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

# Fourier Analysis of P (Pandora Media)

P (Pandora Media) appears to have interesting cyclic behaviour every 33 weeks (.9072*cosine), 20 weeks (.7438*cosine), and 17 weeks (.6236*cosine).

P (Pandora Media) has an average price of 14.72 (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.

## Fourier Analysis

Using data from 6/15/2011 to 6/4/2018 for P (Pandora Media), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
014.71745   0
1-6.88908 3.43909 (1*2π)/365365 weeks
21.20014 -3.1687 (2*2π)/365183 weeks
31.40472 3.35441 (3*2π)/365122 weeks
4-1.33868 1.70876 (4*2π)/36591 weeks
51.5443 -.0895 (5*2π)/36573 weeks
6-.26758 .50275 (6*2π)/36561 weeks
7.17079 .94963 (7*2π)/36552 weeks
8.76195 -.20981 (8*2π)/36546 weeks
9-.14248 .92843 (9*2π)/36541 weeks
10.00823 -.08645 (10*2π)/36537 weeks
11.90716 .14379 (11*2π)/36533 weeks
12-.19854 -.00422 (12*2π)/36530 weeks
13.57768 .21507 (13*2π)/36528 weeks
14-.50017 .64533 (14*2π)/36526 weeks
15.11725 .03733 (15*2π)/36524 weeks
16.39098 .25095 (16*2π)/36523 weeks
17-.36152 .04254 (17*2π)/36521 weeks
18.74376 .00984 (18*2π)/36520 weeks
19-.1844 .37658 (19*2π)/36519 weeks
20.33503 -.13422 (20*2π)/36518 weeks
21.62358 .02715 (21*2π)/36517 weeks
22-.08548 .68874 (22*2π)/36517 weeks
23.36112 .09291 (23*2π)/36516 weeks
24-.02911 .69548 (24*2π)/36515 weeks
25-.19219 .20436 (25*2π)/36515 weeks
26-.02893 .06462 (26*2π)/36514 weeks
27-.39774 .33981 (27*2π)/36514 weeks
28.2334 .19812 (28*2π)/36513 weeks
29-.24567 .10244 (29*2π)/36513 weeks
30-.1063 .13578 (30*2π)/36512 weeks
31.05504 .19941 (31*2π)/36512 weeks
32-.10073 -.18138 (32*2π)/36511 weeks
33.02994 .13384 (33*2π)/36511 weeks
34.07535 -.09229 (34*2π)/36511 weeks
35-.2394 .07253 (35*2π)/36510 weeks
36-.09202 .18342 (36*2π)/36510 weeks
37.28009 .0639 (37*2π)/36510 weeks
38-.19239 .1699 (38*2π)/36510 weeks
39.04425 .03882 (39*2π)/3659 weeks
40-.01746 .03823 (40*2π)/3659 weeks
41.05515 .34762 (41*2π)/3659 weeks
42-.13305 -.05757 (42*2π)/3659 weeks
43.00344 -.01425 (43*2π)/3658 weeks
44.1041 .23951 (44*2π)/3658 weeks
45-.19258 .03083 (45*2π)/3658 weeks
46.14388 .1743 (46*2π)/3658 weeks
47-.02816 .11206 (47*2π)/3658 weeks
48-.20906 -.01937 (48*2π)/3658 weeks
49.07844 .2728 (49*2π)/3657 weeks
50-.26774 .02146 (50*2π)/3657 weeks
51.01347 .08829 (51*2π)/3657 weeks
52.03254 .10607 (52*2π)/3657 weeks
53-.1664 .10735 (53*2π)/3657 weeks
54.02457 .0761 (54*2π)/3657 weeks
55.02202 -.01916 (55*2π)/3657 weeks
56-.14931 .08028 (56*2π)/3657 weeks
57-.00878 -.05958 (57*2π)/3656 weeks
58-.04999 .04703 (58*2π)/3656 weeks
59.02959 .08909 (59*2π)/3656 weeks
60-.02391 .08433 (60*2π)/3656 weeks
61-.12251 -.05266 (61*2π)/3656 weeks
62.15735 .16214 (62*2π)/3656 weeks
63-.13106 -.03995 (63*2π)/3656 weeks
64-.06352 -.01555 (64*2π)/3656 weeks
65.10741 .01036 (65*2π)/3656 weeks
66-.08653 -.08659 (66*2π)/3656 weeks
67-.05144 -.07946 (67*2π)/3655 weeks
68.12419 -.0382 (68*2π)/3655 weeks
69.05408 .00117 (69*2π)/3655 weeks
70-.04231 .07648 (70*2π)/3655 weeks
71.14182 -.11629 (71*2π)/3655 weeks
72-.03994 .17464 (72*2π)/3655 weeks
73.03487 .11599 (73*2π)/3655 weeks
74-.04167 -.00469 (74*2π)/3655 weeks
75.07085 .06349 (75*2π)/3655 weeks
76.06274 .06406 (76*2π)/3655 weeks
77-.12167 -.05882 (77*2π)/3655 weeks
78.04097 .11545 (78*2π)/3655 weeks
79.05174 .02512 (79*2π)/3655 weeks
80-.05228 -.02623 (80*2π)/3655 weeks
81.11449 .02101 (81*2π)/3655 weeks
82.00951 .16662 (82*2π)/3654 weeks
83-.05823 -.1089 (83*2π)/3654 weeks
84-.01366 .11401 (84*2π)/3654 weeks
85-.12083 .05742 (85*2π)/3654 weeks
86.0729 -.01724 (86*2π)/3654 weeks
87-.00261 .01072 (87*2π)/3654 weeks
88-.03136 .01091 (88*2π)/3654 weeks
89.00252 -.09325 (89*2π)/3654 weeks
90-.0059 .05645 (90*2π)/3654 weeks
91-.0816 .03397 (91*2π)/3654 weeks
92-.00815 -.08473 (92*2π)/3654 weeks
93-.00693 .11472 (93*2π)/3654 weeks
94-.05805 .01903 (94*2π)/3654 weeks
95.00907 -.11747 (95*2π)/3654 weeks
96-.03425 .01301 (96*2π)/3654 weeks
97.07951 .01712 (97*2π)/3654 weeks
98-.02707 -.06009 (98*2π)/3654 weeks
99.01844 .08531 (99*2π)/3654 weeks
100-.0322 .01938 (100*2π)/3654 weeks
101.03075 .02953 (101*2π)/3654 weeks
102-.01246 -.01686 (102*2π)/3654 weeks
103-.03612 -.07728 (103*2π)/3654 weeks
104-.02455 .02151 (104*2π)/3654 weeks
105-.01053 -.00523 (105*2π)/3653 weeks
106-.00363 -.01219 (106*2π)/3653 weeks
107-.00433 .09038 (107*2π)/3653 weeks
108-.03439 -.04399 (108*2π)/3653 weeks
109.00684 .07882 (109*2π)/3653 weeks
110.05948 -.01274 (110*2π)/3653 weeks
111-.01185 .01756 (111*2π)/3653 weeks
112-.04954 -.0404 (112*2π)/3653 weeks
113.03061 .02784 (113*2π)/3653 weeks
114-.08495 -.02648 (114*2π)/3653 weeks
115.02535 .00497 (115*2π)/3653 weeks
116-.00157 -.10685 (116*2π)/3653 weeks
117.02758 .00577 (117*2π)/3653 weeks
118-.07227 -.01324 (118*2π)/3653 weeks
119.03198 -.05917 (119*2π)/3653 weeks
120.01861 .06428 (120*2π)/3653 weeks
121.01446 -.09049 (121*2π)/3653 weeks
122.06724 .08087 (122*2π)/3653 weeks
123-.02486 .10133 (123*2π)/3653 weeks
124.01134 -.10396 (124*2π)/3653 weeks
125.01576 -.02635 (125*2π)/3653 weeks
126.03119 .01528 (126*2π)/3653 weeks
127.00882 -.06296 (127*2π)/3653 weeks
128.05497 .07207 (128*2π)/3653 weeks
129.04416 -.04107 (129*2π)/3653 weeks
130-.00261 -.01998 (130*2π)/3653 weeks
131.06581 .10069 (131*2π)/3653 weeks
132-.11596 -.01268 (132*2π)/3653 weeks
133.05335 -.11379 (133*2π)/3653 weeks
134.08156 .08061 (134*2π)/3653 weeks
135-.06807 -.0742 (135*2π)/3653 weeks
136.07748 .01831 (136*2π)/3653 weeks
137-.04903 -.00457 (137*2π)/3653 weeks
138.05442 -.0748 (138*2π)/3653 weeks
139-.00437 -.0691 (139*2π)/3653 weeks
140.01737 -.01174 (140*2π)/3653 weeks
141.01933 .00612 (141*2π)/3653 weeks
142.0282 .00396 (142*2π)/3653 weeks
143.01187 -.0425 (143*2π)/3653 weeks
144.03403 .01621 (144*2π)/3653 weeks
145.0566 -.0456 (145*2π)/3653 weeks
146.04014 -.05204 (146*2π)/3653 weeks
147.05004 .02069 (147*2π)/3652 weeks
148.02724 .01801 (148*2π)/3652 weeks
149.02742 -.01167 (149*2π)/3652 weeks
150.07178 .04344 (150*2π)/3652 weeks
151.02536 .04464 (151*2π)/3652 weeks
152.05179 .02388 (152*2π)/3652 weeks
153.04011 .05717 (153*2π)/3652 weeks
154-.04464 .0079 (154*2π)/3652 weeks
155.0888 -.04515 (155*2π)/3652 weeks
156-.04776 .05623 (156*2π)/3652 weeks
157.05996 -.02968 (157*2π)/3652 weeks
158.05417 .06411 (158*2π)/3652 weeks
159-.07071 .04642 (159*2π)/3652 weeks
160-.0061 .00359 (160*2π)/3652 weeks
161-.04903 -.08912 (161*2π)/3652 weeks
162.02342 .01875 (162*2π)/3652 weeks
163-.00825 -.03431 (163*2π)/3652 weeks
164.00249 -.02086 (164*2π)/3652 weeks
165.12523 -.00234 (165*2π)/3652 weeks
166-.01312 .04327 (166*2π)/3652 weeks
167-.02631 -.09258 (167*2π)/3652 weeks
168.1643 .05118 (168*2π)/3652 weeks
169-.05294 .03279 (169*2π)/3652 weeks
170.12766 -.0096 (170*2π)/3652 weeks
171.00787 .07145 (171*2π)/3652 weeks
172.04441 -.03549 (172*2π)/3652 weeks
173.05922 .08337 (173*2π)/3652 weeks
174.04139 .00997 (174*2π)/3652 weeks
175-.04027 .0514 (175*2π)/3652 weeks
176.05059 -.05506 (176*2π)/3652 weeks
177-.01876 .02335 (177*2π)/3652 weeks
178.02141 .00575 (178*2π)/3652 weeks
179.02583 -.04149 (179*2π)/3652 weeks
180.05043 .01974 (180*2π)/3652 weeks
181-.05539 .08088 (181*2π)/3652 weeks
182.01484 -.06167 (182*2π)/3652 weeks
183.01484 .06167 (183*2π)/3652 weeks
184-.05539 -.08088 (184*2π)/3652 weeks
185.05043 -.01974 (185*2π)/3652 weeks
186.02583 .04149 (186*2π)/3652 weeks
187.02141 -.00575 (187*2π)/3652 weeks
188-.01876 -.02335 (188*2π)/3652 weeks
189.05059 .05506 (189*2π)/3652 weeks
190-.04027 -.0514 (190*2π)/3652 weeks
191.04139 -.00997 (191*2π)/3652 weeks
192.05922 -.08337 (192*2π)/3652 weeks
193.04441 .03549 (193*2π)/3652 weeks
194.00787 -.07145 (194*2π)/3652 weeks
195.12766 .0096 (195*2π)/3652 weeks
196-.05294 -.03279 (196*2π)/3652 weeks
197.1643 -.05118 (197*2π)/3652 weeks
198-.02631 .09258 (198*2π)/3652 weeks
199-.01312 -.04327 (199*2π)/3652 weeks
200.12523 .00234 (200*2π)/3652 weeks
201.00249 .02086 (201*2π)/3652 weeks
202-.00825 .03431 (202*2π)/3652 weeks
203.02342 -.01875 (203*2π)/3652 weeks
204-.04903 .08912 (204*2π)/3652 weeks
205-.0061 -.00359 (205*2π)/3652 weeks
206-.07071 -.04642 (206*2π)/3652 weeks
207.05417 -.06411 (207*2π)/3652 weeks
208.05996 .02968 (208*2π)/3652 weeks
209-.04776 -.05623 (209*2π)/3652 weeks
210.0888 .04515 (210*2π)/3652 weeks
211-.04464 -.0079 (211*2π)/3652 weeks
212.04011 -.05717 (212*2π)/3652 weeks
213.05179 -.02388 (213*2π)/3652 weeks
214.02536 -.04464 (214*2π)/3652 weeks
215.07178 -.04344 (215*2π)/3652 weeks
216.02742 .01167 (216*2π)/3652 weeks
217.02724 -.01801 (217*2π)/3652 weeks
218.05004 -.02069 (218*2π)/3652 weeks
219.04014 .05204 (219*2π)/3652 weeks
220.0566 .0456 (220*2π)/3652 weeks
221.03403 -.01621 (221*2π)/3652 weeks
222.01187 .0425 (222*2π)/3652 weeks
223.0282 -.00396 (223*2π)/3652 weeks
224.01933 -.00612 (224*2π)/3652 weeks
225.01737 .01174 (225*2π)/3652 weeks
226-.00437 .0691 (226*2π)/3652 weeks
227.05442 .0748 (227*2π)/3652 weeks
228-.04903 .00457 (228*2π)/3652 weeks
229.07748 -.01831 (229*2π)/3652 weeks
230-.06807 .0742 (230*2π)/3652 weeks
231.08156 -.08061 (231*2π)/3652 weeks
232.05335 .11379 (232*2π)/3652 weeks
233-.11596 .01268 (233*2π)/3652 weeks
234.06581 -.10069 (234*2π)/3652 weeks
235-.00261 .01998 (235*2π)/3652 weeks
236.04416 .04107 (236*2π)/3652 weeks
237.05497 -.07207 (237*2π)/3652 weeks
238.00882 .06296 (238*2π)/3652 weeks
239.03119 -.01528 (239*2π)/3652 weeks
240.01576 .02635 (240*2π)/3652 weeks
241.01134 .10396 (241*2π)/3652 weeks
242-.02486 -.10133 (242*2π)/3652 weeks
243.06724 -.08087 (243*2π)/3652 weeks
244.01446 .09049 (244*2π)/3651 weeks
245.01861 -.06428 (245*2π)/3651 weeks
246.03198 .05917 (246*2π)/3651 weeks
247-.07227 .01324 (247*2π)/3651 weeks
248.02758 -.00577 (248*2π)/3651 weeks
249-.00157 .10685 (249*2π)/3651 weeks
250.02535 -.00497 (250*2π)/3651 weeks
251-.08495 .02648 (251*2π)/3651 weeks
252.03061 -.02784 (252*2π)/3651 weeks
253-.04954 .0404 (253*2π)/3651 weeks
254-.01185 -.01756 (254*2π)/3651 weeks
255.05948 .01274 (255*2π)/3651 weeks
256.00684 -.07882 (256*2π)/3651 weeks
257-.03439 .04399 (257*2π)/3651 weeks
258-.00433 -.09038 (258*2π)/3651 weeks
259-.00363 .01219 (259*2π)/3651 weeks
260-.01053 .00523 (260*2π)/3651 weeks
261-.02455 -.02151 (261*2π)/3651 weeks
262-.03612 .07728 (262*2π)/3651 weeks
263-.01246 .01686 (263*2π)/3651 weeks
264.03075 -.02953 (264*2π)/3651 weeks
265-.0322 -.01938 (265*2π)/3651 weeks
266.01844 -.08531 (266*2π)/3651 weeks
267-.02707 .06009 (267*2π)/3651 weeks
268.07951 -.01712 (268*2π)/3651 weeks
269-.03425 -.01301 (269*2π)/3651 weeks
270.00907 .11747 (270*2π)/3651 weeks
271-.05805 -.01903 (271*2π)/3651 weeks
272-.00693 -.11472 (272*2π)/3651 weeks
273-.00815 .08473 (273*2π)/3651 weeks
274-.0816 -.03397 (274*2π)/3651 weeks
275-.0059 -.05645 (275*2π)/3651 weeks
276.00252 .09325 (276*2π)/3651 weeks
277-.03136 -.01091 (277*2π)/3651 weeks
278-.00261 -.01072 (278*2π)/3651 weeks
279.0729 .01724 (279*2π)/3651 weeks
280-.12083 -.05742 (280*2π)/3651 weeks
281-.01366 -.11401 (281*2π)/3651 weeks
282-.05823 .1089 (282*2π)/3651 weeks
283.00951 -.16662 (283*2π)/3651 weeks
284.11449 -.02101 (284*2π)/3651 weeks
285-.05228 .02623 (285*2π)/3651 weeks
286.05174 -.02512 (286*2π)/3651 weeks
287.04097 -.11545 (287*2π)/3651 weeks
288-.12167 .05882 (288*2π)/3651 weeks
289.06274 -.06406 (289*2π)/3651 weeks
290.07085 -.06349 (290*2π)/3651 weeks
291-.04167 .00469 (291*2π)/3651 weeks
292.03487 -.11599 (292*2π)/3651 weeks
293-.03994 -.17464 (293*2π)/3651 weeks
294.14182 .11629 (294*2π)/3651 weeks
295-.04231 -.07648 (295*2π)/3651 weeks
296.05408 -.00117 (296*2π)/3651 weeks
297.12419 .0382 (297*2π)/3651 weeks
298-.05144 .07946 (298*2π)/3651 weeks
299-.08653 .08659 (299*2π)/3651 weeks
300.10741 -.01036 (300*2π)/3651 weeks
301-.06352 .01555 (301*2π)/3651 weeks
302-.13106 .03995 (302*2π)/3651 weeks
303.15735 -.16214 (303*2π)/3651 weeks
304-.12251 .05266 (304*2π)/3651 weeks
305-.02391 -.08433 (305*2π)/3651 weeks
306.02959 -.08909 (306*2π)/3651 weeks
307-.04999 -.04703 (307*2π)/3651 weeks
308-.00878 .05958 (308*2π)/3651 weeks
309-.14931 -.08028 (309*2π)/3651 weeks
310.02202 .01916 (310*2π)/3651 weeks
311.02457 -.0761 (311*2π)/3651 weeks
312-.1664 -.10735 (312*2π)/3651 weeks
313.03254 -.10607 (313*2π)/3651 weeks
314.01347 -.08829 (314*2π)/3651 weeks
315-.26774 -.02146 (315*2π)/3651 weeks
316.07844 -.2728 (316*2π)/3651 weeks
317-.20906 .01937 (317*2π)/3651 weeks
318-.02816 -.11206 (318*2π)/3651 weeks
319.14388 -.1743 (319*2π)/3651 weeks
320-.19258 -.03083 (320*2π)/3651 weeks
321.1041 -.23951 (321*2π)/3651 weeks
322.00344 .01425 (322*2π)/3651 weeks
323-.13305 .05757 (323*2π)/3651 weeks
324.05515 -.34762 (324*2π)/3651 weeks
325-.01746 -.03823 (325*2π)/3651 weeks
326.04425 -.03882 (326*2π)/3651 weeks
327-.19239 -.1699 (327*2π)/3651 weeks
328.28009 -.0639 (328*2π)/3651 weeks
329-.09202 -.18342 (329*2π)/3651 weeks
330-.2394 -.07253 (330*2π)/3651 weeks
331.07535 .09229 (331*2π)/3651 weeks
332.02994 -.13384 (332*2π)/3651 weeks
333-.10073 .18138 (333*2π)/3651 weeks
334.05504 -.19941 (334*2π)/3651 weeks
335-.1063 -.13578 (335*2π)/3651 weeks
336-.24567 -.10244 (336*2π)/3651 weeks
337.2334 -.19812 (337*2π)/3651 weeks
338-.39774 -.33981 (338*2π)/3651 weeks
339-.02893 -.06462 (339*2π)/3651 weeks
340-.19219 -.20436 (340*2π)/3651 weeks
341-.02911 -.69548 (341*2π)/3651 weeks
342.36112 -.09291 (342*2π)/3651 weeks
343-.08548 -.68874 (343*2π)/3651 weeks
344.62358 -.02715 (344*2π)/3651 weeks
345.33503 .13422 (345*2π)/3651 weeks
346-.1844 -.37658 (346*2π)/3651 weeks
347.74376 -.00984 (347*2π)/3651 weeks
348-.36152 -.04254 (348*2π)/3651 weeks
349.39098 -.25095 (349*2π)/3651 weeks
350.11725 -.03733 (350*2π)/3651 weeks
351-.50017 -.64533 (351*2π)/3651 weeks
352.57768 -.21507 (352*2π)/3651 weeks
353-.19854 .00422 (353*2π)/3651 weeks
354.90716 -.14379 (354*2π)/3651 weeks
355.00823 .08645 (355*2π)/3651 weeks
356-.14248 -.92843 (356*2π)/3651 weeks
357.76195 .20981 (357*2π)/3651 weeks
358.17079 -.94963 (358*2π)/3651 weeks
359-.26758 -.50275 (359*2π)/3651 weeks
3601.5443 .0895 (360*2π)/3651 weeks
361-1.33868 -1.70876 (361*2π)/3651 weeks
3621.40472 -3.35441 (362*2π)/3651 weeks
3631.20014 3.1687 (363*2π)/3651 weeks