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# Fourier Analysis of PRTA (Prothena Corporation plc)

PRTA (Prothena Corporation plc) appears to have interesting cyclic behaviour every 18 weeks (2.8134*sine), 23 weeks (2.6985*sine), and 20 weeks (2.46*sine).

PRTA (Prothena Corporation plc) has an average price of 37.4 (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 12/21/2012 to 4/23/2018 for PRTA (Prothena Corporation plc), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
037.39956   0
1-7.84294 -17.95969 (1*2π)/280280 weeks
2-2.05325 -4.07375 (2*2π)/280140 weeks
3-9.40826 -5.51903 (3*2π)/28093 weeks
42.36879 -3.91527 (4*2π)/28070 weeks
5-4.01044 -1.41416 (5*2π)/28056 weeks
6.89546 2.00813 (6*2π)/28047 weeks
7.11944 -1.4029 (7*2π)/28040 weeks
8.1365 -1.13092 (8*2π)/28035 weeks
91.90673 -.70879 (9*2π)/28031 weeks
10-.40857 -.87843 (10*2π)/28028 weeks
11.15346 -1.07531 (11*2π)/28025 weeks
12-.81593 -2.6985 (12*2π)/28023 weeks
13.347 1.17277 (13*2π)/28022 weeks
14-.33038 -2.46002 (14*2π)/28020 weeks
15-1.485 1.37919 (15*2π)/28019 weeks
16.38091 -2.81342 (16*2π)/28018 weeks
17-1.10212 .6865 (17*2π)/28016 weeks
18.93774 .17465 (18*2π)/28016 weeks
19-.32006 -.1795 (19*2π)/28015 weeks
20-.2389 -.52699 (20*2π)/28014 weeks
21.02847 -1.41003 (21*2π)/28013 weeks
22.42122 .06351 (22*2π)/28013 weeks
23-.5919 -1.00913 (23*2π)/28012 weeks
24-.79143 -.32852 (24*2π)/28012 weeks
25-.49331 -.80621 (25*2π)/28011 weeks
26-.13667 .26597 (26*2π)/28011 weeks
27-.35177 -.37037 (27*2π)/28010 weeks
28-.10762 -1.00375 (28*2π)/28010 weeks
29-.93489 -.10956 (29*2π)/28010 weeks
30-.58926 .08899 (30*2π)/2809 weeks
31-.17858 -.21455 (31*2π)/2809 weeks
32-1.06823 .58226 (32*2π)/2809 weeks
33.33026 .71385 (33*2π)/2808 weeks
34.17254 -.56419 (34*2π)/2808 weeks
35-.13898 -.8292 (35*2π)/2808 weeks
36-.39701 .81711 (36*2π)/2808 weeks
37.71572 -.67268 (37*2π)/2808 weeks
38-1.35875 -.21166 (38*2π)/2807 weeks
39.31155 .03997 (39*2π)/2807 weeks
40-.23837 .27462 (40*2π)/2807 weeks
41.18715 .09051 (41*2π)/2807 weeks
42-.62443 -.4885 (42*2π)/2807 weeks
43-.10286 -.29151 (43*2π)/2807 weeks
44-.02661 .0758 (44*2π)/2806 weeks
45.01829 -.38932 (45*2π)/2806 weeks
46-.86612 -.07186 (46*2π)/2806 weeks
47-.37029 -.0294 (47*2π)/2806 weeks
48.23565 .03539 (48*2π)/2806 weeks
49-.48302 .03769 (49*2π)/2806 weeks
50-.32768 .35938 (50*2π)/2806 weeks
51-.5511 -.33591 (51*2π)/2805 weeks
52-.03234 .22045 (52*2π)/2805 weeks
53.08785 .22546 (53*2π)/2805 weeks
54-.55132 .31877 (54*2π)/2805 weeks
55.23328 .01405 (55*2π)/2805 weeks
56.08712 .02099 (56*2π)/2805 weeks
57.12681 -.03382 (57*2π)/2805 weeks
58-.66945 .19072 (58*2π)/2805 weeks
59.03768 -.00059 (59*2π)/2805 weeks
60-.30022 -.18143 (60*2π)/2805 weeks
61-.0918 .42481 (61*2π)/2805 weeks
62.14484 .05425 (62*2π)/2805 weeks
63-.10002 -.16141 (63*2π)/2804 weeks
64.20329 -.32509 (64*2π)/2804 weeks
65-.35006 .56019 (65*2π)/2804 weeks
66.01364 -.11989 (66*2π)/2804 weeks
67-.15659 -.18691 (67*2π)/2804 weeks
68-.16182 -.17478 (68*2π)/2804 weeks
69.03821 .15341 (69*2π)/2804 weeks
70-.45243 .12713 (70*2π)/2804 weeks
71-.43774 -.17401 (71*2π)/2804 weeks
72-.27817 .08358 (72*2π)/2804 weeks
73.14256 .75397 (73*2π)/2804 weeks
74-.03686 -.00088 (74*2π)/2804 weeks
75-.4219 -.02109 (75*2π)/2804 weeks
76-.08753 .06245 (76*2π)/2804 weeks
77.27543 .43658 (77*2π)/2804 weeks
78-.01883 .10914 (78*2π)/2804 weeks
79-.17102 .13872 (79*2π)/2804 weeks
80.00272 .02118 (80*2π)/2804 weeks
81.21761 .13607 (81*2π)/2803 weeks
82.0282 .06051 (82*2π)/2803 weeks
83-.23968 .06825 (83*2π)/2803 weeks
84.14549 .17799 (84*2π)/2803 weeks
85-.09445 -.0737 (85*2π)/2803 weeks
86.05375 .01001 (86*2π)/2803 weeks
87-.08876 .23247 (87*2π)/2803 weeks
88.40965 -.03699 (88*2π)/2803 weeks
89-.04325 -.03165 (89*2π)/2803 weeks
90-.10563 -.13424 (90*2π)/2803 weeks
91-.31801 -.13701 (91*2π)/2803 weeks
92.04799 .32573 (92*2π)/2803 weeks
93-.25261 .06934 (93*2π)/2803 weeks
94.05764 .05158 (94*2π)/2803 weeks
95-.06166 .0532 (95*2π)/2803 weeks
96.05289 .07611 (96*2π)/2803 weeks
97-.11822 .39782 (97*2π)/2803 weeks
98-.11567 .16565 (98*2π)/2803 weeks
99.0486 .10839 (99*2π)/2803 weeks
100.0675 -.0273 (100*2π)/2803 weeks
101-.0478 .37261 (101*2π)/2803 weeks
102.14801 -.01804 (102*2π)/2803 weeks
103.09573 .0585 (103*2π)/2803 weeks
104.10395 .02264 (104*2π)/2803 weeks
105.11212 .36152 (105*2π)/2803 weeks
106.29333 -.07807 (106*2π)/2803 weeks
107-.20993 -.34205 (107*2π)/2803 weeks
108.28053 .15501 (108*2π)/2803 weeks
109-.19615 .20325 (109*2π)/2803 weeks
110.06312 -.0441 (110*2π)/2803 weeks
111-.32393 -.12831 (111*2π)/2803 weeks
112.39605 .22397 (112*2π)/2803 weeks
113-.11258 -.06003 (113*2π)/2802 weeks
114-.20657 -.09535 (114*2π)/2802 weeks
115-.22884 -.03264 (115*2π)/2802 weeks
116.25578 .43864 (116*2π)/2802 weeks
117.13776 .05569 (117*2π)/2802 weeks
118-.16682 .14148 (118*2π)/2802 weeks
119.02075 -.02778 (119*2π)/2802 weeks
120.19683 -.07141 (120*2π)/2802 weeks
121-.11357 .12134 (121*2π)/2802 weeks
122-.01291 .27877 (122*2π)/2802 weeks
123.0481 .09617 (123*2π)/2802 weeks
124.2446 -.08758 (124*2π)/2802 weeks
125-.00965 .15588 (125*2π)/2802 weeks
126.09666 .29748 (126*2π)/2802 weeks
127.16839 .00537 (127*2π)/2802 weeks
128.12445 .01524 (128*2π)/2802 weeks
129.19469 -.07207 (129*2π)/2802 weeks
130.04644 .1528 (130*2π)/2802 weeks
131.09734 -.2548 (131*2π)/2802 weeks
132-.04407 .08164 (132*2π)/2802 weeks
133-.01439 .05238 (133*2π)/2802 weeks
134.05228 .15506 (134*2π)/2802 weeks
135.0076 -.13833 (135*2π)/2802 weeks
136.13663 .18116 (136*2π)/2802 weeks
137.09301 .27896 (137*2π)/2802 weeks
138.3442 .02218 (138*2π)/2802 weeks
139.10657 -.30866 (139*2π)/2802 weeks
140-.13227   (140*2π)/2802 weeks
141.10657 .30866 (141*2π)/2802 weeks
142.3442 -.02218 (142*2π)/2802 weeks
143.09301 -.27896 (143*2π)/2802 weeks
144.13663 -.18116 (144*2π)/2802 weeks
145.0076 .13833 (145*2π)/2802 weeks
146.05228 -.15506 (146*2π)/2802 weeks
147-.01439 -.05238 (147*2π)/2802 weeks
148-.04407 -.08164 (148*2π)/2802 weeks
149.09734 .2548 (149*2π)/2802 weeks
150.04644 -.1528 (150*2π)/2802 weeks
151.19469 .07207 (151*2π)/2802 weeks
152.12445 -.01524 (152*2π)/2802 weeks
153.16839 -.00537 (153*2π)/2802 weeks
154.09666 -.29748 (154*2π)/2802 weeks
155-.00965 -.15588 (155*2π)/2802 weeks
156.2446 .08758 (156*2π)/2802 weeks
157.0481 -.09617 (157*2π)/2802 weeks
158-.01291 -.27877 (158*2π)/2802 weeks
159-.11357 -.12134 (159*2π)/2802 weeks
160.19683 .07141 (160*2π)/2802 weeks
161.02075 .02778 (161*2π)/2802 weeks
162-.16682 -.14148 (162*2π)/2802 weeks
163.13776 -.05569 (163*2π)/2802 weeks
164.25578 -.43864 (164*2π)/2802 weeks
165-.22884 .03264 (165*2π)/2802 weeks
166-.20657 .09535 (166*2π)/2802 weeks
167-.11258 .06003 (167*2π)/2802 weeks
168.39605 -.22397 (168*2π)/2802 weeks
169-.32393 .12831 (169*2π)/2802 weeks
170.06312 .0441 (170*2π)/2802 weeks
171-.19615 -.20325 (171*2π)/2802 weeks
172.28053 -.15501 (172*2π)/2802 weeks
173-.20993 .34205 (173*2π)/2802 weeks
174.29333 .07807 (174*2π)/2802 weeks
175.11212 -.36152 (175*2π)/2802 weeks
176.10395 -.02264 (176*2π)/2802 weeks
177.09573 -.0585 (177*2π)/2802 weeks
178.14801 .01804 (178*2π)/2802 weeks
179-.0478 -.37261 (179*2π)/2802 weeks
180.0675 .0273 (180*2π)/2802 weeks
181.0486 -.10839 (181*2π)/2802 weeks
182-.11567 -.16565 (182*2π)/2802 weeks
183-.11822 -.39782 (183*2π)/2802 weeks
184.05289 -.07611 (184*2π)/2802 weeks
185-.06166 -.0532 (185*2π)/2802 weeks
186.05764 -.05158 (186*2π)/2802 weeks
187-.25261 -.06934 (187*2π)/2801 weeks
188.04799 -.32573 (188*2π)/2801 weeks
189-.31801 .13701 (189*2π)/2801 weeks
190-.10563 .13424 (190*2π)/2801 weeks
191-.04325 .03165 (191*2π)/2801 weeks
192.40965 .03699 (192*2π)/2801 weeks
193-.08876 -.23247 (193*2π)/2801 weeks
194.05375 -.01001 (194*2π)/2801 weeks
195-.09445 .0737 (195*2π)/2801 weeks
196.14549 -.17799 (196*2π)/2801 weeks
197-.23968 -.06825 (197*2π)/2801 weeks
198.0282 -.06051 (198*2π)/2801 weeks
199.21761 -.13607 (199*2π)/2801 weeks
200.00272 -.02118 (200*2π)/2801 weeks
201-.17102 -.13872 (201*2π)/2801 weeks
202-.01883 -.10914 (202*2π)/2801 weeks
203.27543 -.43658 (203*2π)/2801 weeks
204-.08753 -.06245 (204*2π)/2801 weeks
205-.4219 .02109 (205*2π)/2801 weeks
206-.03686 .00088 (206*2π)/2801 weeks
207.14256 -.75397 (207*2π)/2801 weeks
208-.27817 -.08358 (208*2π)/2801 weeks
209-.43774 .17401 (209*2π)/2801 weeks
210-.45243 -.12713 (210*2π)/2801 weeks
211.03821 -.15341 (211*2π)/2801 weeks
212-.16182 .17478 (212*2π)/2801 weeks
213-.15659 .18691 (213*2π)/2801 weeks
214.01364 .11989 (214*2π)/2801 weeks
215-.35006 -.56019 (215*2π)/2801 weeks
216.20329 .32509 (216*2π)/2801 weeks
217-.10002 .16141 (217*2π)/2801 weeks
218.14484 -.05425 (218*2π)/2801 weeks
219-.0918 -.42481 (219*2π)/2801 weeks
220-.30022 .18143 (220*2π)/2801 weeks
221.03768 .00059 (221*2π)/2801 weeks
222-.66945 -.19072 (222*2π)/2801 weeks
223.12681 .03382 (223*2π)/2801 weeks
224.08712 -.02099 (224*2π)/2801 weeks
225.23328 -.01405 (225*2π)/2801 weeks
226-.55132 -.31877 (226*2π)/2801 weeks
227.08785 -.22546 (227*2π)/2801 weeks
228-.03234 -.22045 (228*2π)/2801 weeks
229-.5511 .33591 (229*2π)/2801 weeks
230-.32768 -.35938 (230*2π)/2801 weeks
231-.48302 -.03769 (231*2π)/2801 weeks
232.23565 -.03539 (232*2π)/2801 weeks
233-.37029 .0294 (233*2π)/2801 weeks
234-.86612 .07186 (234*2π)/2801 weeks
235.01829 .38932 (235*2π)/2801 weeks
236-.02661 -.0758 (236*2π)/2801 weeks
237-.10286 .29151 (237*2π)/2801 weeks
238-.62443 .4885 (238*2π)/2801 weeks
239.18715 -.09051 (239*2π)/2801 weeks
240-.23837 -.27462 (240*2π)/2801 weeks
241.31155 -.03997 (241*2π)/2801 weeks
242-1.35875 .21166 (242*2π)/2801 weeks
243.71572 .67268 (243*2π)/2801 weeks
244-.39701 -.81711 (244*2π)/2801 weeks
245-.13898 .8292 (245*2π)/2801 weeks
246.17254 .56419 (246*2π)/2801 weeks
247.33026 -.71385 (247*2π)/2801 weeks
248-1.06823 -.58226 (248*2π)/2801 weeks
249-.17858 .21455 (249*2π)/2801 weeks
250-.58926 -.08899 (250*2π)/2801 weeks
251-.93489 .10956 (251*2π)/2801 weeks
252-.10762 1.00375 (252*2π)/2801 weeks
253-.35177 .37037 (253*2π)/2801 weeks
254-.13667 -.26597 (254*2π)/2801 weeks
255-.49331 .80621 (255*2π)/2801 weeks
256-.79143 .32852 (256*2π)/2801 weeks
257-.5919 1.00913 (257*2π)/2801 weeks
258.42122 -.06351 (258*2π)/2801 weeks
259.02847 1.41003 (259*2π)/2801 weeks
260-.2389 .52699 (260*2π)/2801 weeks
261-.32006 .1795 (261*2π)/2801 weeks
262.93774 -.17465 (262*2π)/2801 weeks
263-1.10212 -.6865 (263*2π)/2801 weeks
264.38091 2.81342 (264*2π)/2801 weeks
265-1.485 -1.37919 (265*2π)/2801 weeks
266-.33038 2.46002 (266*2π)/2801 weeks
267.347 -1.17277 (267*2π)/2801 weeks
268-.81593 2.6985 (268*2π)/2801 weeks
269.15346 1.07531 (269*2π)/2801 weeks
270-.40857 .87843 (270*2π)/2801 weeks
2711.90673 .70879 (271*2π)/2801 weeks
272.1365 1.13092 (272*2π)/2801 weeks
273.11944 1.4029 (273*2π)/2801 weeks
274.89546 -2.00813 (274*2π)/2801 weeks
275-4.01044 1.41416 (275*2π)/2801 weeks
2762.36879 3.91527 (276*2π)/2801 weeks
277-9.40826 5.51903 (277*2π)/2801 weeks
278-2.05325 4.07375 (278*2π)/2801 weeks