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# Fourier Analysis of PANW (Palo Alto Networks)

PANW (Palo Alto Networks) appears to have interesting cyclic behaviour every 20 weeks (6.9395*sine), 15 weeks (4.9*sine), and 30 weeks (4.5789*sine).

PANW (Palo Alto Networks) has an average price of 113.39 (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 7/20/2012 to 4/23/2018 for PANW (Palo Alto Networks), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0113.3879   0
1-23.95644 -46.56215 (1*2π)/302302 weeks
223.14999 -10.70994 (2*2π)/302151 weeks
3-1.28558 -12.02639 (3*2π)/302101 weeks
47.55551 -6.75498 (4*2π)/30276 weeks
5-1.01926 -11.27276 (5*2π)/30260 weeks
6-1.86929 -5.75519 (6*2π)/30250 weeks
72.54233 -4.24761 (7*2π)/30243 weeks
84.09146 -3.69232 (8*2π)/30238 weeks
9-.25871 -6.05697 (9*2π)/30234 weeks
10.74193 -4.57889 (10*2π)/30230 weeks
11.15659 -3.74555 (11*2π)/30227 weeks
12.14257 -2.98273 (12*2π)/30225 weeks
13-3.53229 -2.74962 (13*2π)/30223 weeks
142.20105 -2.00361 (14*2π)/30222 weeks
15.37933 -6.93953 (15*2π)/30220 weeks
16-3.48361 -2.10015 (16*2π)/30219 weeks
17-1.5428 -2.3722 (17*2π)/30218 weeks
18-1.01768 -.77674 (18*2π)/30217 weeks
19.71327 -1.23675 (19*2π)/30216 weeks
20-.00271 -4.89996 (20*2π)/30215 weeks
21-2.09532 -2.52134 (21*2π)/30214 weeks
22.58002 -.5283 (22*2π)/30214 weeks
23-2.46444 -2.83987 (23*2π)/30213 weeks
24.61838 -1.17388 (24*2π)/30213 weeks
25-1.25483 -3.0329 (25*2π)/30212 weeks
26-2.87587 -.56228 (26*2π)/30212 weeks
27.91628 -1.32519 (27*2π)/30211 weeks
28-.76629 -2.04388 (28*2π)/30211 weeks
29.5352 -1.25235 (29*2π)/30210 weeks
30-1.64272 -1.71017 (30*2π)/30210 weeks
31-.99033 -.38477 (31*2π)/30210 weeks
32-.67582 -1.2945 (32*2π)/3029 weeks
33.40973 -1.07892 (33*2π)/3029 weeks
34-.72216 -1.92771 (34*2π)/3029 weeks
35-.46333 -.07309 (35*2π)/3029 weeks
36.12836 -1.53622 (36*2π)/3028 weeks
37-.90552 -.33886 (37*2π)/3028 weeks
38.22498 -1.36956 (38*2π)/3028 weeks
39-.80451 -1.37952 (39*2π)/3028 weeks
40.35221 -1.45846 (40*2π)/3028 weeks
41-1.37008 -1.00456 (41*2π)/3027 weeks
42-.23137 -.89312 (42*2π)/3027 weeks
43.62509 -.63359 (43*2π)/3027 weeks
44-.03778 -2.02612 (44*2π)/3027 weeks
45-.97455 -1.44457 (45*2π)/3027 weeks
46.00273 -1.65891 (46*2π)/3027 weeks
47-1.24585 -.71524 (47*2π)/3026 weeks
48.1525 -1.09521 (48*2π)/3026 weeks
49-1.1344 -1.53361 (49*2π)/3026 weeks
50-1.09659 -.09674 (50*2π)/3026 weeks
51-.41351 -.36664 (51*2π)/3026 weeks
52.01717 -.76807 (52*2π)/3026 weeks
53-.53847 -1.23425 (53*2π)/3026 weeks
54-.71798 -.52456 (54*2π)/3026 weeks
55-.77143 -1.07084 (55*2π)/3025 weeks
56-.46272 -.68096 (56*2π)/3025 weeks
57-1.12499 -.08767 (57*2π)/3025 weeks
58-.38703 -.70104 (58*2π)/3025 weeks
59-.23741 -.60398 (59*2π)/3025 weeks
60-.9767 -.53018 (60*2π)/3025 weeks
61-1.14116 -.25911 (61*2π)/3025 weeks
62-.20778 -.51145 (62*2π)/3025 weeks
63-.25247 -.46704 (63*2π)/3025 weeks
64-.31857 -.95975 (64*2π)/3025 weeks
65-1.12995 -1.04696 (65*2π)/3025 weeks
66-.1093 -.06602 (66*2π)/3025 weeks
67-.04285 -.84207 (67*2π)/3025 weeks
68-.97749 -.35094 (68*2π)/3024 weeks
69.40807 -.76146 (69*2π)/3024 weeks
70-.7472 -.10941 (70*2π)/3024 weeks
71-.24039 -.12251 (71*2π)/3024 weeks
72-.02857 -.60933 (72*2π)/3024 weeks
73-.97778 -1.1985 (73*2π)/3024 weeks
74-.49137 .22731 (74*2π)/3024 weeks
75-.38697 -.57353 (75*2π)/3024 weeks
76-.22138 -.06412 (76*2π)/3024 weeks
77.13899 -.79376 (77*2π)/3024 weeks
78-.58584 -.49611 (78*2π)/3024 weeks
79-.11022 -.10564 (79*2π)/3024 weeks
80-.31952 -.7463 (80*2π)/3024 weeks
81.13623 -.5091 (81*2π)/3024 weeks
82-.3929 -.2362 (82*2π)/3024 weeks
83.08888 -.70437 (83*2π)/3024 weeks
84-.41928 -.67235 (84*2π)/3024 weeks
85-1.03539 -.12747 (85*2π)/3024 weeks
86-.28551 .13971 (86*2π)/3024 weeks
87-.35129 -.07545 (87*2π)/3023 weeks
88-.1019 -.3681 (88*2π)/3023 weeks
89-.19782 -1.0813 (89*2π)/3023 weeks
90-.89519 -.23858 (90*2π)/3023 weeks
91-.52766 -.16457 (91*2π)/3023 weeks
92.03054 -.44082 (92*2π)/3023 weeks
93-.61637 -.66645 (93*2π)/3023 weeks
94-.78668 -.08128 (94*2π)/3023 weeks
95.05805 -.48047 (95*2π)/3023 weeks
96-.7368 -.54542 (96*2π)/3023 weeks
97-.43926 -.37625 (97*2π)/3023 weeks
98-.766 -.42958 (98*2π)/3023 weeks
99-1.10893 .06992 (99*2π)/3023 weeks
100-.24926 -.15773 (100*2π)/3023 weeks
101-.91822 .26252 (101*2π)/3023 weeks
102-.55965 -.17616 (102*2π)/3023 weeks
103-.2901 -.28815 (103*2π)/3023 weeks
104-.73205 -.40043 (104*2π)/3023 weeks
105-.45853 .05828 (105*2π)/3023 weeks
106-.15781 .32118 (106*2π)/3023 weeks
107-.35299 -.52088 (107*2π)/3023 weeks
108-.55633 -.24324 (108*2π)/3023 weeks
109-.88849 -.60885 (109*2π)/3023 weeks
110-.46851 -.17937 (110*2π)/3023 weeks
111-.56507 .29797 (111*2π)/3023 weeks
112-.53212 -.38629 (112*2π)/3023 weeks
113-.42124 -.21034 (113*2π)/3023 weeks
114-.84008 -.01802 (114*2π)/3023 weeks
115-.36337 -.33216 (115*2π)/3023 weeks
116-.80579 -.06248 (116*2π)/3023 weeks
117-.55657 -.48568 (117*2π)/3023 weeks
118-.53869 -.01978 (118*2π)/3023 weeks
119-.52353 -.26605 (119*2π)/3023 weeks
120-.63776 .22216 (120*2π)/3023 weeks
121.00276 -.14602 (121*2π)/3022 weeks
122-.72509 -.20879 (122*2π)/3022 weeks
123-.48096 -.58895 (123*2π)/3022 weeks
124-.82977 .08448 (124*2π)/3022 weeks
125-.5079 .03003 (125*2π)/3022 weeks
126-.60067 .24251 (126*2π)/3022 weeks
127.03491 .17809 (127*2π)/3022 weeks
128-.55983 -.39979 (128*2π)/3022 weeks
129-.83777 .21788 (129*2π)/3022 weeks
130-.33049 -.0477 (130*2π)/3022 weeks
131-.54687 -.03799 (131*2π)/3022 weeks
132-.23311 -.14245 (132*2π)/3022 weeks
133-.35395 -.24677 (133*2π)/3022 weeks
134-.66652 -.26387 (134*2π)/3022 weeks
135-.69325 .49452 (135*2π)/3022 weeks
136.07116 .15484 (136*2π)/3022 weeks
137-.76626 -.02492 (137*2π)/3022 weeks
138-.43674 .26355 (138*2π)/3022 weeks
139-.38749 -.12669 (139*2π)/3022 weeks
140-.2147 .01057 (140*2π)/3022 weeks
141-.41885 -.04366 (141*2π)/3022 weeks
142-.40813 -.20022 (142*2π)/3022 weeks
143-.4433 .14365 (143*2π)/3022 weeks
144-.81358 .03694 (144*2π)/3022 weeks
145-.07804 .38974 (145*2π)/3022 weeks
146-.22155 -.1198 (146*2π)/3022 weeks
147-.37128 -.28432 (147*2π)/3022 weeks
148-.676 .08686 (148*2π)/3022 weeks
149-.2194 -.35083 (149*2π)/3022 weeks
150-.80665 .31174 (150*2π)/3022 weeks
151-.23947   (151*2π)/3022 weeks
152-.80665 -.31174 (152*2π)/3022 weeks
153-.2194 .35083 (153*2π)/3022 weeks
154-.676 -.08686 (154*2π)/3022 weeks
155-.37128 .28432 (155*2π)/3022 weeks
156-.22155 .1198 (156*2π)/3022 weeks
157-.07804 -.38974 (157*2π)/3022 weeks
158-.81358 -.03694 (158*2π)/3022 weeks
159-.4433 -.14365 (159*2π)/3022 weeks
160-.40813 .20022 (160*2π)/3022 weeks
161-.41885 .04366 (161*2π)/3022 weeks
162-.2147 -.01057 (162*2π)/3022 weeks
163-.38749 .12669 (163*2π)/3022 weeks
164-.43674 -.26355 (164*2π)/3022 weeks
165-.76626 .02492 (165*2π)/3022 weeks
166.07116 -.15484 (166*2π)/3022 weeks
167-.69325 -.49452 (167*2π)/3022 weeks
168-.66652 .26387 (168*2π)/3022 weeks
169-.35395 .24677 (169*2π)/3022 weeks
170-.23311 .14245 (170*2π)/3022 weeks
171-.54687 .03799 (171*2π)/3022 weeks
172-.33049 .0477 (172*2π)/3022 weeks
173-.83777 -.21788 (173*2π)/3022 weeks
174-.55983 .39979 (174*2π)/3022 weeks
175.03491 -.17809 (175*2π)/3022 weeks
176-.60067 -.24251 (176*2π)/3022 weeks
177-.5079 -.03003 (177*2π)/3022 weeks
178-.82977 -.08448 (178*2π)/3022 weeks
179-.48096 .58895 (179*2π)/3022 weeks
180-.72509 .20879 (180*2π)/3022 weeks
181.00276 .14602 (181*2π)/3022 weeks
182-.63776 -.22216 (182*2π)/3022 weeks
183-.52353 .26605 (183*2π)/3022 weeks
184-.53869 .01978 (184*2π)/3022 weeks
185-.55657 .48568 (185*2π)/3022 weeks
186-.80579 .06248 (186*2π)/3022 weeks
187-.36337 .33216 (187*2π)/3022 weeks
188-.84008 .01802 (188*2π)/3022 weeks
189-.42124 .21034 (189*2π)/3022 weeks
190-.53212 .38629 (190*2π)/3022 weeks
191-.56507 -.29797 (191*2π)/3022 weeks
192-.46851 .17937 (192*2π)/3022 weeks
193-.88849 .60885 (193*2π)/3022 weeks
194-.55633 .24324 (194*2π)/3022 weeks
195-.35299 .52088 (195*2π)/3022 weeks
196-.15781 -.32118 (196*2π)/3022 weeks
197-.45853 -.05828 (197*2π)/3022 weeks
198-.73205 .40043 (198*2π)/3022 weeks
199-.2901 .28815 (199*2π)/3022 weeks
200-.55965 .17616 (200*2π)/3022 weeks
201-.91822 -.26252 (201*2π)/3022 weeks
202-.24926 .15773 (202*2π)/3021 weeks
203-1.10893 -.06992 (203*2π)/3021 weeks
204-.766 .42958 (204*2π)/3021 weeks
205-.43926 .37625 (205*2π)/3021 weeks
206-.7368 .54542 (206*2π)/3021 weeks
207.05805 .48047 (207*2π)/3021 weeks
208-.78668 .08128 (208*2π)/3021 weeks
209-.61637 .66645 (209*2π)/3021 weeks
210.03054 .44082 (210*2π)/3021 weeks
211-.52766 .16457 (211*2π)/3021 weeks
212-.89519 .23858 (212*2π)/3021 weeks
213-.19782 1.0813 (213*2π)/3021 weeks
214-.1019 .3681 (214*2π)/3021 weeks
215-.35129 .07545 (215*2π)/3021 weeks
216-.28551 -.13971 (216*2π)/3021 weeks
217-1.03539 .12747 (217*2π)/3021 weeks
218-.41928 .67235 (218*2π)/3021 weeks
219.08888 .70437 (219*2π)/3021 weeks
220-.3929 .2362 (220*2π)/3021 weeks
221.13623 .5091 (221*2π)/3021 weeks
222-.31952 .7463 (222*2π)/3021 weeks
223-.11022 .10564 (223*2π)/3021 weeks
224-.58584 .49611 (224*2π)/3021 weeks
225.13899 .79376 (225*2π)/3021 weeks
226-.22138 .06412 (226*2π)/3021 weeks
227-.38697 .57353 (227*2π)/3021 weeks
228-.49137 -.22731 (228*2π)/3021 weeks
229-.97778 1.1985 (229*2π)/3021 weeks
230-.02857 .60933 (230*2π)/3021 weeks
231-.24039 .12251 (231*2π)/3021 weeks
232-.7472 .10941 (232*2π)/3021 weeks
233.40807 .76146 (233*2π)/3021 weeks
234-.97749 .35094 (234*2π)/3021 weeks
235-.04285 .84207 (235*2π)/3021 weeks
236-.1093 .06602 (236*2π)/3021 weeks
237-1.12995 1.04696 (237*2π)/3021 weeks
238-.31857 .95975 (238*2π)/3021 weeks
239-.25247 .46704 (239*2π)/3021 weeks
240-.20778 .51145 (240*2π)/3021 weeks
241-1.14116 .25911 (241*2π)/3021 weeks
242-.9767 .53018 (242*2π)/3021 weeks
243-.23741 .60398 (243*2π)/3021 weeks
244-.38703 .70104 (244*2π)/3021 weeks
245-1.12499 .08767 (245*2π)/3021 weeks
246-.46272 .68096 (246*2π)/3021 weeks
247-.77143 1.07084 (247*2π)/3021 weeks
248-.71798 .52456 (248*2π)/3021 weeks
249-.53847 1.23425 (249*2π)/3021 weeks
250.01717 .76807 (250*2π)/3021 weeks
251-.41351 .36664 (251*2π)/3021 weeks
252-1.09659 .09674 (252*2π)/3021 weeks
253-1.1344 1.53361 (253*2π)/3021 weeks
254.1525 1.09521 (254*2π)/3021 weeks
255-1.24585 .71524 (255*2π)/3021 weeks
256.00273 1.65891 (256*2π)/3021 weeks
257-.97455 1.44457 (257*2π)/3021 weeks
258-.03778 2.02612 (258*2π)/3021 weeks
259.62509 .63359 (259*2π)/3021 weeks
260-.23137 .89312 (260*2π)/3021 weeks
261-1.37008 1.00456 (261*2π)/3021 weeks
262.35221 1.45846 (262*2π)/3021 weeks
263-.80451 1.37952 (263*2π)/3021 weeks
264.22498 1.36956 (264*2π)/3021 weeks
265-.90552 .33886 (265*2π)/3021 weeks
266.12836 1.53622 (266*2π)/3021 weeks
267-.46333 .07309 (267*2π)/3021 weeks
268-.72216 1.92771 (268*2π)/3021 weeks
269.40973 1.07892 (269*2π)/3021 weeks
270-.67582 1.2945 (270*2π)/3021 weeks
271-.99033 .38477 (271*2π)/3021 weeks
272-1.64272 1.71017 (272*2π)/3021 weeks
273.5352 1.25235 (273*2π)/3021 weeks
274-.76629 2.04388 (274*2π)/3021 weeks
275.91628 1.32519 (275*2π)/3021 weeks
276-2.87587 .56228 (276*2π)/3021 weeks
277-1.25483 3.0329 (277*2π)/3021 weeks
278.61838 1.17388 (278*2π)/3021 weeks
279-2.46444 2.83987 (279*2π)/3021 weeks
280.58002 .5283 (280*2π)/3021 weeks
281-2.09532 2.52134 (281*2π)/3021 weeks
282-.00271 4.89996 (282*2π)/3021 weeks
283.71327 1.23675 (283*2π)/3021 weeks
284-1.01768 .77674 (284*2π)/3021 weeks
285-1.5428 2.3722 (285*2π)/3021 weeks
286-3.48361 2.10015 (286*2π)/3021 weeks
287.37933 6.93953 (287*2π)/3021 weeks
2882.20105 2.00361 (288*2π)/3021 weeks
289-3.53229 2.74962 (289*2π)/3021 weeks
290.14257 2.98273 (290*2π)/3021 weeks
291.15659 3.74555 (291*2π)/3021 weeks
292.74193 4.57889 (292*2π)/3021 weeks
293-.25871 6.05697 (293*2π)/3021 weeks
2944.09146 3.69232 (294*2π)/3021 weeks
2952.54233 4.24761 (295*2π)/3021 weeks
296-1.86929 5.75519 (296*2π)/3021 weeks
297-1.01926 11.27276 (297*2π)/3021 weeks
2987.55551 6.75498 (298*2π)/3021 weeks
299-1.28558 12.02639 (299*2π)/3021 weeks
30023.14999 10.70994 (300*2π)/3021 weeks