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# Fourier Analysis of RARE (Ultragenyx Pharmaceutical Inc)

RARE (Ultragenyx Pharmaceutical Inc) appears to have interesting cyclic behaviour every 22 weeks (5.2422*cosine), 15 weeks (2.7777*cosine), and 8 weeks (2.6544*cosine).

RARE (Ultragenyx Pharmaceutical Inc) has an average price of 64.98 (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 1/31/2014 to 3/12/2018 for RARE (Ultragenyx Pharmaceutical Inc), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
064.98419   0
1-18.85563 2.15713 (1*2π)/216216 weeks
2-2.20454 -12.58055 (2*2π)/216108 weeks
36.77741 10.2746 (3*2π)/21672 weeks
4-5.09242 -2.66838 (4*2π)/21654 weeks
52.41593 -2.62132 (5*2π)/21643 weeks
62.00558 1.93553 (6*2π)/21636 weeks
71.37483 .42938 (7*2π)/21631 weeks
81.39448 -.86605 (8*2π)/21627 weeks
91.4539 1.98703 (9*2π)/21624 weeks
10-5.24219 1.4182 (10*2π)/21622 weeks
112.58307 -.15656 (11*2π)/21620 weeks
12-1.34968 1.32104 (12*2π)/21618 weeks
131.64573 -1.22693 (13*2π)/21617 weeks
14-2.77766 .42463 (14*2π)/21615 weeks
15-.62978 .86235 (15*2π)/21614 weeks
16-.61457 .7735 (16*2π)/21614 weeks
17-.8326 -2.05272 (17*2π)/21613 weeks
18-.15269 1.41809 (18*2π)/21612 weeks
19-.09457 -1.11228 (19*2π)/21611 weeks
20.83904 -.62091 (20*2π)/21611 weeks
21-.79215 -.54149 (21*2π)/21610 weeks
22-.01064 .22822 (22*2π)/21610 weeks
23.13898 .37079 (23*2π)/2169 weeks
24-.31965 .73779 (24*2π)/2169 weeks
25.18224 -1.30904 (25*2π)/2169 weeks
26.43913 -.04346 (26*2π)/2168 weeks
27-2.16408 .78935 (27*2π)/2168 weeks
282.65444 -1.97198 (28*2π)/2168 weeks
29-1.83629 .14788 (29*2π)/2167 weeks
30-.36695 -1.14775 (30*2π)/2167 weeks
31.62433 .36603 (31*2π)/2167 weeks
32-.37539 -.12014 (32*2π)/2167 weeks
33-.56061 -.68942 (33*2π)/2167 weeks
34.06331 .00019 (34*2π)/2166 weeks
35-1.32779 -.64145 (35*2π)/2166 weeks
36-.34938 .11166 (36*2π)/2166 weeks
37.14232 -.84377 (37*2π)/2166 weeks
38.09255 -.79292 (38*2π)/2166 weeks
39-.02168 -.49073 (39*2π)/2166 weeks
40-.10472 -.11708 (40*2π)/2165 weeks
41.37292 -.77817 (41*2π)/2165 weeks
42-.54875 -.15876 (42*2π)/2165 weeks
43-.14446 .40896 (43*2π)/2165 weeks
44.37753 -.58385 (44*2π)/2165 weeks
45-.16032 -.06638 (45*2π)/2165 weeks
46.10081 .4288 (46*2π)/2165 weeks
47-.61247 -.47213 (47*2π)/2165 weeks
48.43536 .35974 (48*2π)/2165 weeks
49-.49023 .44313 (49*2π)/2164 weeks
50.13077 -.42458 (50*2π)/2164 weeks
51-.13237 .13167 (51*2π)/2164 weeks
52.07318 .45433 (52*2π)/2164 weeks
53-.56129 -.38749 (53*2π)/2164 weeks
54.02093 -.2044 (54*2π)/2164 weeks
55-.03428 .62805 (55*2π)/2164 weeks
56.14568 -1.41305 (56*2π)/2164 weeks
57.00556 .0703 (57*2π)/2164 weeks
58-.77726 -.29807 (58*2π)/2164 weeks
59.21392 -.67171 (59*2π)/2164 weeks
60-.54865 -.74272 (60*2π)/2164 weeks
61.56858 -.81265 (61*2π)/2164 weeks
62.13891 -.16254 (62*2π)/2163 weeks
63.3187 -.30253 (63*2π)/2163 weeks
64-.15041 -.0819 (64*2π)/2163 weeks
65.44507 -.17471 (65*2π)/2163 weeks
66.19728 -.28519 (66*2π)/2163 weeks
67.35676 .03357 (67*2π)/2163 weeks
68.1555 -.00345 (68*2π)/2163 weeks
69.05921 -.0396 (69*2π)/2163 weeks
70-.25304 .10421 (70*2π)/2163 weeks
71.29388 -.04487 (71*2π)/2163 weeks
72-.53322 .80769 (72*2π)/2163 weeks
73-.40539 -.10173 (73*2π)/2163 weeks
74.34884 -.31989 (74*2π)/2163 weeks
75-.29723 .63759 (75*2π)/2163 weeks
76.13956 .03478 (76*2π)/2163 weeks
77.05543 -.09102 (77*2π)/2163 weeks
78-.33816 .18788 (78*2π)/2163 weeks
79.39453 .12509 (79*2π)/2163 weeks
80.18168 -.02078 (80*2π)/2163 weeks
81-.11629 .1149 (81*2π)/2163 weeks
82.49504 .52549 (82*2π)/2163 weeks
83-.5422 -.91217 (83*2π)/2163 weeks
84.51819 -.19771 (84*2π)/2163 weeks
85-.26773 .44146 (85*2π)/2163 weeks
86.07185 -.96533 (86*2π)/2163 weeks
87.33205 .56522 (87*2π)/2162 weeks
88.18166 -.031 (88*2π)/2162 weeks
89.28119 -.02589 (89*2π)/2162 weeks
90-.50046 .28168 (90*2π)/2162 weeks
91.06408 -.28058 (91*2π)/2162 weeks
92-.28666 .31407 (92*2π)/2162 weeks
93-.55477 .36491 (93*2π)/2162 weeks
94.15833 -.34206 (94*2π)/2162 weeks
95-.0645 .29327 (95*2π)/2162 weeks
96-.38502 -.04775 (96*2π)/2162 weeks
97.54312 .35112 (97*2π)/2162 weeks
98-.21874 -.29061 (98*2π)/2162 weeks
99.36308 -.24516 (99*2π)/2162 weeks
100-.44101 .3487 (100*2π)/2162 weeks
101-.25607 -.22404 (101*2π)/2162 weeks
102-.12511 .1779 (102*2π)/2162 weeks
103-.04446 .24311 (103*2π)/2162 weeks
104-.17257 -.22777 (104*2π)/2162 weeks
105-.29231 .27045 (105*2π)/2162 weeks
106.37286 -.24039 (106*2π)/2162 weeks
107.05973 -.53192 (107*2π)/2162 weeks
108-.40431   (108*2π)/2162 weeks
109.05973 .53192 (109*2π)/2162 weeks
110.37286 .24039 (110*2π)/2162 weeks
111-.29231 -.27045 (111*2π)/2162 weeks
112-.17257 .22777 (112*2π)/2162 weeks
113-.04446 -.24311 (113*2π)/2162 weeks
114-.12511 -.1779 (114*2π)/2162 weeks
115-.25607 .22404 (115*2π)/2162 weeks
116-.44101 -.3487 (116*2π)/2162 weeks
117.36308 .24516 (117*2π)/2162 weeks
118-.21874 .29061 (118*2π)/2162 weeks
119.54312 -.35112 (119*2π)/2162 weeks
120-.38502 .04775 (120*2π)/2162 weeks
121-.0645 -.29327 (121*2π)/2162 weeks
122.15833 .34206 (122*2π)/2162 weeks
123-.55477 -.36491 (123*2π)/2162 weeks
124-.28666 -.31407 (124*2π)/2162 weeks
125.06408 .28058 (125*2π)/2162 weeks
126-.50046 -.28168 (126*2π)/2162 weeks
127.28119 .02589 (127*2π)/2162 weeks
128.18166 .031 (128*2π)/2162 weeks
129.33205 -.56522 (129*2π)/2162 weeks
130.07185 .96533 (130*2π)/2162 weeks
131-.26773 -.44146 (131*2π)/2162 weeks
132.51819 .19771 (132*2π)/2162 weeks
133-.5422 .91217 (133*2π)/2162 weeks
134.49504 -.52549 (134*2π)/2162 weeks
135-.11629 -.1149 (135*2π)/2162 weeks
136.18168 .02078 (136*2π)/2162 weeks
137.39453 -.12509 (137*2π)/2162 weeks
138-.33816 -.18788 (138*2π)/2162 weeks
139.05543 .09102 (139*2π)/2162 weeks
140.13956 -.03478 (140*2π)/2162 weeks
141-.29723 -.63759 (141*2π)/2162 weeks
142.34884 .31989 (142*2π)/2162 weeks
143-.40539 .10173 (143*2π)/2162 weeks
144-.53322 -.80769 (144*2π)/2162 weeks
145.29388 .04487 (145*2π)/2161 weeks
146-.25304 -.10421 (146*2π)/2161 weeks
147.05921 .0396 (147*2π)/2161 weeks
148.1555 .00345 (148*2π)/2161 weeks
149.35676 -.03357 (149*2π)/2161 weeks
150.19728 .28519 (150*2π)/2161 weeks
151.44507 .17471 (151*2π)/2161 weeks
152-.15041 .0819 (152*2π)/2161 weeks
153.3187 .30253 (153*2π)/2161 weeks
154.13891 .16254 (154*2π)/2161 weeks
155.56858 .81265 (155*2π)/2161 weeks
156-.54865 .74272 (156*2π)/2161 weeks
157.21392 .67171 (157*2π)/2161 weeks
158-.77726 .29807 (158*2π)/2161 weeks
159.00556 -.0703 (159*2π)/2161 weeks
160.14568 1.41305 (160*2π)/2161 weeks
161-.03428 -.62805 (161*2π)/2161 weeks
162.02093 .2044 (162*2π)/2161 weeks
163-.56129 .38749 (163*2π)/2161 weeks
164.07318 -.45433 (164*2π)/2161 weeks
165-.13237 -.13167 (165*2π)/2161 weeks
166.13077 .42458 (166*2π)/2161 weeks
167-.49023 -.44313 (167*2π)/2161 weeks
168.43536 -.35974 (168*2π)/2161 weeks
169-.61247 .47213 (169*2π)/2161 weeks
170.10081 -.4288 (170*2π)/2161 weeks
171-.16032 .06638 (171*2π)/2161 weeks
172.37753 .58385 (172*2π)/2161 weeks
173-.14446 -.40896 (173*2π)/2161 weeks
174-.54875 .15876 (174*2π)/2161 weeks
175.37292 .77817 (175*2π)/2161 weeks
176-.10472 .11708 (176*2π)/2161 weeks
177-.02168 .49073 (177*2π)/2161 weeks
178.09255 .79292 (178*2π)/2161 weeks
179.14232 .84377 (179*2π)/2161 weeks
180-.34938 -.11166 (180*2π)/2161 weeks
181-1.32779 .64145 (181*2π)/2161 weeks
182.06331 -.00019 (182*2π)/2161 weeks
183-.56061 .68942 (183*2π)/2161 weeks
184-.37539 .12014 (184*2π)/2161 weeks
185.62433 -.36603 (185*2π)/2161 weeks
186-.36695 1.14775 (186*2π)/2161 weeks
187-1.83629 -.14788 (187*2π)/2161 weeks
1882.65444 1.97198 (188*2π)/2161 weeks
189-2.16408 -.78935 (189*2π)/2161 weeks
190.43913 .04346 (190*2π)/2161 weeks
191.18224 1.30904 (191*2π)/2161 weeks
192-.31965 -.73779 (192*2π)/2161 weeks
193.13898 -.37079 (193*2π)/2161 weeks
194-.01064 -.22822 (194*2π)/2161 weeks
195-.79215 .54149 (195*2π)/2161 weeks
196.83904 .62091 (196*2π)/2161 weeks
197-.09457 1.11228 (197*2π)/2161 weeks
198-.15269 -1.41809 (198*2π)/2161 weeks
199-.8326 2.05272 (199*2π)/2161 weeks
200-.61457 -.7735 (200*2π)/2161 weeks
201-.62978 -.86235 (201*2π)/2161 weeks
202-2.77766 -.42463 (202*2π)/2161 weeks
2031.64573 1.22693 (203*2π)/2161 weeks
204-1.34968 -1.32104 (204*2π)/2161 weeks
2052.58307 .15656 (205*2π)/2161 weeks
206-5.24219 -1.4182 (206*2π)/2161 weeks
2071.4539 -1.98703 (207*2π)/2161 weeks
2081.39448 .86605 (208*2π)/2161 weeks
2091.37483 -.42938 (209*2π)/2161 weeks
2102.00558 -1.93553 (210*2π)/2161 weeks
2112.41593 2.62132 (211*2π)/2161 weeks
212-5.09242 2.66838 (212*2π)/2161 weeks
2136.77741 -10.2746 (213*2π)/2161 weeks
214-2.20454 12.58055 (214*2π)/2161 weeks