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Fourier Analysis of VMMSX (Vanguard Emerging Markets Selec)


VMMSX (Vanguard Emerging Markets Selec) appears to have interesting cyclic behaviour every 21 weeks (.3504*cosine), 19 weeks (.1998*cosine), and 11 weeks (.1298*cosine).

VMMSX (Vanguard Emerging Markets Selec) has an average price of 17.56 (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 6/27/2011 to 1/9/2017 for VMMSX (Vanguard Emerging Markets Selec), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
017.56261   0 
1-1.33833 .31549 (1*2π)/290290 weeks
2.61409 .37052 (2*2π)/290145 weeks
3.63303 -.62312 (3*2π)/29097 weeks
4.28627 -.19018 (4*2π)/29073 weeks
5-.36279 -.44046 (5*2π)/29058 weeks
6-.1161 -.03586 (6*2π)/29048 weeks
7.58923 -.30769 (7*2π)/29041 weeks
8-.10245 .09127 (8*2π)/29036 weeks
9.34813 .11451 (9*2π)/29032 weeks
10.18474 .19241 (10*2π)/29029 weeks
11-.16446 .02526 (11*2π)/29026 weeks
12-.11375 .19737 (12*2π)/29024 weeks
13.06214 .13343 (13*2π)/29022 weeks
14.35041 -.12289 (14*2π)/29021 weeks
15.19981 -.04754 (15*2π)/29019 weeks
16.03076 .02208 (16*2π)/29018 weeks
17.02294 .01606 (17*2π)/29017 weeks
18.09539 .17683 (18*2π)/29016 weeks
19.04058 .13733 (19*2π)/29015 weeks
20.01891 .05848 (20*2π)/29015 weeks
21.05375 .0522 (21*2π)/29014 weeks
22.03273 .12397 (22*2π)/29013 weeks
23.00193 -.01903 (23*2π)/29013 weeks
24-.0863 -.04994 (24*2π)/29012 weeks
25-.06045 .11127 (25*2π)/29012 weeks
26.12981 -.14013 (26*2π)/29011 weeks
27.03863 -.01622 (27*2π)/29011 weeks
28.00495 .04135 (28*2π)/29010 weeks
29.02716 -.04546 (29*2π)/29010 weeks
30.01839 .10539 (30*2π)/29010 weeks
31-.01683 -.01204 (31*2π)/2909 weeks
32.04549 -.01212 (32*2π)/2909 weeks
33.03285 .026 (33*2π)/2909 weeks
34-.00021 .04934 (34*2π)/2909 weeks
35.08209 .08624 (35*2π)/2908 weeks
36.03306 .06838 (36*2π)/2908 weeks
37-.02754 .07988 (37*2π)/2908 weeks
38.04146 .04771 (38*2π)/2908 weeks
39-.0245 .02922 (39*2π)/2907 weeks
40.02726 .05725 (40*2π)/2907 weeks
41-.04196 .06922 (41*2π)/2907 weeks
42-.03408 .04622 (42*2π)/2907 weeks
43-.09222 .04529 (43*2π)/2907 weeks
44-.00292 -.01037 (44*2π)/2907 weeks
45-.03524 -.05754 (45*2π)/2906 weeks
46.05023 -.0147 (46*2π)/2906 weeks
47-.00885 -.05659 (47*2π)/2906 weeks
48-.03125 -.05085 (48*2π)/2906 weeks
49-.0211 -.00142 (49*2π)/2906 weeks
50.02163 -.04231 (50*2π)/2906 weeks
51.0047 .05021 (51*2π)/2906 weeks
52.04897 -.00465 (52*2π)/2906 weeks
53.05689 -.03917 (53*2π)/2905 weeks
54.00607 -.08043 (54*2π)/2905 weeks
55-.02729 -.01678 (55*2π)/2905 weeks
56-.03611 .02802 (56*2π)/2905 weeks
57.01186 -.01128 (57*2π)/2905 weeks
58.03656 -.05066 (58*2π)/2905 weeks
59-.01046 -.03395 (59*2π)/2905 weeks
60.02871 -.00919 (60*2π)/2905 weeks
61-.0092 .04176 (61*2π)/2905 weeks
62.02923 -.01264 (62*2π)/2905 weeks
63.0289 -.02091 (63*2π)/2905 weeks
64-.00104 -.01085 (64*2π)/2905 weeks
65.0242 -.02534 (65*2π)/2904 weeks
66.00561 .03468 (66*2π)/2904 weeks
67.0112 .02955 (67*2π)/2904 weeks
68-.00314 .00315 (68*2π)/2904 weeks
69.00917 .0209 (69*2π)/2904 weeks
70.01438 -.01407 (70*2π)/2904 weeks
71-.04318 -.00402 (71*2π)/2904 weeks
72-.01025 .01592 (72*2π)/2904 weeks
73.02263 -.00673 (73*2π)/2904 weeks
74.00684 -.01657 (74*2π)/2904 weeks
75.01226 -.03401 (75*2π)/2904 weeks
76-.01126 -.02078 (76*2π)/2904 weeks
77.01003 .00299 (77*2π)/2904 weeks
78.05261 -.00866 (78*2π)/2904 weeks
79.0264 .00496 (79*2π)/2904 weeks
80.00572 .00058 (80*2π)/2904 weeks
81.00339 .01921 (81*2π)/2904 weeks
82-.0187 .01686 (82*2π)/2904 weeks
83.03297 .02057 (83*2π)/2903 weeks
84-.01973 .02443 (84*2π)/2903 weeks
85-.01012 .00401 (85*2π)/2903 weeks
86-.01723 .01873 (86*2π)/2903 weeks
87.02186 .00994 (87*2π)/2903 weeks
88.00908 .01588 (88*2π)/2903 weeks
89.0219 .01697 (89*2π)/2903 weeks
90-.01148 .01887 (90*2π)/2903 weeks
91.03008 -.0068 (91*2π)/2903 weeks
92.02139 -.00424 (92*2π)/2903 weeks
93-.00835 .00847 (93*2π)/2903 weeks
94-.00493 .01686 (94*2π)/2903 weeks
95-.00763 .01787 (95*2π)/2903 weeks
96.01717 .01789 (96*2π)/2903 weeks
97-.0169 -.01595 (97*2π)/2903 weeks
98-.00317 .00302 (98*2π)/2903 weeks
99.00494 .00176 (99*2π)/2903 weeks
100.03875 -.00809 (100*2π)/2903 weeks
101-.01519 -.02514 (101*2π)/2903 weeks
102.025 .02734 (102*2π)/2903 weeks
103.05551 -.00166 (103*2π)/2903 weeks
104.0078 .00016 (104*2π)/2903 weeks
105.00933 .00813 (105*2π)/2903 weeks
106.00851 .04061 (106*2π)/2903 weeks
107-.00248 .03783 (107*2π)/2903 weeks
108-.01366 .0194 (108*2π)/2903 weeks
109-.00106 -.00105 (109*2π)/2903 weeks
110-.01275 -.00024 (110*2π)/2903 weeks
111-.01219 -.00251 (111*2π)/2903 weeks
112.0121 .01744 (112*2π)/2903 weeks
113-.0506 -.0146 (113*2π)/2903 weeks
114-.0061 .00244 (114*2π)/2903 weeks
115.03133 -.01491 (115*2π)/2903 weeks
116-.00519 -.00394 (116*2π)/2903 weeks
117.00225 .009 (117*2π)/2902 weeks
118.01691 .00577 (118*2π)/2902 weeks
119.00277 .01717 (119*2π)/2902 weeks
120.01357 .00762 (120*2π)/2902 weeks
121-.0101 -.01979 (121*2π)/2902 weeks
122-.02666 -.00803 (122*2π)/2902 weeks
123-.01281 .00303 (123*2π)/2902 weeks
124-.01442 -.00259 (124*2π)/2902 weeks
125-.01879 -.01318 (125*2π)/2902 weeks
126-.04367 .00087 (126*2π)/2902 weeks
127-.02866 -.00603 (127*2π)/2902 weeks
128.01258 -.02134 (128*2π)/2902 weeks
129-.00086 -.01657 (129*2π)/2902 weeks
130-.00803 -.00347 (130*2π)/2902 weeks
131.03682 -.00044 (131*2π)/2902 weeks
132.01302 .00313 (132*2π)/2902 weeks
133.0391 -.01261 (133*2π)/2902 weeks
134.00872 -.01285 (134*2π)/2902 weeks
135.00353 .01459 (135*2π)/2902 weeks
136.00656 .01783 (136*2π)/2902 weeks
137.01204 .03321 (137*2π)/2902 weeks
138.01676 .02578 (138*2π)/2902 weeks
139.0342 -.02128 (139*2π)/2902 weeks
140.02829 -.01842 (140*2π)/2902 weeks
141-.03619 .01814 (141*2π)/2902 weeks
142.00034 .02812 (142*2π)/2902 weeks
143.01419 .02236 (143*2π)/2902 weeks
144-.02556 .00171 (144*2π)/2902 weeks
145-.02591   (145*2π)/2902 weeks
146-.02556 -.00171 (146*2π)/2902 weeks
147.01419 -.02236 (147*2π)/2902 weeks
148.00034 -.02812 (148*2π)/2902 weeks
149-.03619 -.01814 (149*2π)/2902 weeks
150.02829 .01842 (150*2π)/2902 weeks
151.0342 .02128 (151*2π)/2902 weeks
152.01676 -.02578 (152*2π)/2902 weeks
153.01204 -.03321 (153*2π)/2902 weeks
154.00656 -.01783 (154*2π)/2902 weeks
155.00353 -.01459 (155*2π)/2902 weeks
156.00872 .01285 (156*2π)/2902 weeks
157.0391 .01261 (157*2π)/2902 weeks
158.01302 -.00313 (158*2π)/2902 weeks
159.03682 .00044 (159*2π)/2902 weeks
160-.00803 .00347 (160*2π)/2902 weeks
161-.00086 .01657 (161*2π)/2902 weeks
162.01258 .02134 (162*2π)/2902 weeks
163-.02866 .00603 (163*2π)/2902 weeks
164-.04367 -.00087 (164*2π)/2902 weeks
165-.01879 .01318 (165*2π)/2902 weeks
166-.01442 .00259 (166*2π)/2902 weeks
167-.01281 -.00303 (167*2π)/2902 weeks
168-.02666 .00803 (168*2π)/2902 weeks
169-.0101 .01979 (169*2π)/2902 weeks
170.01357 -.00762 (170*2π)/2902 weeks
171.00277 -.01717 (171*2π)/2902 weeks
172.01691 -.00577 (172*2π)/2902 weeks
173.00225 -.009 (173*2π)/2902 weeks
174-.00519 .00394 (174*2π)/2902 weeks
175.03133 .01491 (175*2π)/2902 weeks
176-.0061 -.00244 (176*2π)/2902 weeks
177-.0506 .0146 (177*2π)/2902 weeks
178.0121 -.01744 (178*2π)/2902 weeks
179-.01219 .00251 (179*2π)/2902 weeks
180-.01275 .00024 (180*2π)/2902 weeks
181-.00106 .00105 (181*2π)/2902 weeks
182-.01366 -.0194 (182*2π)/2902 weeks
183-.00248 -.03783 (183*2π)/2902 weeks
184.00851 -.04061 (184*2π)/2902 weeks
185.00933 -.00813 (185*2π)/2902 weeks
186.0078 -.00016 (186*2π)/2902 weeks
187.05551 .00166 (187*2π)/2902 weeks
188.025 -.02734 (188*2π)/2902 weeks
189-.01519 .02514 (189*2π)/2902 weeks
190.03875 .00809 (190*2π)/2902 weeks
191.00494 -.00176 (191*2π)/2902 weeks
192-.00317 -.00302 (192*2π)/2902 weeks
193-.0169 .01595 (193*2π)/2902 weeks
194.01717 -.01789 (194*2π)/2901 weeks
195-.00763 -.01787 (195*2π)/2901 weeks
196-.00493 -.01686 (196*2π)/2901 weeks
197-.00835 -.00847 (197*2π)/2901 weeks
198.02139 .00424 (198*2π)/2901 weeks
199.03008 .0068 (199*2π)/2901 weeks
200-.01148 -.01887 (200*2π)/2901 weeks
201.0219 -.01697 (201*2π)/2901 weeks
202.00908 -.01588 (202*2π)/2901 weeks
203.02186 -.00994 (203*2π)/2901 weeks
204-.01723 -.01873 (204*2π)/2901 weeks
205-.01012 -.00401 (205*2π)/2901 weeks
206-.01973 -.02443 (206*2π)/2901 weeks
207.03297 -.02057 (207*2π)/2901 weeks
208-.0187 -.01686 (208*2π)/2901 weeks
209.00339 -.01921 (209*2π)/2901 weeks
210.00572 -.00058 (210*2π)/2901 weeks
211.0264 -.00496 (211*2π)/2901 weeks
212.05261 .00866 (212*2π)/2901 weeks
213.01003 -.00299 (213*2π)/2901 weeks
214-.01126 .02078 (214*2π)/2901 weeks
215.01226 .03401 (215*2π)/2901 weeks
216.00684 .01657 (216*2π)/2901 weeks
217.02263 .00673 (217*2π)/2901 weeks
218-.01025 -.01592 (218*2π)/2901 weeks
219-.04318 .00402 (219*2π)/2901 weeks
220.01438 .01407 (220*2π)/2901 weeks
221.00917 -.0209 (221*2π)/2901 weeks
222-.00314 -.00315 (222*2π)/2901 weeks
223.0112 -.02955 (223*2π)/2901 weeks
224.00561 -.03468 (224*2π)/2901 weeks
225.0242 .02534 (225*2π)/2901 weeks
226-.00104 .01085 (226*2π)/2901 weeks
227.0289 .02091 (227*2π)/2901 weeks
228.02923 .01264 (228*2π)/2901 weeks
229-.0092 -.04176 (229*2π)/2901 weeks
230.02871 .00919 (230*2π)/2901 weeks
231-.01046 .03395 (231*2π)/2901 weeks
232.03656 .05066 (232*2π)/2901 weeks
233.01186 .01128 (233*2π)/2901 weeks
234-.03611 -.02802 (234*2π)/2901 weeks
235-.02729 .01678 (235*2π)/2901 weeks
236.00607 .08043 (236*2π)/2901 weeks
237.05689 .03917 (237*2π)/2901 weeks
238.04897 .00465 (238*2π)/2901 weeks
239.0047 -.05021 (239*2π)/2901 weeks
240.02163 .04231 (240*2π)/2901 weeks
241-.0211 .00142 (241*2π)/2901 weeks
242-.03125 .05085 (242*2π)/2901 weeks
243-.00885 .05659 (243*2π)/2901 weeks
244.05023 .0147 (244*2π)/2901 weeks
245-.03524 .05754 (245*2π)/2901 weeks
246-.00292 .01037 (246*2π)/2901 weeks
247-.09222 -.04529 (247*2π)/2901 weeks
248-.03408 -.04622 (248*2π)/2901 weeks
249-.04196 -.06922 (249*2π)/2901 weeks
250.02726 -.05725 (250*2π)/2901 weeks
251-.0245 -.02922 (251*2π)/2901 weeks
252.04146 -.04771 (252*2π)/2901 weeks
253-.02754 -.07988 (253*2π)/2901 weeks
254.03306 -.06838 (254*2π)/2901 weeks
255.08209 -.08624 (255*2π)/2901 weeks
256-.00021 -.04934 (256*2π)/2901 weeks
257.03285 -.026 (257*2π)/2901 weeks
258.04549 .01212 (258*2π)/2901 weeks
259-.01683 .01204 (259*2π)/2901 weeks
260.01839 -.10539 (260*2π)/2901 weeks
261.02716 .04546 (261*2π)/2901 weeks
262.00495 -.04135 (262*2π)/2901 weeks
263.03863 .01622 (263*2π)/2901 weeks
264.12981 .14013 (264*2π)/2901 weeks
265-.06045 -.11127 (265*2π)/2901 weeks
266-.0863 .04994 (266*2π)/2901 weeks
267.00193 .01903 (267*2π)/2901 weeks
268.03273 -.12397 (268*2π)/2901 weeks
269.05375 -.0522 (269*2π)/2901 weeks
270.01891 -.05848 (270*2π)/2901 weeks
271.04058 -.13733 (271*2π)/2901 weeks
272.09539 -.17683 (272*2π)/2901 weeks
273.02294 -.01606 (273*2π)/2901 weeks
274.03076 -.02208 (274*2π)/2901 weeks
275.19981 .04754 (275*2π)/2901 weeks
276.35041 .12289 (276*2π)/2901 weeks
277.06214 -.13343 (277*2π)/2901 weeks
278-.11375 -.19737 (278*2π)/2901 weeks
279-.16446 -.02526 (279*2π)/2901 weeks
280.18474 -.19241 (280*2π)/2901 weeks
281.34813 -.11451 (281*2π)/2901 weeks
282-.10245 -.09127 (282*2π)/2901 weeks
283.58923 .30769 (283*2π)/2901 weeks
284-.1161 .03586 (284*2π)/2901 weeks
285-.36279 .44046 (285*2π)/2901 weeks
286.28627 .19018 (286*2π)/2901 weeks
287.63303 .62312 (287*2π)/2901 weeks
288.61409 -.37052 (288*2π)/2901 weeks

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