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Fourier Analysis of VDVIX (Vanguard Developed Markets Inde)


VDVIX (Vanguard Developed Markets Inde) appears to have interesting cyclic behaviour every 12 weeks (.0668*sine), 11 weeks (.0578*sine), and 12 weeks (.0493*sine).

VDVIX (Vanguard Developed Markets Inde) has an average price of 9.17 (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 12/20/2013 to 1/17/2017 for VDVIX (Vanguard Developed Markets Inde), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
09.17492   0 
1.02709 .40649 (1*2π)/162162 weeks
2.20911 .01274 (2*2π)/16281 weeks
3-.27151 .06467 (3*2π)/16254 weeks
4-.01184 -.10452 (4*2π)/16241 weeks
5.0857 .05089 (5*2π)/16232 weeks
6-.00115 -.0455 (6*2π)/16227 weeks
7.01658 .12915 (7*2π)/16223 weeks
8.11048 -.00346 (8*2π)/16220 weeks
9-.02753 -.08009 (9*2π)/16218 weeks
10.01883 .02414 (10*2π)/16216 weeks
11-.01175 -.02078 (11*2π)/16215 weeks
12-.00774 -.01382 (12*2π)/16214 weeks
13.04464 -.04926 (13*2π)/16212 weeks
14.02615 .06677 (14*2π)/16212 weeks
15-.02785 -.05783 (15*2π)/16211 weeks
16-.02394 -.00895 (16*2π)/16210 weeks
17.03749 .01292 (17*2π)/16210 weeks
18.00496 .02211 (18*2π)/1629 weeks
19.00335 .03394 (19*2π)/1629 weeks
20-.00348 -.00945 (20*2π)/1628 weeks
21.0167 .00313 (21*2π)/1628 weeks
22-.00279 .01805 (22*2π)/1627 weeks
23-.02776 .02281 (23*2π)/1627 weeks
24.0048 .00105 (24*2π)/1627 weeks
25.00475 -.01064 (25*2π)/1626 weeks
26-.03662 -.02439 (26*2π)/1626 weeks
27-.01755 .01809 (27*2π)/1626 weeks
28-.00559 -.00346 (28*2π)/1626 weeks
29.02956 -.02986 (29*2π)/1626 weeks
30-.04375 -.03565 (30*2π)/1625 weeks
31-.01157 .0096 (31*2π)/1625 weeks
32.0218 -.03582 (32*2π)/1625 weeks
33-.01499 .00063 (33*2π)/1625 weeks
34.00695 .01333 (34*2π)/1625 weeks
35-.01197 -.01682 (35*2π)/1625 weeks
36-.01021 .00567 (36*2π)/1625 weeks
37.02644 .0213 (37*2π)/1624 weeks
38-.0182 .00819 (38*2π)/1624 weeks
39-.02431 -.0271 (39*2π)/1624 weeks
40.02231 .01268 (40*2π)/1624 weeks
41-.01423 -.02403 (41*2π)/1624 weeks
42-.01213 .00472 (42*2π)/1624 weeks
43.01623 .00849 (43*2π)/1624 weeks
44-.00656 .00096 (44*2π)/1624 weeks
45.00081 .0127 (45*2π)/1624 weeks
46.01686 .00715 (46*2π)/1624 weeks
47.01111 .00833 (47*2π)/1623 weeks
48.01037 .01308 (48*2π)/1623 weeks
49.00374 .00326 (49*2π)/1623 weeks
50-.00749 .00333 (50*2π)/1623 weeks
51-.02369 -.01229 (51*2π)/1623 weeks
52-.00037 .01357 (52*2π)/1623 weeks
53-.00162 .00457 (53*2π)/1623 weeks
54-.01453 .00513 (54*2π)/1623 weeks
55.01036 -.00526 (55*2π)/1623 weeks
56-.01289 .00448 (56*2π)/1623 weeks
57.01213 -.02156 (57*2π)/1623 weeks
58-.00961 .00874 (58*2π)/1623 weeks
59-.00004 .00959 (59*2π)/1623 weeks
60-.0057 .004 (60*2π)/1623 weeks
61-.00441 -.00386 (61*2π)/1623 weeks
62.00261 .00284 (62*2π)/1623 weeks
63-.00272 .01093 (63*2π)/1623 weeks
64-.00519 -.00967 (64*2π)/1623 weeks
65.00291 .00554 (65*2π)/1622 weeks
66-.00715 -.00257 (66*2π)/1622 weeks
67-.01412 -.00664 (67*2π)/1622 weeks
68.00064 .01379 (68*2π)/1622 weeks
69.00482 .00377 (69*2π)/1622 weeks
70.00629 .01322 (70*2π)/1622 weeks
71-.00518 -.01371 (71*2π)/1622 weeks
72.00341 .0083 (72*2π)/1622 weeks
73-.01214 -.0151 (73*2π)/1622 weeks
74-.00076 -.00616 (74*2π)/1622 weeks
75.01191 -.00115 (75*2π)/1622 weeks
76.01187 .00009 (76*2π)/1622 weeks
77-.01347 -.01834 (77*2π)/1622 weeks
78-.02027 .01658 (78*2π)/1622 weeks
79.00104 -.00444 (79*2π)/1622 weeks
80-.01453 .00674 (80*2π)/1622 weeks
81.00996   (81*2π)/1622 weeks
82-.01453 -.00674 (82*2π)/1622 weeks
83.00104 .00444 (83*2π)/1622 weeks
84-.02027 -.01658 (84*2π)/1622 weeks
85-.01347 .01834 (85*2π)/1622 weeks
86.01187 -.00009 (86*2π)/1622 weeks
87.01191 .00115 (87*2π)/1622 weeks
88-.00076 .00616 (88*2π)/1622 weeks
89-.01214 .0151 (89*2π)/1622 weeks
90.00341 -.0083 (90*2π)/1622 weeks
91-.00518 .01371 (91*2π)/1622 weeks
92.00629 -.01322 (92*2π)/1622 weeks
93.00482 -.00377 (93*2π)/1622 weeks
94.00064 -.01379 (94*2π)/1622 weeks
95-.01412 .00664 (95*2π)/1622 weeks
96-.00715 .00257 (96*2π)/1622 weeks
97.00291 -.00554 (97*2π)/1622 weeks
98-.00519 .00967 (98*2π)/1622 weeks
99-.00272 -.01093 (99*2π)/1622 weeks
100.00261 -.00284 (100*2π)/1622 weeks
101-.00441 .00386 (101*2π)/1622 weeks
102-.0057 -.004 (102*2π)/1622 weeks
103-.00004 -.00959 (103*2π)/1622 weeks
104-.00961 -.00874 (104*2π)/1622 weeks
105.01213 .02156 (105*2π)/1622 weeks
106-.01289 -.00448 (106*2π)/1622 weeks
107.01036 .00526 (107*2π)/1622 weeks
108-.01453 -.00513 (108*2π)/1622 weeks
109-.00162 -.00457 (109*2π)/1621 weeks
110-.00037 -.01357 (110*2π)/1621 weeks
111-.02369 .01229 (111*2π)/1621 weeks
112-.00749 -.00333 (112*2π)/1621 weeks
113.00374 -.00326 (113*2π)/1621 weeks
114.01037 -.01308 (114*2π)/1621 weeks
115.01111 -.00833 (115*2π)/1621 weeks
116.01686 -.00715 (116*2π)/1621 weeks
117.00081 -.0127 (117*2π)/1621 weeks
118-.00656 -.00096 (118*2π)/1621 weeks
119.01623 -.00849 (119*2π)/1621 weeks
120-.01213 -.00472 (120*2π)/1621 weeks
121-.01423 .02403 (121*2π)/1621 weeks
122.02231 -.01268 (122*2π)/1621 weeks
123-.02431 .0271 (123*2π)/1621 weeks
124-.0182 -.00819 (124*2π)/1621 weeks
125.02644 -.0213 (125*2π)/1621 weeks
126-.01021 -.00567 (126*2π)/1621 weeks
127-.01197 .01682 (127*2π)/1621 weeks
128.00695 -.01333 (128*2π)/1621 weeks
129-.01499 -.00063 (129*2π)/1621 weeks
130.0218 .03582 (130*2π)/1621 weeks
131-.01157 -.0096 (131*2π)/1621 weeks
132-.04375 .03565 (132*2π)/1621 weeks
133.02956 .02986 (133*2π)/1621 weeks
134-.00559 .00346 (134*2π)/1621 weeks
135-.01755 -.01809 (135*2π)/1621 weeks
136-.03662 .02439 (136*2π)/1621 weeks
137.00475 .01064 (137*2π)/1621 weeks
138.0048 -.00105 (138*2π)/1621 weeks
139-.02776 -.02281 (139*2π)/1621 weeks
140-.00279 -.01805 (140*2π)/1621 weeks
141.0167 -.00313 (141*2π)/1621 weeks
142-.00348 .00945 (142*2π)/1621 weeks
143.00335 -.03394 (143*2π)/1621 weeks
144.00496 -.02211 (144*2π)/1621 weeks
145.03749 -.01292 (145*2π)/1621 weeks
146-.02394 .00895 (146*2π)/1621 weeks
147-.02785 .05783 (147*2π)/1621 weeks
148.02615 -.06677 (148*2π)/1621 weeks
149.04464 .04926 (149*2π)/1621 weeks
150-.00774 .01382 (150*2π)/1621 weeks
151-.01175 .02078 (151*2π)/1621 weeks
152.01883 -.02414 (152*2π)/1621 weeks
153-.02753 .08009 (153*2π)/1621 weeks
154.11048 .00346 (154*2π)/1621 weeks
155.01658 -.12915 (155*2π)/1621 weeks
156-.00115 .0455 (156*2π)/1621 weeks
157.0857 -.05089 (157*2π)/1621 weeks
158-.01184 .10452 (158*2π)/1621 weeks
159-.27151 -.06467 (159*2π)/1621 weeks
160.20911 -.01274 (160*2π)/1621 weeks

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