Back to list of Stocks    See Also: Seasonal Analysis of VEMPXGenetic Algorithms Stock Portfolio Generator, and Best Months to Buy/Sell Stocks

Fourier Analysis of VEMPX (Vanguard Extended Market Inde)


VEMPX (Vanguard Extended Market Inde) appears to have interesting cyclic behaviour every 33 weeks (4.7795*sine), 30 weeks (3.3942*sine), and 36 weeks (3.3526*sine).

VEMPX (Vanguard Extended Market Inde) has an average price of 138.48 (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 12/13/2010 to 10/16/2017 for VEMPX (Vanguard Extended Market Inde), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0138.4774   0 
1-5.04083 -34.59935 (1*2π)/358358 weeks
210.99046 -15.49469 (2*2π)/358179 weeks
32.94342 -12.8438 (3*2π)/358119 weeks
4-2.25812 -10.0461 (4*2π)/35890 weeks
5.51128 -3.21982 (5*2π)/35872 weeks
61.70663 -4.67748 (6*2π)/35860 weeks
7-1.72216 -3.48898 (7*2π)/35851 weeks
8-1.80063 -3.09225 (8*2π)/35845 weeks
9-.93103 -3.61392 (9*2π)/35840 weeks
10-.13211 -3.35258 (10*2π)/35836 weeks
11.63562 -4.77951 (11*2π)/35833 weeks
12-.24108 -3.39425 (12*2π)/35830 weeks
13-.44806 -1.97015 (13*2π)/35828 weeks
14-.41217 -1.88715 (14*2π)/35826 weeks
15.06388 -3.23988 (15*2π)/35824 weeks
16-.35651 -1.29174 (16*2π)/35822 weeks
17.58632 -.5617 (17*2π)/35821 weeks
18.1617 -1.86662 (18*2π)/35820 weeks
19-.37414 -3.04137 (19*2π)/35819 weeks
20-1.41996 -1.51966 (20*2π)/35818 weeks
21.17995 -1.47412 (21*2π)/35817 weeks
22.28679 -2.15062 (22*2π)/35816 weeks
23.2691 -1.96613 (23*2π)/35816 weeks
24.22845 -1.26221 (24*2π)/35815 weeks
25-.28537 -1.4453 (25*2π)/35814 weeks
26.12269 -1.19188 (26*2π)/35814 weeks
27-.81602 -1.49309 (27*2π)/35813 weeks
28-.84794 -.74703 (28*2π)/35813 weeks
29-.47306 -1.52059 (29*2π)/35812 weeks
30-.28421 -.99676 (30*2π)/35812 weeks
31.07462 -2.13896 (31*2π)/35812 weeks
32-.45861 -.82701 (32*2π)/35811 weeks
33-.47602 -1.71247 (33*2π)/35811 weeks
34-.25218 -1.49891 (34*2π)/35811 weeks
35-.36505 -1.34172 (35*2π)/35810 weeks
36-.5847 -1.07168 (36*2π)/35810 weeks
37.16189 -.2542 (37*2π)/35810 weeks
38-.30997 -.96418 (38*2π)/3589 weeks
39.07676 -.82966 (39*2π)/3589 weeks
40-.29574 -.82586 (40*2π)/3589 weeks
41-.66908 -.42769 (41*2π)/3589 weeks
42-.60458 -1.12792 (42*2π)/3589 weeks
43-.65598 -.19153 (43*2π)/3588 weeks
44-.49104 -1.18689 (44*2π)/3588 weeks
45-.12563 -.78334 (45*2π)/3588 weeks
46-.01579 -.93672 (46*2π)/3588 weeks
47-.33457 -1.04985 (47*2π)/3588 weeks
48-.16754 -.27598 (48*2π)/3587 weeks
49.05872 -.34622 (49*2π)/3587 weeks
50-.42022 -.03792 (50*2π)/3587 weeks
51-.30972 -.42178 (51*2π)/3587 weeks
52-.70089 -.38779 (52*2π)/3587 weeks
53-.3953 -.63847 (53*2π)/3587 weeks
54-.24929 -.88608 (54*2π)/3587 weeks
55-.15818 -.80589 (55*2π)/3587 weeks
56-.32533 -.64478 (56*2π)/3586 weeks
57-.6085 -.40082 (57*2π)/3586 weeks
58-.10263 -.34142 (58*2π)/3586 weeks
59-.18292 -.71492 (59*2π)/3586 weeks
60-.36919 -.79587 (60*2π)/3586 weeks
61-.62436 -.71245 (61*2π)/3586 weeks
62-.62216 -.67501 (62*2π)/3586 weeks
63-.3527 -.41249 (63*2π)/3586 weeks
64-.278 -.48414 (64*2π)/3586 weeks
65-.38239 -.69319 (65*2π)/3586 weeks
66-.5806 -.33416 (66*2π)/3585 weeks
67-.28858 -.27137 (67*2π)/3585 weeks
68-.40774 -.35399 (68*2π)/3585 weeks
69-.4306 -.83272 (69*2π)/3585 weeks
70-.34894 -.24046 (70*2π)/3585 weeks
71-.04778 -.30039 (71*2π)/3585 weeks
72-.38568 -.59216 (72*2π)/3585 weeks
73-.47013 -.42936 (73*2π)/3585 weeks
74-.29172 -.50108 (74*2π)/3585 weeks
75-.10452 -.42659 (75*2π)/3585 weeks
76-.42646 -.58132 (76*2π)/3585 weeks
77-.46694 -.25766 (77*2π)/3585 weeks
78-.16776 .04218 (78*2π)/3585 weeks
79-.20333 -.44759 (79*2π)/3585 weeks
80-.19232 -.25023 (80*2π)/3584 weeks
81-.55631 -.14609 (81*2π)/3584 weeks
82-.09297 -.17252 (82*2π)/3584 weeks
83-.24718 -.49821 (83*2π)/3584 weeks
84-.30347 -.27297 (84*2π)/3584 weeks
85-.45714 -.41909 (85*2π)/3584 weeks
86-.28872 -.05273 (86*2π)/3584 weeks
87.00737 -.4003 (87*2π)/3584 weeks
88-.51049 -.6713 (88*2π)/3584 weeks
89-.27493 -.29886 (89*2π)/3584 weeks
90-.12943 -.58318 (90*2π)/3584 weeks
91-.21827 -.62088 (91*2π)/3584 weeks
92-.38098 -.125 (92*2π)/3584 weeks
93-.33252 .04363 (93*2π)/3584 weeks
94.06966 -.1132 (94*2π)/3584 weeks
95-.2784 -.35927 (95*2π)/3584 weeks
96-.39787 -.18823 (96*2π)/3584 weeks
97-.2689 -.42411 (97*2π)/3584 weeks
98-.34887 -.46685 (98*2π)/3584 weeks
99-.28284 -.24968 (99*2π)/3584 weeks
100-.2541 .00034 (100*2π)/3584 weeks
101-.11598 -.14705 (101*2π)/3584 weeks
102-.14399 -.32239 (102*2π)/3584 weeks
103-.40658 -.12863 (103*2π)/3583 weeks
104-.42466 -.24844 (104*2π)/3583 weeks
105-.37672 -.29136 (105*2π)/3583 weeks
106-.47217 -.26148 (106*2π)/3583 weeks
107-.29777 .01519 (107*2π)/3583 weeks
108-.37953 -.15443 (108*2π)/3583 weeks
109-.33168 -.24675 (109*2π)/3583 weeks
110-.29417 -.27577 (110*2π)/3583 weeks
111-.22868 -.18797 (111*2π)/3583 weeks
112-.47461 -.27664 (112*2π)/3583 weeks
113-.34737 -.08286 (113*2π)/3583 weeks
114-.20948 -.18181 (114*2π)/3583 weeks
115-.34569 -.25236 (115*2π)/3583 weeks
116-.31511 -.08221 (116*2π)/3583 weeks
117-.34956 -.03902 (117*2π)/3583 weeks
118-.23566 -.11395 (118*2π)/3583 weeks
119-.42018 -.22971 (119*2π)/3583 weeks
120-.16714 -.0424 (120*2π)/3583 weeks
121-.17403 -.03808 (121*2π)/3583 weeks
122-.3547 -.21451 (122*2π)/3583 weeks
123-.22498 -.08758 (123*2π)/3583 weeks
124-.35213 -.25466 (124*2π)/3583 weeks
125-.35699 -.23048 (125*2π)/3583 weeks
126-.2173 -.27409 (126*2π)/3583 weeks
127-.16634 -.32752 (127*2π)/3583 weeks
128-.23478 .058 (128*2π)/3583 weeks
129-.3774 -.03275 (129*2π)/3583 weeks
130-.23832 .05862 (130*2π)/3583 weeks
131-.46204 .00213 (131*2π)/3583 weeks
132-.39626 -.30683 (132*2π)/3583 weeks
133-.38377 -.27421 (133*2π)/3583 weeks
134-.23468 -.07263 (134*2π)/3583 weeks
135-.26659 -.27046 (135*2π)/3583 weeks
136-.23014 -.11082 (136*2π)/3583 weeks
137-.18186 -.18995 (137*2π)/3583 weeks
138-.3713 -.14095 (138*2π)/3583 weeks
139-.27891 .04975 (139*2π)/3583 weeks
140-.40551 -.15267 (140*2π)/3583 weeks
141-.40364 -.09446 (141*2π)/3583 weeks
142-.37088 -.04543 (142*2π)/3583 weeks
143-.32389 -.1155 (143*2π)/3583 weeks
144-.3995 -.05912 (144*2π)/3582 weeks
145-.33853 -.19051 (145*2π)/3582 weeks
146-.3683 -.15567 (146*2π)/3582 weeks
147-.25911 -.28972 (147*2π)/3582 weeks
148-.26027 -.16947 (148*2π)/3582 weeks
149-.18428 .03662 (149*2π)/3582 weeks
150-.18894 -.28848 (150*2π)/3582 weeks
151-.48781 -.13167 (151*2π)/3582 weeks
152-.425 -.01771 (152*2π)/3582 weeks
153-.44026 -.0339 (153*2π)/3582 weeks
154-.35915 .01098 (154*2π)/3582 weeks
155-.5218 .00383 (155*2π)/3582 weeks
156-.04184 -.24915 (156*2π)/3582 weeks
157-.09653 -.14165 (157*2π)/3582 weeks
158-.23172 -.00573 (158*2π)/3582 weeks
159-.36416 -.08294 (159*2π)/3582 weeks
160-.47067 -.07575 (160*2π)/3582 weeks
161-.46246 .17448 (161*2π)/3582 weeks
162-.31888 -.19206 (162*2π)/3582 weeks
163-.37321 .07135 (163*2π)/3582 weeks
164-.31691 -.15337 (164*2π)/3582 weeks
165-.38083 .07587 (165*2π)/3582 weeks
166-.12406 -.1978 (166*2π)/3582 weeks
167-.2429 -.00102 (167*2π)/3582 weeks
168-.29349 -.01056 (168*2π)/3582 weeks
169-.37577 .15386 (169*2π)/3582 weeks
170-.33068 .02435 (170*2π)/3582 weeks
171-.04725 -.01829 (171*2π)/3582 weeks
172-.29114 -.0915 (172*2π)/3582 weeks
173-.48217 .02822 (173*2π)/3582 weeks
174-.2149 -.01332 (174*2π)/3582 weeks
175-.34324 -.12156 (175*2π)/3582 weeks
176-.45285 .05868 (176*2π)/3582 weeks
177-.11891 .25457 (177*2π)/3582 weeks
178-.25968 .08864 (178*2π)/3582 weeks
179-.3261   (179*2π)/3582 weeks
180-.25968 -.08864 (180*2π)/3582 weeks
181-.11891 -.25457 (181*2π)/3582 weeks
182-.45285 -.05868 (182*2π)/3582 weeks
183-.34324 .12156 (183*2π)/3582 weeks
184-.2149 .01332 (184*2π)/3582 weeks
185-.48217 -.02822 (185*2π)/3582 weeks
186-.29114 .0915 (186*2π)/3582 weeks
187-.04725 .01829 (187*2π)/3582 weeks
188-.33068 -.02435 (188*2π)/3582 weeks
189-.37577 -.15386 (189*2π)/3582 weeks
190-.29349 .01056 (190*2π)/3582 weeks
191-.2429 .00102 (191*2π)/3582 weeks
192-.12406 .1978 (192*2π)/3582 weeks
193-.38083 -.07587 (193*2π)/3582 weeks
194-.31691 .15337 (194*2π)/3582 weeks
195-.37321 -.07135 (195*2π)/3582 weeks
196-.31888 .19206 (196*2π)/3582 weeks
197-.46246 -.17448 (197*2π)/3582 weeks
198-.47067 .07575 (198*2π)/3582 weeks
199-.36416 .08294 (199*2π)/3582 weeks
200-.23172 .00573 (200*2π)/3582 weeks
201-.09653 .14165 (201*2π)/3582 weeks
202-.04184 .24915 (202*2π)/3582 weeks
203-.5218 -.00383 (203*2π)/3582 weeks
204-.35915 -.01098 (204*2π)/3582 weeks
205-.44026 .0339 (205*2π)/3582 weeks
206-.425 .01771 (206*2π)/3582 weeks
207-.48781 .13167 (207*2π)/3582 weeks
208-.18894 .28848 (208*2π)/3582 weeks
209-.18428 -.03662 (209*2π)/3582 weeks
210-.26027 .16947 (210*2π)/3582 weeks
211-.25911 .28972 (211*2π)/3582 weeks
212-.3683 .15567 (212*2π)/3582 weeks
213-.33853 .19051 (213*2π)/3582 weeks
214-.3995 .05912 (214*2π)/3582 weeks
215-.32389 .1155 (215*2π)/3582 weeks
216-.37088 .04543 (216*2π)/3582 weeks
217-.40364 .09446 (217*2π)/3582 weeks
218-.40551 .15267 (218*2π)/3582 weeks
219-.27891 -.04975 (219*2π)/3582 weeks
220-.3713 .14095 (220*2π)/3582 weeks
221-.18186 .18995 (221*2π)/3582 weeks
222-.23014 .11082 (222*2π)/3582 weeks
223-.26659 .27046 (223*2π)/3582 weeks
224-.23468 .07263 (224*2π)/3582 weeks
225-.38377 .27421 (225*2π)/3582 weeks
226-.39626 .30683 (226*2π)/3582 weeks
227-.46204 -.00213 (227*2π)/3582 weeks
228-.23832 -.05862 (228*2π)/3582 weeks
229-.3774 .03275 (229*2π)/3582 weeks
230-.23478 -.058 (230*2π)/3582 weeks
231-.16634 .32752 (231*2π)/3582 weeks
232-.2173 .27409 (232*2π)/3582 weeks
233-.35699 .23048 (233*2π)/3582 weeks
234-.35213 .25466 (234*2π)/3582 weeks
235-.22498 .08758 (235*2π)/3582 weeks
236-.3547 .21451 (236*2π)/3582 weeks
237-.17403 .03808 (237*2π)/3582 weeks
238-.16714 .0424 (238*2π)/3582 weeks
239-.42018 .22971 (239*2π)/3581 weeks
240-.23566 .11395 (240*2π)/3581 weeks
241-.34956 .03902 (241*2π)/3581 weeks
242-.31511 .08221 (242*2π)/3581 weeks
243-.34569 .25236 (243*2π)/3581 weeks
244-.20948 .18181 (244*2π)/3581 weeks
245-.34737 .08286 (245*2π)/3581 weeks
246-.47461 .27664 (246*2π)/3581 weeks
247-.22868 .18797 (247*2π)/3581 weeks
248-.29417 .27577 (248*2π)/3581 weeks
249-.33168 .24675 (249*2π)/3581 weeks
250-.37953 .15443 (250*2π)/3581 weeks
251-.29777 -.01519 (251*2π)/3581 weeks
252-.47217 .26148 (252*2π)/3581 weeks
253-.37672 .29136 (253*2π)/3581 weeks
254-.42466 .24844 (254*2π)/3581 weeks
255-.40658 .12863 (255*2π)/3581 weeks
256-.14399 .32239 (256*2π)/3581 weeks
257-.11598 .14705 (257*2π)/3581 weeks
258-.2541 -.00034 (258*2π)/3581 weeks
259-.28284 .24968 (259*2π)/3581 weeks
260-.34887 .46685 (260*2π)/3581 weeks
261-.2689 .42411 (261*2π)/3581 weeks
262-.39787 .18823 (262*2π)/3581 weeks
263-.2784 .35927 (263*2π)/3581 weeks
264.06966 .1132 (264*2π)/3581 weeks
265-.33252 -.04363 (265*2π)/3581 weeks
266-.38098 .125 (266*2π)/3581 weeks
267-.21827 .62088 (267*2π)/3581 weeks
268-.12943 .58318 (268*2π)/3581 weeks
269-.27493 .29886 (269*2π)/3581 weeks
270-.51049 .6713 (270*2π)/3581 weeks
271.00737 .4003 (271*2π)/3581 weeks
272-.28872 .05273 (272*2π)/3581 weeks
273-.45714 .41909 (273*2π)/3581 weeks
274-.30347 .27297 (274*2π)/3581 weeks
275-.24718 .49821 (275*2π)/3581 weeks
276-.09297 .17252 (276*2π)/3581 weeks
277-.55631 .14609 (277*2π)/3581 weeks
278-.19232 .25023 (278*2π)/3581 weeks
279-.20333 .44759 (279*2π)/3581 weeks
280-.16776 -.04218 (280*2π)/3581 weeks
281-.46694 .25766 (281*2π)/3581 weeks
282-.42646 .58132 (282*2π)/3581 weeks
283-.10452 .42659 (283*2π)/3581 weeks
284-.29172 .50108 (284*2π)/3581 weeks
285-.47013 .42936 (285*2π)/3581 weeks
286-.38568 .59216 (286*2π)/3581 weeks
287-.04778 .30039 (287*2π)/3581 weeks
288-.34894 .24046 (288*2π)/3581 weeks
289-.4306 .83272 (289*2π)/3581 weeks
290-.40774 .35399 (290*2π)/3581 weeks
291-.28858 .27137 (291*2π)/3581 weeks
292-.5806 .33416 (292*2π)/3581 weeks
293-.38239 .69319 (293*2π)/3581 weeks
294-.278 .48414 (294*2π)/3581 weeks
295-.3527 .41249 (295*2π)/3581 weeks
296-.62216 .67501 (296*2π)/3581 weeks
297-.62436 .71245 (297*2π)/3581 weeks
298-.36919 .79587 (298*2π)/3581 weeks
299-.18292 .71492 (299*2π)/3581 weeks
300-.10263 .34142 (300*2π)/3581 weeks
301-.6085 .40082 (301*2π)/3581 weeks
302-.32533 .64478 (302*2π)/3581 weeks
303-.15818 .80589 (303*2π)/3581 weeks
304-.24929 .88608 (304*2π)/3581 weeks
305-.3953 .63847 (305*2π)/3581 weeks
306-.70089 .38779 (306*2π)/3581 weeks
307-.30972 .42178 (307*2π)/3581 weeks
308-.42022 .03792 (308*2π)/3581 weeks
309.05872 .34622 (309*2π)/3581 weeks
310-.16754 .27598 (310*2π)/3581 weeks
311-.33457 1.04985 (311*2π)/3581 weeks
312-.01579 .93672 (312*2π)/3581 weeks
313-.12563 .78334 (313*2π)/3581 weeks
314-.49104 1.18689 (314*2π)/3581 weeks
315-.65598 .19153 (315*2π)/3581 weeks
316-.60458 1.12792 (316*2π)/3581 weeks
317-.66908 .42769 (317*2π)/3581 weeks
318-.29574 .82586 (318*2π)/3581 weeks
319.07676 .82966 (319*2π)/3581 weeks
320-.30997 .96418 (320*2π)/3581 weeks
321.16189 .2542 (321*2π)/3581 weeks
322-.5847 1.07168 (322*2π)/3581 weeks
323-.36505 1.34172 (323*2π)/3581 weeks
324-.25218 1.49891 (324*2π)/3581 weeks
325-.47602 1.71247 (325*2π)/3581 weeks
326-.45861 .82701 (326*2π)/3581 weeks
327.07462 2.13896 (327*2π)/3581 weeks
328-.28421 .99676 (328*2π)/3581 weeks
329-.47306 1.52059 (329*2π)/3581 weeks
330-.84794 .74703 (330*2π)/3581 weeks
331-.81602 1.49309 (331*2π)/3581 weeks
332.12269 1.19188 (332*2π)/3581 weeks
333-.28537 1.4453 (333*2π)/3581 weeks
334.22845 1.26221 (334*2π)/3581 weeks
335.2691 1.96613 (335*2π)/3581 weeks
336.28679 2.15062 (336*2π)/3581 weeks
337.17995 1.47412 (337*2π)/3581 weeks
338-1.41996 1.51966 (338*2π)/3581 weeks
339-.37414 3.04137 (339*2π)/3581 weeks
340.1617 1.86662 (340*2π)/3581 weeks
341.58632 .5617 (341*2π)/3581 weeks
342-.35651 1.29174 (342*2π)/3581 weeks
343.06388 3.23988 (343*2π)/3581 weeks
344-.41217 1.88715 (344*2π)/3581 weeks
345-.44806 1.97015 (345*2π)/3581 weeks
346-.24108 3.39425 (346*2π)/3581 weeks
347.63562 4.77951 (347*2π)/3581 weeks
348-.13211 3.35258 (348*2π)/3581 weeks
349-.93103 3.61392 (349*2π)/3581 weeks
350-1.80063 3.09225 (350*2π)/3581 weeks
351-1.72216 3.48898 (351*2π)/3581 weeks
3521.70663 4.67748 (352*2π)/3581 weeks
353.51128 3.21982 (353*2π)/3581 weeks
354-2.25812 10.0461 (354*2π)/3581 weeks
3552.94342 12.8438 (355*2π)/3581 weeks
35610.99046 15.49469 (356*2π)/3581 weeks



Back to list of Stocks