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# Fourier Analysis of VIPS (Vipshop Holdings Limited)

VIPS (Vipshop Holdings Limited) appears to have interesting cyclic behaviour every 25 weeks (.675*cosine), 18 weeks (.6173*sine), and 29 weeks (.5692*cosine).

VIPS (Vipshop Holdings Limited) has an average price of 12.06 (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 3/23/2012 to 5/29/2018 for VIPS (Vipshop Holdings Limited), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
012.0638   0
1-7.66947 -2.71757 (1*2π)/324324 weeks
23.02384 -4.16626 (2*2π)/324162 weeks
3-.59523 -.07568 (3*2π)/324108 weeks
41.11022 -1.17448 (4*2π)/32481 weeks
5-.11513 -1.61812 (5*2π)/32465 weeks
6.74011 -1.02278 (6*2π)/32454 weeks
7-.2346 -1.23761 (7*2π)/32446 weeks
8.06563 -1.36601 (8*2π)/32441 weeks
9-1.19588 -.38948 (9*2π)/32436 weeks
10-.03831 -.50359 (10*2π)/32432 weeks
11-.56917 -.27556 (11*2π)/32429 weeks
12.01726 -.55402 (12*2π)/32427 weeks
13-.67505 -.05957 (13*2π)/32425 weeks
14-.00159 .13595 (14*2π)/32423 weeks
15-.18395 -.29868 (15*2π)/32422 weeks
16.08343 -.17331 (16*2π)/32420 weeks
17-.03947 .14658 (17*2π)/32419 weeks
18-.08603 -.61729 (18*2π)/32418 weeks
19.04374 .07734 (19*2π)/32417 weeks
20-.0621 -.19155 (20*2π)/32416 weeks
21-.00117 -.27389 (21*2π)/32415 weeks
22-.13836 -.21828 (22*2π)/32415 weeks
23.05186 -.0485 (23*2π)/32414 weeks
24-.02072 -.28864 (24*2π)/32414 weeks
25-.30184 -.18775 (25*2π)/32413 weeks
26.0679 -.08411 (26*2π)/32412 weeks
27-.31509 -.11183 (27*2π)/32412 weeks
28.10784 -.07544 (28*2π)/32412 weeks
29-.06564 .03135 (29*2π)/32411 weeks
30-.09861 -.16567 (30*2π)/32411 weeks
31.11126 -.20058 (31*2π)/32410 weeks
32-.2406 -.14953 (32*2π)/32410 weeks
33.07652 .03247 (33*2π)/32410 weeks
34-.2169 -.12249 (34*2π)/32410 weeks
35.09961 -.0733 (35*2π)/3249 weeks
36-.14839 -.15108 (36*2π)/3249 weeks
37-.02295 -.12768 (37*2π)/3249 weeks
38-.01139 -.06755 (38*2π)/3249 weeks
39-.31773 -.08942 (39*2π)/3248 weeks
40-.02479 -.00309 (40*2π)/3248 weeks
41-.03989 -.02519 (41*2π)/3248 weeks
42-.03608 .03474 (42*2π)/3248 weeks
43-.06182 .06818 (43*2π)/3248 weeks
44.07632 -.13497 (44*2π)/3247 weeks
45.09234 -.03211 (45*2π)/3247 weeks
46-.17526 -.11737 (46*2π)/3247 weeks
47.00848 -.05991 (47*2π)/3247 weeks
48-.00948 -.05893 (48*2π)/3247 weeks
49-.09931 -.01947 (49*2π)/3247 weeks
50.0284 -.04566 (50*2π)/3246 weeks
51-.00689 -.00737 (51*2π)/3246 weeks
52.0404 -.04412 (52*2π)/3246 weeks
53-.05765 -.20723 (53*2π)/3246 weeks
54-.11225 -.05725 (54*2π)/3246 weeks
55.02104 .03919 (55*2π)/3246 weeks
56-.08314 -.09129 (56*2π)/3246 weeks
57.02661 -.04108 (57*2π)/3246 weeks
58-.07492 .01914 (58*2π)/3246 weeks
59-.09789 -.10993 (59*2π)/3245 weeks
60.07261 -.04679 (60*2π)/3245 weeks
61-.16903 .03669 (61*2π)/3245 weeks
62.06288 -.00631 (62*2π)/3245 weeks
63-.07606 -.07849 (63*2π)/3245 weeks
64.04517 .06444 (64*2π)/3245 weeks
65-.05061 -.02416 (65*2π)/3245 weeks
66.0628 -.01543 (66*2π)/3245 weeks
67.03042 -.0806 (67*2π)/3245 weeks
68.00557 -.00476 (68*2π)/3245 weeks
69.04534 -.12608 (69*2π)/3245 weeks
70-.01478 -.03948 (70*2π)/3245 weeks
71-.01711 -.12025 (71*2π)/3245 weeks
72-.02905 -.11159 (72*2π)/3245 weeks
73-.08724 -.05065 (73*2π)/3244 weeks
74-.08205 -.05239 (74*2π)/3244 weeks
75-.06206 -.02027 (75*2π)/3244 weeks
76-.00516 -.00777 (76*2π)/3244 weeks
77-.04374 -.04192 (77*2π)/3244 weeks
78-.09289 .04766 (78*2π)/3244 weeks
79.08275 -.05936 (79*2π)/3244 weeks
80-.07746 .01412 (80*2π)/3244 weeks
81.0735 -.01094 (81*2π)/3244 weeks
82-.0888 -.13471 (82*2π)/3244 weeks
83.10772 .08601 (83*2π)/3244 weeks
84-.00671 -.15891 (84*2π)/3244 weeks
85-.05206 -.04549 (85*2π)/3244 weeks
86.04004 -.04878 (86*2π)/3244 weeks
87-.05249 -.09224 (87*2π)/3244 weeks
88-.03921 -.05775 (88*2π)/3244 weeks
89-.04403 -.1162 (89*2π)/3244 weeks
90-.09342 -.02638 (90*2π)/3244 weeks
91-.02431 -.03808 (91*2π)/3244 weeks
92-.0171 -.04952 (92*2π)/3244 weeks
93-.05472 -.02604 (93*2π)/3243 weeks
94-.12557 -.07523 (94*2π)/3243 weeks
95-.06687 -.05161 (95*2π)/3243 weeks
96.02296 .08312 (96*2π)/3243 weeks
97-.15619 -.05903 (97*2π)/3243 weeks
98.08252 -.0225 (98*2π)/3243 weeks
99-.06292 -.0205 (99*2π)/3243 weeks
100-.04281 .01012 (100*2π)/3243 weeks
101-.02723 -.11434 (101*2π)/3243 weeks
102-.08271 .08153 (102*2π)/3243 weeks
103-.00491 -.06323 (103*2π)/3243 weeks
104-.04135 .00013 (104*2π)/3243 weeks
105-.01847 -.01732 (105*2π)/3243 weeks
106-.03356 -.10093 (106*2π)/3243 weeks
107-.06631 .0603 (107*2π)/3243 weeks
108.01029 -.10817 (108*2π)/3243 weeks
109-.0682 .07318 (109*2π)/3243 weeks
110-.01029 -.04609 (110*2π)/3243 weeks
111-.02736 -.06319 (111*2π)/3243 weeks
112-.02768 -.03756 (112*2π)/3243 weeks
113-.02797 -.06528 (113*2π)/3243 weeks
114-.13454 -.03722 (114*2π)/3243 weeks
115-.06835 .01135 (115*2π)/3243 weeks
116-.06562 .01858 (116*2π)/3243 weeks
117-.02782 -.07254 (117*2π)/3243 weeks
118-.0636 .05443 (118*2π)/3243 weeks
119-.10151 .02656 (119*2π)/3243 weeks
120.019 .00167 (120*2π)/3243 weeks
121-.03062 .01212 (121*2π)/3243 weeks
122.02412 .03527 (122*2π)/3243 weeks
123-.03658 -.06337 (123*2π)/3243 weeks
124-.01127 -.02634 (124*2π)/3243 weeks
125-.04465 -.04655 (125*2π)/3243 weeks
126-.12586 -.04284 (126*2π)/3243 weeks
127.07868 .04923 (127*2π)/3243 weeks
128-.11575 -.08382 (128*2π)/3243 weeks
129-.08558 .03667 (129*2π)/3243 weeks
130-.02217 -.01531 (130*2π)/3242 weeks
131-.11006 .04141 (131*2π)/3242 weeks
132.0157 .01964 (132*2π)/3242 weeks
133-.06782 -.01343 (133*2π)/3242 weeks
134.01015 .08844 (134*2π)/3242 weeks
135-.02304 -.0343 (135*2π)/3242 weeks
136-.00511 .03904 (136*2π)/3242 weeks
137.01058 -.04881 (137*2π)/3242 weeks
138-.04159 -.03024 (138*2π)/3242 weeks
139.01475 -.01539 (139*2π)/3242 weeks
140-.10783 -.05469 (140*2π)/3242 weeks
141.0208 .05453 (141*2π)/3242 weeks
142-.11143 -.05777 (142*2π)/3242 weeks
143-.01599 .04686 (143*2π)/3242 weeks
144-.04595 -.00844 (144*2π)/3242 weeks
145.00678 .04194 (145*2π)/3242 weeks
146-.06195 -.04743 (146*2π)/3242 weeks
147.06415 -.00592 (147*2π)/3242 weeks
148-.12916 .04537 (148*2π)/3242 weeks
149.01025 -.03754 (149*2π)/3242 weeks
150-.01991 .00287 (150*2π)/3242 weeks
151-.02007 .00014 (151*2π)/3242 weeks
152-.09784 -.02505 (152*2π)/3242 weeks
153.01786 .01567 (153*2π)/3242 weeks
154-.01621 -.01682 (154*2π)/3242 weeks
155-.07951 .03164 (155*2π)/3242 weeks
156.02884 .022 (156*2π)/3242 weeks
157-.05857 -.06371 (157*2π)/3242 weeks
158.00013 .0655 (158*2π)/3242 weeks
159-.03491 -.04106 (159*2π)/3242 weeks
160-.03527 .02487 (160*2π)/3242 weeks
161-.07426 -.03902 (161*2π)/3242 weeks
162.06527   (162*2π)/3242 weeks
163-.07426 .03902 (163*2π)/3242 weeks
164-.03527 -.02487 (164*2π)/3242 weeks
165-.03491 .04106 (165*2π)/3242 weeks
166.00013 -.0655 (166*2π)/3242 weeks
167-.05857 .06371 (167*2π)/3242 weeks
168.02884 -.022 (168*2π)/3242 weeks
169-.07951 -.03164 (169*2π)/3242 weeks
170-.01621 .01682 (170*2π)/3242 weeks
171.01786 -.01567 (171*2π)/3242 weeks
172-.09784 .02505 (172*2π)/3242 weeks
173-.02007 -.00014 (173*2π)/3242 weeks
174-.01991 -.00287 (174*2π)/3242 weeks
175.01025 .03754 (175*2π)/3242 weeks
176-.12916 -.04537 (176*2π)/3242 weeks
177.06415 .00592 (177*2π)/3242 weeks
178-.06195 .04743 (178*2π)/3242 weeks
179.00678 -.04194 (179*2π)/3242 weeks
180-.04595 .00844 (180*2π)/3242 weeks
181-.01599 -.04686 (181*2π)/3242 weeks
182-.11143 .05777 (182*2π)/3242 weeks
183.0208 -.05453 (183*2π)/3242 weeks
184-.10783 .05469 (184*2π)/3242 weeks
185.01475 .01539 (185*2π)/3242 weeks
186-.04159 .03024 (186*2π)/3242 weeks
187.01058 .04881 (187*2π)/3242 weeks
188-.00511 -.03904 (188*2π)/3242 weeks
189-.02304 .0343 (189*2π)/3242 weeks
190.01015 -.08844 (190*2π)/3242 weeks
191-.06782 .01343 (191*2π)/3242 weeks
192.0157 -.01964 (192*2π)/3242 weeks
193-.11006 -.04141 (193*2π)/3242 weeks
194-.02217 .01531 (194*2π)/3242 weeks
195-.08558 -.03667 (195*2π)/3242 weeks
196-.11575 .08382 (196*2π)/3242 weeks
197.07868 -.04923 (197*2π)/3242 weeks
198-.12586 .04284 (198*2π)/3242 weeks
199-.04465 .04655 (199*2π)/3242 weeks
200-.01127 .02634 (200*2π)/3242 weeks
201-.03658 .06337 (201*2π)/3242 weeks
202.02412 -.03527 (202*2π)/3242 weeks
203-.03062 -.01212 (203*2π)/3242 weeks
204.019 -.00167 (204*2π)/3242 weeks
205-.10151 -.02656 (205*2π)/3242 weeks
206-.0636 -.05443 (206*2π)/3242 weeks
207-.02782 .07254 (207*2π)/3242 weeks
208-.06562 -.01858 (208*2π)/3242 weeks
209-.06835 -.01135 (209*2π)/3242 weeks
210-.13454 .03722 (210*2π)/3242 weeks
211-.02797 .06528 (211*2π)/3242 weeks
212-.02768 .03756 (212*2π)/3242 weeks
213-.02736 .06319 (213*2π)/3242 weeks
214-.01029 .04609 (214*2π)/3242 weeks
215-.0682 -.07318 (215*2π)/3242 weeks
216.01029 .10817 (216*2π)/3242 weeks
217-.06631 -.0603 (217*2π)/3241 weeks
218-.03356 .10093 (218*2π)/3241 weeks
219-.01847 .01732 (219*2π)/3241 weeks
220-.04135 -.00013 (220*2π)/3241 weeks
221-.00491 .06323 (221*2π)/3241 weeks
222-.08271 -.08153 (222*2π)/3241 weeks
223-.02723 .11434 (223*2π)/3241 weeks
224-.04281 -.01012 (224*2π)/3241 weeks
225-.06292 .0205 (225*2π)/3241 weeks
226.08252 .0225 (226*2π)/3241 weeks
227-.15619 .05903 (227*2π)/3241 weeks
228.02296 -.08312 (228*2π)/3241 weeks
229-.06687 .05161 (229*2π)/3241 weeks
230-.12557 .07523 (230*2π)/3241 weeks
231-.05472 .02604 (231*2π)/3241 weeks
232-.0171 .04952 (232*2π)/3241 weeks
233-.02431 .03808 (233*2π)/3241 weeks
234-.09342 .02638 (234*2π)/3241 weeks
235-.04403 .1162 (235*2π)/3241 weeks
236-.03921 .05775 (236*2π)/3241 weeks
237-.05249 .09224 (237*2π)/3241 weeks
238.04004 .04878 (238*2π)/3241 weeks
239-.05206 .04549 (239*2π)/3241 weeks
240-.00671 .15891 (240*2π)/3241 weeks
241.10772 -.08601 (241*2π)/3241 weeks
242-.0888 .13471 (242*2π)/3241 weeks
243.0735 .01094 (243*2π)/3241 weeks
244-.07746 -.01412 (244*2π)/3241 weeks
245.08275 .05936 (245*2π)/3241 weeks
246-.09289 -.04766 (246*2π)/3241 weeks
247-.04374 .04192 (247*2π)/3241 weeks
248-.00516 .00777 (248*2π)/3241 weeks
249-.06206 .02027 (249*2π)/3241 weeks
250-.08205 .05239 (250*2π)/3241 weeks
251-.08724 .05065 (251*2π)/3241 weeks
252-.02905 .11159 (252*2π)/3241 weeks
253-.01711 .12025 (253*2π)/3241 weeks
254-.01478 .03948 (254*2π)/3241 weeks
255.04534 .12608 (255*2π)/3241 weeks
256.00557 .00476 (256*2π)/3241 weeks
257.03042 .0806 (257*2π)/3241 weeks
258.0628 .01543 (258*2π)/3241 weeks
259-.05061 .02416 (259*2π)/3241 weeks
260.04517 -.06444 (260*2π)/3241 weeks
261-.07606 .07849 (261*2π)/3241 weeks
262.06288 .00631 (262*2π)/3241 weeks
263-.16903 -.03669 (263*2π)/3241 weeks
264.07261 .04679 (264*2π)/3241 weeks
265-.09789 .10993 (265*2π)/3241 weeks
266-.07492 -.01914 (266*2π)/3241 weeks
267.02661 .04108 (267*2π)/3241 weeks
268-.08314 .09129 (268*2π)/3241 weeks
269.02104 -.03919 (269*2π)/3241 weeks
270-.11225 .05725 (270*2π)/3241 weeks
271-.05765 .20723 (271*2π)/3241 weeks
272.0404 .04412 (272*2π)/3241 weeks
273-.00689 .00737 (273*2π)/3241 weeks
274.0284 .04566 (274*2π)/3241 weeks
275-.09931 .01947 (275*2π)/3241 weeks
276-.00948 .05893 (276*2π)/3241 weeks
277.00848 .05991 (277*2π)/3241 weeks
278-.17526 .11737 (278*2π)/3241 weeks
279.09234 .03211 (279*2π)/3241 weeks
280.07632 .13497 (280*2π)/3241 weeks
281-.06182 -.06818 (281*2π)/3241 weeks
282-.03608 -.03474 (282*2π)/3241 weeks
283-.03989 .02519 (283*2π)/3241 weeks
284-.02479 .00309 (284*2π)/3241 weeks
285-.31773 .08942 (285*2π)/3241 weeks
286-.01139 .06755 (286*2π)/3241 weeks
287-.02295 .12768 (287*2π)/3241 weeks
288-.14839 .15108 (288*2π)/3241 weeks
289.09961 .0733 (289*2π)/3241 weeks
290-.2169 .12249 (290*2π)/3241 weeks
291.07652 -.03247 (291*2π)/3241 weeks
292-.2406 .14953 (292*2π)/3241 weeks
293.11126 .20058 (293*2π)/3241 weeks
294-.09861 .16567 (294*2π)/3241 weeks
295-.06564 -.03135 (295*2π)/3241 weeks
296.10784 .07544 (296*2π)/3241 weeks
297-.31509 .11183 (297*2π)/3241 weeks
298.0679 .08411 (298*2π)/3241 weeks
299-.30184 .18775 (299*2π)/3241 weeks
300-.02072 .28864 (300*2π)/3241 weeks
301.05186 .0485 (301*2π)/3241 weeks
302-.13836 .21828 (302*2π)/3241 weeks
303-.00117 .27389 (303*2π)/3241 weeks
304-.0621 .19155 (304*2π)/3241 weeks
305.04374 -.07734 (305*2π)/3241 weeks
306-.08603 .61729 (306*2π)/3241 weeks
307-.03947 -.14658 (307*2π)/3241 weeks
308.08343 .17331 (308*2π)/3241 weeks
309-.18395 .29868 (309*2π)/3241 weeks
310-.00159 -.13595 (310*2π)/3241 weeks
311-.67505 .05957 (311*2π)/3241 weeks
312.01726 .55402 (312*2π)/3241 weeks
313-.56917 .27556 (313*2π)/3241 weeks
314-.03831 .50359 (314*2π)/3241 weeks
315-1.19588 .38948 (315*2π)/3241 weeks
316.06563 1.36601 (316*2π)/3241 weeks
317-.2346 1.23761 (317*2π)/3241 weeks
318.74011 1.02278 (318*2π)/3241 weeks
319-.11513 1.61812 (319*2π)/3241 weeks
3201.11022 1.17448 (320*2π)/3241 weeks
321-.59523 .07568 (321*2π)/3241 weeks
3223.02384 4.16626 (322*2π)/3241 weeks