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Fourier Analysis of VTWG (Vanguard Russell 2000 Growth ET)


VTWG (Vanguard Russell 2000 Growth ET) appears to have interesting cyclic behaviour every 18 weeks (2.1564*sine), 25 weeks (2.1438*sine), and 28 weeks (1.944*sine).

VTWG (Vanguard Russell 2000 Growth ET) has an average price of 83.68 (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 9/22/2010 to 1/17/2017 for VTWG (Vanguard Russell 2000 Growth ET), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
083.67849   0 
1-3.79668 -22.64516 (1*2π)/331331 weeks
21.93061 -4.26463 (2*2π)/331166 weeks
3.3217 -2.58026 (3*2π)/331110 weeks
43.55663 -4.40947 (4*2π)/33183 weeks
5-1.49119 -4.59261 (5*2π)/33166 weeks
6-2.22405 -2.85999 (6*2π)/33155 weeks
7-1.40043 -3.3169 (7*2π)/33147 weeks
8-.11854 -2.78605 (8*2π)/33141 weeks
9.15282 -2.13409 (9*2π)/33137 weeks
10.75401 -1.0271 (10*2π)/33133 weeks
11-.00648 -1.43766 (11*2π)/33130 weeks
12-.40892 -1.944 (12*2π)/33128 weeks
13.01093 -2.14377 (13*2π)/33125 weeks
14-1.04876 -.78331 (14*2π)/33124 weeks
15-.0816 -1.17094 (15*2π)/33122 weeks
16.61327 -1.70596 (16*2π)/33121 weeks
17.61544 -1.35544 (17*2π)/33119 weeks
18-.29419 -2.15644 (18*2π)/33118 weeks
19-1.13209 -.91163 (19*2π)/33117 weeks
20-.75132 -.84819 (20*2π)/33117 weeks
21-.38486 -1.18011 (21*2π)/33116 weeks
22.10953 -1.25657 (22*2π)/33115 weeks
23-.11362 -.79629 (23*2π)/33114 weeks
24.19679 -.87165 (24*2π)/33114 weeks
25-.51979 -.89621 (25*2π)/33113 weeks
26-.73685 -.11513 (26*2π)/33113 weeks
27-.41792 -.87258 (27*2π)/33112 weeks
28-.56835 -.65541 (28*2π)/33112 weeks
29.33878 -.53517 (29*2π)/33111 weeks
30-.54612 -.7978 (30*2π)/33111 weeks
31.0441 -.61715 (31*2π)/33111 weeks
32-.03136 -.47377 (32*2π)/33110 weeks
33-.19626 -.29744 (33*2π)/33110 weeks
34-.21706 .10337 (34*2π)/33110 weeks
35-.17294 -.54144 (35*2π)/3319 weeks
36-.23244 -.11006 (36*2π)/3319 weeks
37-.21313 -.433 (37*2π)/3319 weeks
38-.16037 -.8508 (38*2π)/3319 weeks
39-.02799 -.20644 (39*2π)/3318 weeks
40.24499 -.82431 (40*2π)/3318 weeks
41-.1384 -.1626 (41*2π)/3318 weeks
42-.03514 -.4814 (42*2π)/3318 weeks
43-.30877 -.72615 (43*2π)/3318 weeks
44-.59868 -.83618 (44*2π)/3318 weeks
45-.44845 -.61649 (45*2π)/3317 weeks
46.18986 -.62706 (46*2π)/3317 weeks
47-.1111 -.39477 (47*2π)/3317 weeks
48-.01264 -.09579 (48*2π)/3317 weeks
49-.27794 -.29843 (49*2π)/3317 weeks
50-.29712 -.44007 (50*2π)/3317 weeks
51-.19537 -.59847 (51*2π)/3316 weeks
52-.25009 -.4792 (52*2π)/3316 weeks
53-.54863 -.34654 (53*2π)/3316 weeks
54-.38689 -.10908 (54*2π)/3316 weeks
55-.30952 -.21751 (55*2π)/3316 weeks
56-.24085 -.1586 (56*2π)/3316 weeks
57-.14574 -.29839 (57*2π)/3316 weeks
58-.04941 -.25013 (58*2π)/3316 weeks
59-.03851 -.27243 (59*2π)/3316 weeks
60-.02416 -.40667 (60*2π)/3316 weeks
61-.28854 -.36913 (61*2π)/3315 weeks
62-.26449 -.22904 (62*2π)/3315 weeks
63-.20995 -.30795 (63*2π)/3315 weeks
64.08859 -.00067 (64*2π)/3315 weeks
65-.09585 -.29644 (65*2π)/3315 weeks
66-.20357 -.38739 (66*2π)/3315 weeks
67-.22622 -.21034 (67*2π)/3315 weeks
68-.0967 -.07523 (68*2π)/3315 weeks
69-.22584 -.10779 (69*2π)/3315 weeks
70-.10154 -.24397 (70*2π)/3315 weeks
71-.15383 -.38582 (71*2π)/3315 weeks
72-.27931 -.59006 (72*2π)/3315 weeks
73-.42435 -.18311 (73*2π)/3315 weeks
74-.21661 -.27796 (74*2π)/3314 weeks
75-.15358 -.04269 (75*2π)/3314 weeks
76-.04649 -.2501 (76*2π)/3314 weeks
77-.30106 -.33973 (77*2π)/3314 weeks
78-.22511 -.22342 (78*2π)/3314 weeks
79-.29147 -.42052 (79*2π)/3314 weeks
80-.46436 -.24534 (80*2π)/3314 weeks
81-.4499 -.00583 (81*2π)/3314 weeks
82-.08918 -.22581 (82*2π)/3314 weeks
83-.2035 -.44696 (83*2π)/3314 weeks
84-.18418 -.3666 (84*2π)/3314 weeks
85-.32838 -.04785 (85*2π)/3314 weeks
86-.38356 .03529 (86*2π)/3314 weeks
87-.24225 .15493 (87*2π)/3314 weeks
88-.11934 -.08617 (88*2π)/3314 weeks
89-.22449 -.28108 (89*2π)/3314 weeks
90-.19693 -.10516 (90*2π)/3314 weeks
91-.20754 .02933 (91*2π)/3314 weeks
92-.27473 .05648 (92*2π)/3314 weeks
93-.11202 -.09373 (93*2π)/3314 weeks
94-.12077 -.20061 (94*2π)/3314 weeks
95-.21245 -.3526 (95*2π)/3313 weeks
96-.13292 -.19709 (96*2π)/3313 weeks
97-.17123 -.13438 (97*2π)/3313 weeks
98-.1128 -.0561 (98*2π)/3313 weeks
99-.03193 -.28118 (99*2π)/3313 weeks
100-.1095 -.15423 (100*2π)/3313 weeks
101-.18936 -.11133 (101*2π)/3313 weeks
102-.19084 -.16084 (102*2π)/3313 weeks
103-.10763 -.1575 (103*2π)/3313 weeks
104-.21741 -.18935 (104*2π)/3313 weeks
105-.29566 -.1467 (105*2π)/3313 weeks
106-.20202 -.03729 (106*2π)/3313 weeks
107-.08539 -.13795 (107*2π)/3313 weeks
108-.13584 -.06962 (108*2π)/3313 weeks
109-.17304 -.18221 (109*2π)/3313 weeks
110-.34553 -.15656 (110*2π)/3313 weeks
111-.10919 -.02325 (111*2π)/3313 weeks
112-.21653 -.00944 (112*2π)/3313 weeks
113-.20472 -.1683 (113*2π)/3313 weeks
114-.27921 -.05816 (114*2π)/3313 weeks
115-.15376 -.14802 (115*2π)/3313 weeks
116-.07583 -.14091 (116*2π)/3313 weeks
117-.12865 -.07657 (117*2π)/3313 weeks
118-.30191 .1184 (118*2π)/3313 weeks
119-.28211 -.15909 (119*2π)/3313 weeks
120-.2671 -.09514 (120*2π)/3313 weeks
121-.15127 -.22996 (121*2π)/3313 weeks
122-.04977 .04269 (122*2π)/3313 weeks
123-.07153 .03082 (123*2π)/3313 weeks
124-.17751 -.12835 (124*2π)/3313 weeks
125-.2215 -.01926 (125*2π)/3313 weeks
126-.16035 -.12059 (126*2π)/3313 weeks
127-.19698 -.1765 (127*2π)/3313 weeks
128-.28319 -.04883 (128*2π)/3313 weeks
129-.10281 .01636 (129*2π)/3313 weeks
130-.14396 -.01538 (130*2π)/3313 weeks
131-.17101 -.05005 (131*2π)/3313 weeks
132-.26252 -.01975 (132*2π)/3313 weeks
133-.21257 .03733 (133*2π)/3312 weeks
134-.29315 -.04831 (134*2π)/3312 weeks
135-.32032 -.00259 (135*2π)/3312 weeks
136-.20202 -.15926 (136*2π)/3312 weeks
137-.21231 -.13731 (137*2π)/3312 weeks
138-.29034 .1331 (138*2π)/3312 weeks
139-.04328 .09571 (139*2π)/3312 weeks
140-.1279 -.013 (140*2π)/3312 weeks
141-.21769 -.03277 (141*2π)/3312 weeks
142-.16003 -.04938 (142*2π)/3312 weeks
143-.2577 -.0427 (143*2π)/3312 weeks
144.10965 .00888 (144*2π)/3312 weeks
145-.11528 .06726 (145*2π)/3312 weeks
146-.24309 .02019 (146*2π)/3312 weeks
147-.15921 -.05673 (147*2π)/3312 weeks
148-.09193 -.08469 (148*2π)/3312 weeks
149-.07454 -.23318 (149*2π)/3312 weeks
150-.21006 .01527 (150*2π)/3312 weeks
151-.07587 -.09371 (151*2π)/3312 weeks
152-.25037 -.02488 (152*2π)/3312 weeks
153-.08609 .12006 (153*2π)/3312 weeks
154-.23542 -.15538 (154*2π)/3312 weeks
155-.14544 -.09519 (155*2π)/3312 weeks
156-.14401 -.22332 (156*2π)/3312 weeks
157-.225 -.00893 (157*2π)/3312 weeks
158-.2315 -.16618 (158*2π)/3312 weeks
159-.24767 -.05334 (159*2π)/3312 weeks
160-.22143 .07451 (160*2π)/3312 weeks
161-.08734 -.05958 (161*2π)/3312 weeks
162-.16961 -.14937 (162*2π)/3312 weeks
163-.31772 -.10959 (163*2π)/3312 weeks
164-.21381 .13201 (164*2π)/3312 weeks
165-.26409 .05031 (165*2π)/3312 weeks
166-.26409 -.05031 (166*2π)/3312 weeks
167-.21381 -.13201 (167*2π)/3312 weeks
168-.31772 .10959 (168*2π)/3312 weeks
169-.16961 .14937 (169*2π)/3312 weeks
170-.08734 .05958 (170*2π)/3312 weeks
171-.22143 -.07451 (171*2π)/3312 weeks
172-.24767 .05334 (172*2π)/3312 weeks
173-.2315 .16618 (173*2π)/3312 weeks
174-.225 .00893 (174*2π)/3312 weeks
175-.14401 .22332 (175*2π)/3312 weeks
176-.14544 .09519 (176*2π)/3312 weeks
177-.23542 .15538 (177*2π)/3312 weeks
178-.08609 -.12006 (178*2π)/3312 weeks
179-.25037 .02488 (179*2π)/3312 weeks
180-.07587 .09371 (180*2π)/3312 weeks
181-.21006 -.01527 (181*2π)/3312 weeks
182-.07454 .23318 (182*2π)/3312 weeks
183-.09193 .08469 (183*2π)/3312 weeks
184-.15921 .05673 (184*2π)/3312 weeks
185-.24309 -.02019 (185*2π)/3312 weeks
186-.11528 -.06726 (186*2π)/3312 weeks
187.10965 -.00888 (187*2π)/3312 weeks
188-.2577 .0427 (188*2π)/3312 weeks
189-.16003 .04938 (189*2π)/3312 weeks
190-.21769 .03277 (190*2π)/3312 weeks
191-.1279 .013 (191*2π)/3312 weeks
192-.04328 -.09571 (192*2π)/3312 weeks
193-.29034 -.1331 (193*2π)/3312 weeks
194-.21231 .13731 (194*2π)/3312 weeks
195-.20202 .15926 (195*2π)/3312 weeks
196-.32032 .00259 (196*2π)/3312 weeks
197-.29315 .04831 (197*2π)/3312 weeks
198-.21257 -.03733 (198*2π)/3312 weeks
199-.26252 .01975 (199*2π)/3312 weeks
200-.17101 .05005 (200*2π)/3312 weeks
201-.14396 .01538 (201*2π)/3312 weeks
202-.10281 -.01636 (202*2π)/3312 weeks
203-.28319 .04883 (203*2π)/3312 weeks
204-.19698 .1765 (204*2π)/3312 weeks
205-.16035 .12059 (205*2π)/3312 weeks
206-.2215 .01926 (206*2π)/3312 weeks
207-.17751 .12835 (207*2π)/3312 weeks
208-.07153 -.03082 (208*2π)/3312 weeks
209-.04977 -.04269 (209*2π)/3312 weeks
210-.15127 .22996 (210*2π)/3312 weeks
211-.2671 .09514 (211*2π)/3312 weeks
212-.28211 .15909 (212*2π)/3312 weeks
213-.30191 -.1184 (213*2π)/3312 weeks
214-.12865 .07657 (214*2π)/3312 weeks
215-.07583 .14091 (215*2π)/3312 weeks
216-.15376 .14802 (216*2π)/3312 weeks
217-.27921 .05816 (217*2π)/3312 weeks
218-.20472 .1683 (218*2π)/3312 weeks
219-.21653 .00944 (219*2π)/3312 weeks
220-.10919 .02325 (220*2π)/3312 weeks
221-.34553 .15656 (221*2π)/3311 weeks
222-.17304 .18221 (222*2π)/3311 weeks
223-.13584 .06962 (223*2π)/3311 weeks
224-.08539 .13795 (224*2π)/3311 weeks
225-.20202 .03729 (225*2π)/3311 weeks
226-.29566 .1467 (226*2π)/3311 weeks
227-.21741 .18935 (227*2π)/3311 weeks
228-.10763 .1575 (228*2π)/3311 weeks
229-.19084 .16084 (229*2π)/3311 weeks
230-.18936 .11133 (230*2π)/3311 weeks
231-.1095 .15423 (231*2π)/3311 weeks
232-.03193 .28118 (232*2π)/3311 weeks
233-.1128 .0561 (233*2π)/3311 weeks
234-.17123 .13438 (234*2π)/3311 weeks
235-.13292 .19709 (235*2π)/3311 weeks
236-.21245 .3526 (236*2π)/3311 weeks
237-.12077 .20061 (237*2π)/3311 weeks
238-.11202 .09373 (238*2π)/3311 weeks
239-.27473 -.05648 (239*2π)/3311 weeks
240-.20754 -.02933 (240*2π)/3311 weeks
241-.19693 .10516 (241*2π)/3311 weeks
242-.22449 .28108 (242*2π)/3311 weeks
243-.11934 .08617 (243*2π)/3311 weeks
244-.24225 -.15493 (244*2π)/3311 weeks
245-.38356 -.03529 (245*2π)/3311 weeks
246-.32838 .04785 (246*2π)/3311 weeks
247-.18418 .3666 (247*2π)/3311 weeks
248-.2035 .44696 (248*2π)/3311 weeks
249-.08918 .22581 (249*2π)/3311 weeks
250-.4499 .00583 (250*2π)/3311 weeks
251-.46436 .24534 (251*2π)/3311 weeks
252-.29147 .42052 (252*2π)/3311 weeks
253-.22511 .22342 (253*2π)/3311 weeks
254-.30106 .33973 (254*2π)/3311 weeks
255-.04649 .2501 (255*2π)/3311 weeks
256-.15358 .04269 (256*2π)/3311 weeks
257-.21661 .27796 (257*2π)/3311 weeks
258-.42435 .18311 (258*2π)/3311 weeks
259-.27931 .59006 (259*2π)/3311 weeks
260-.15383 .38582 (260*2π)/3311 weeks
261-.10154 .24397 (261*2π)/3311 weeks
262-.22584 .10779 (262*2π)/3311 weeks
263-.0967 .07523 (263*2π)/3311 weeks
264-.22622 .21034 (264*2π)/3311 weeks
265-.20357 .38739 (265*2π)/3311 weeks
266-.09585 .29644 (266*2π)/3311 weeks
267.08859 .00067 (267*2π)/3311 weeks
268-.20995 .30795 (268*2π)/3311 weeks
269-.26449 .22904 (269*2π)/3311 weeks
270-.28854 .36913 (270*2π)/3311 weeks
271-.02416 .40667 (271*2π)/3311 weeks
272-.03851 .27243 (272*2π)/3311 weeks
273-.04941 .25013 (273*2π)/3311 weeks
274-.14574 .29839 (274*2π)/3311 weeks
275-.24085 .1586 (275*2π)/3311 weeks
276-.30952 .21751 (276*2π)/3311 weeks
277-.38689 .10908 (277*2π)/3311 weeks
278-.54863 .34654 (278*2π)/3311 weeks
279-.25009 .4792 (279*2π)/3311 weeks
280-.19537 .59847 (280*2π)/3311 weeks
281-.29712 .44007 (281*2π)/3311 weeks
282-.27794 .29843 (282*2π)/3311 weeks
283-.01264 .09579 (283*2π)/3311 weeks
284-.1111 .39477 (284*2π)/3311 weeks
285.18986 .62706 (285*2π)/3311 weeks
286-.44845 .61649 (286*2π)/3311 weeks
287-.59868 .83618 (287*2π)/3311 weeks
288-.30877 .72615 (288*2π)/3311 weeks
289-.03514 .4814 (289*2π)/3311 weeks
290-.1384 .1626 (290*2π)/3311 weeks
291.24499 .82431 (291*2π)/3311 weeks
292-.02799 .20644 (292*2π)/3311 weeks
293-.16037 .8508 (293*2π)/3311 weeks
294-.21313 .433 (294*2π)/3311 weeks
295-.23244 .11006 (295*2π)/3311 weeks
296-.17294 .54144 (296*2π)/3311 weeks
297-.21706 -.10337 (297*2π)/3311 weeks
298-.19626 .29744 (298*2π)/3311 weeks
299-.03136 .47377 (299*2π)/3311 weeks
300.0441 .61715 (300*2π)/3311 weeks
301-.54612 .7978 (301*2π)/3311 weeks
302.33878 .53517 (302*2π)/3311 weeks
303-.56835 .65541 (303*2π)/3311 weeks
304-.41792 .87258 (304*2π)/3311 weeks
305-.73685 .11513 (305*2π)/3311 weeks
306-.51979 .89621 (306*2π)/3311 weeks
307.19679 .87165 (307*2π)/3311 weeks
308-.11362 .79629 (308*2π)/3311 weeks
309.10953 1.25657 (309*2π)/3311 weeks
310-.38486 1.18011 (310*2π)/3311 weeks
311-.75132 .84819 (311*2π)/3311 weeks
312-1.13209 .91163 (312*2π)/3311 weeks
313-.29419 2.15644 (313*2π)/3311 weeks
314.61544 1.35544 (314*2π)/3311 weeks
315.61327 1.70596 (315*2π)/3311 weeks
316-.0816 1.17094 (316*2π)/3311 weeks
317-1.04876 .78331 (317*2π)/3311 weeks
318.01093 2.14377 (318*2π)/3311 weeks
319-.40892 1.944 (319*2π)/3311 weeks
320-.00648 1.43766 (320*2π)/3311 weeks
321.75401 1.0271 (321*2π)/3311 weeks
322.15282 2.13409 (322*2π)/3311 weeks
323-.11854 2.78605 (323*2π)/3311 weeks
324-1.40043 3.3169 (324*2π)/3311 weeks
325-2.22405 2.85999 (325*2π)/3311 weeks
326-1.49119 4.59261 (326*2π)/3311 weeks
3273.55663 4.40947 (327*2π)/3311 weeks
328.3217 2.58026 (328*2π)/3311 weeks
3291.93061 4.26463 (329*2π)/3311 weeks

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