 .02336 (203*2π)/3252 weeks
204-.01505 .01385 (204*2π)/3252 weeks
205.01027 .09552 (205*2π)/3252 weeks
206-.06883 .08751 (206*2π)/3252 weeks
207-.09168 -.00269 (207*2π)/3252 weeks
208-.05363 .00184 (208*2π)/3252 weeks
209-.09664 -.04698 (209*2π)/3252 weeks
210.00655 .09398 (210*2π)/3252 weeks
211.02979 .05573 (211*2π)/3252 weeks
212-.00712 .00488 (212*2π)/3252 weeks
213-.10629 .05729 (213*2π)/3252 weeks
214-.03278 .02869 (214*2π)/3252 weeks
215.01161 .00728 (215*2π)/3252 weeks
216-.05168 -.02136 (216*2π)/3252 weeks
217-.02383 .04637 (217*2π)/3251 weeks
218-.03111 -.02491 (218*2π)/3251 weeks
219-.0533 -.04925 (219*2π)/3251 weeks
220-.02787 -.00139 (220*2π)/3251 weeks
221-.04711 -.02998 (221*2π)/3251 weeks
222-.05295 .03842 (222*2π)/3251 weeks
223-.09576 .08512 (223*2π)/3251 weeks
224.01218 .03152 (224*2π)/3251 weeks
225-.07489 .06356 (225*2π)/3251 weeks
226-.00354 .0251 (226*2π)/3251 weeks
227-.04052 -.02331 (227*2π)/3251 weeks
228.03005 .02015 (228*2π)/3251 weeks
229-.02723 .01194 (229*2π)/3251 weeks
230-.02234 .01953 (230*2π)/3251 weeks
231.04439 -.04466 (231*2π)/3251 weeks
232.03064 .05308 (232*2π)/3251 weeks
233.01598 .0106 (233*2π)/3251 weeks
234-.00052 .04079 (234*2π)/3251 weeks
235-.08136 .0362 (235*2π)/3251 weeks
236-.04537 -.00158 (236*2π)/3251 weeks
237-.05334 -.04171 (237*2π)/3251 weeks
238.02616 .02574 (238*2π)/3251 weeks
239.05163 .03545 (239*2π)/3251 weeks
240-.05932 -.00101 (240*2π)/3251 weeks
241-.07623 .02667 (241*2π)/3251 weeks
242-.14341 -.00934 (242*2π)/3251 weeks
243-.03152 .03764 (243*2π)/3251 weeks
244-.01101 .05528 (244*2π)/3251 weeks
245.05001 -.03951 (245*2π)/3251 weeks
246-.07363 -.01315 (246*2π)/3251 weeks
247.01869 .06697 (247*2π)/3251 weeks
248.06602 -.01429 (248*2π)/3251 weeks
249.01454 .0159 (249*2π)/3251 weeks
250.06673 .05379 (250*2π)/3251 weeks
251.08078 .05009 (251*2π)/3251 weeks
252-.1332 -.0257 (252*2π)/3251 weeks
253-.03899 -.01721 (253*2π)/3251 weeks
254-.14792 .09051 (254*2π)/3251 weeks
255-.03908 .00014 (255*2π)/3251 weeks
256.03106 .05241 (256*2π)/3251 weeks
257-.05129 -.10659 (257*2π)/3251 weeks
258.0207 .01943 (258*2π)/3251 weeks
259-.14173 .06178 (259*2π)/3251 weeks
260-.07387 .12175 (260*2π)/3251 weeks
261-.01648 .0603 (261*2π)/3251 weeks
262-.00138 .0084 (262*2π)/3251 weeks
263-.11159 .05342 (263*2π)/3251 weeks
264-.10246 .03364 (264*2π)/3251 weeks
265-.11473 .15985 (265*2π)/3251 weeks
266.03136 .16544 (266*2π)/3251 weeks
267.05812 .14061 (267*2π)/3251 weeks
268.03612 .01209 (268*2π)/3251 weeks
269-.02853 .17849 (269*2π)/3251 weeks
270-.0183 .01015 (270*2π)/3251 weeks
271-.05738 .0052 (271*2π)/3251 weeks
272-.07213 .07103 (272*2π)/3251 weeks
273-.01858 .16362 (273*2π)/3251 weeks
274.12177 .07051 (274*2π)/3251 weeks
275-.03225 .19424 (275*2π)/3251 weeks
276-.09778 .18711 (276*2π)/3251 weeks
277-.20248 -.02837 (277*2π)/3251 weeks
278.02307 -.06263 (278*2π)/3251 weeks
279-.01432 -.11564 (279*2π)/3251 weeks
280.12434 .14412 (280*2π)/3251 weeks
281-.00308 .07221 (281*2π)/3251 weeks
282.00127 .20892 (282*2π)/3251 weeks
283-.00107 .1393 (283*2π)/3251 weeks
284-.09325 .12027 (284*2π)/3251 weeks
285-.09847 .07522 (285*2π)/3251 weeks
286.14022 .03855 (286*2π)/3251 weeks
287.07885 -.02552 (287*2π)/3251 weeks
288.08006 .15776 (288*2π)/3251 weeks
289-.12261 .18426 (289*2π)/3251 weeks
290-.0615 .13835 (290*2π)/3251 weeks
291.11451 .18015 (291*2π)/3251 weeks
292-.0945 -.03885 (292*2π)/3251 weeks
293-.0723 .16804 (293*2π)/3251 weeks
294-.19974 .13628 (294*2π)/3251 weeks
295.06087 .15507 (295*2π)/3251 weeks
296.10772 .45632 (296*2π)/3251 weeks
297.09274 -.14357 (297*2π)/3251 weeks
298-.21241 .14766 (298*2π)/3251 weeks
299.06463 .16498 (299*2π)/3251 weeks
300.43183 .30371 (300*2π)/3251 weeks
301-.23072 .29546 (301*2π)/3251 weeks
302.09453 .25394 (302*2π)/3251 weeks
303-.17219 .41409 (303*2π)/3251 weeks
304-.10704 .00917 (304*2π)/3251 weeks
305.04809 .02423 (305*2π)/3251 weeks
306-.17902 .18057 (306*2π)/3251 weeks
307.10252 .36237 (307*2π)/3251 weeks
308.14959 .73 (308*2π)/3251 weeks
309-.15769 .40958 (309*2π)/3251 weeks
310.50163 -.11158 (310*2π)/3251 weeks
311.00905 -.12036 (311*2π)/3251 weeks
312-.13999 .0353 (312*2π)/3251 weeks
313-.3156 .56621 (313*2π)/3251 weeks
314-.15848 -.21545 (314*2π)/3251 weeks
315.698 .29714 (315*2π)/3251 weeks
316-.26267 .03515 (316*2π)/3251 weeks
317.03415 1.15072 (317*2π)/3251 weeks
318-.49538 .35464 (318*2π)/3251 weeks
319-1.29511 .10484 (319*2π)/3251 weeks
320-.58068 1.2636 (320*2π)/3251 weeks
321-.6648 1.07033 (321*2π)/3251 weeks
3221.80041 .34082 (322*2π)/3251 weeks
3231.41371 2.72784 (323*2π)/3251 weeks

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