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Fourier Analysis of RARE (Ultragenyx Pharmaceutical Inc.)


RARE (Ultragenyx Pharmaceutical Inc.) appears to have interesting cyclic behaviour every 8 weeks (3.6903*sine), 16 weeks (2.7663*cosine), and 13 weeks (2.7258*cosine).

RARE (Ultragenyx Pharmaceutical Inc.) has an average price of 67.52 (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 1/31/2014 to 1/9/2017 for RARE (Ultragenyx Pharmaceutical Inc.), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
067.52461   0 
1-18.99121 -13.17866 (1*2π)/155155 weeks
215.19198 2.30052 (2*2π)/15578 weeks
3-5.39017 -8.72672 (3*2π)/15552 weeks
43.89759 -2.035 (4*2π)/15539 weeks
5.29449 -1.24467 (5*2π)/15531 weeks
61.95426 -1.25987 (6*2π)/15526 weeks
7-4.86738 3.26045 (7*2π)/15522 weeks
83.37007 -.80458 (8*2π)/15519 weeks
9-1.40524 -3.27541 (9*2π)/15517 weeks
10-2.76632 .61357 (10*2π)/15516 weeks
11-.99809 -.12787 (11*2π)/15514 weeks
12-2.72584 -2.09321 (12*2π)/15513 weeks
13-1.01089 1.06338 (13*2π)/15512 weeks
14.40994 -1.50799 (14*2π)/15511 weeks
15-.71795 -.26796 (15*2π)/15510 weeks
16.08057 .13804 (16*2π)/15510 weeks
17-.20472 .82144 (17*2π)/1559 weeks
18.06429 -1.39531 (18*2π)/1559 weeks
19.05944 1.59202 (19*2π)/1558 weeks
201.92583 -3.69032 (20*2π)/1558 weeks
21-2.54232 -1.01291 (21*2π)/1557 weeks
22.69972 -.93759 (22*2π)/1557 weeks
23-1.00024 -.40331 (23*2π)/1557 weeks
24-.33344 -1.27195 (24*2π)/1556 weeks
25-1.86207 -.7375 (25*2π)/1556 weeks
26-1.03473 -.6538 (26*2π)/1556 weeks
27-.16384 -.96379 (27*2π)/1556 weeks
28-.02802 -.72222 (28*2π)/1556 weeks
29-.55708 -.79809 (29*2π)/1555 weeks
30-.30369 .04227 (30*2π)/1555 weeks
31-.50436 .06555 (31*2π)/1555 weeks
32.38381 .17805 (32*2π)/1555 weeks
33.35592 .48861 (33*2π)/1555 weeks
34.27617 -1.01426 (34*2π)/1555 weeks
35-.46074 .5335 (35*2π)/1554 weeks
36.3038 -.59492 (36*2π)/1554 weeks
37.10449 -.22895 (37*2π)/1554 weeks
38-.9241 -.68859 (38*2π)/1554 weeks
39.20772 -.46359 (39*2π)/1554 weeks
40-1.2388 -1.44776 (40*2π)/1554 weeks
41-.33295 .34109 (41*2π)/1554 weeks
42-.72309 -1.2296 (42*2π)/1554 weeks
43-.9139 -.74601 (43*2π)/1554 weeks
44.73793 -.53652 (44*2π)/1554 weeks
45.20296 -.55708 (45*2π)/1553 weeks
46-.27808 -.32973 (46*2π)/1553 weeks
47.14497 -.06117 (47*2π)/1553 weeks
48.4492 .04998 (48*2π)/1553 weeks
49.1192 .09635 (49*2π)/1553 weeks
50.0143 .25341 (50*2π)/1553 weeks
51.65402 -.05629 (51*2π)/1553 weeks
52-.97061 .04401 (52*2π)/1553 weeks
53.17456 -.7805 (53*2π)/1553 weeks
54-.76552 .1432 (54*2π)/1553 weeks
55-.32086 -.07739 (55*2π)/1553 weeks
56-.63604 .0221 (56*2π)/1553 weeks
57-.14759 .23416 (57*2π)/1553 weeks
58-.38133 .29941 (58*2π)/1553 weeks
59-.36372 1.04789 (59*2π)/1553 weeks
60.59753 -.7778 (60*2π)/1553 weeks
61-.40217 .69038 (61*2π)/1553 weeks
621.14023 -.56679 (62*2π)/1553 weeks
63-.08128 -.0309 (63*2π)/1552 weeks
64.31316 .28721 (64*2π)/1552 weeks
65-.5013 -.45623 (65*2π)/1552 weeks
66-.23511 .35668 (66*2π)/1552 weeks
67-.88693 -.27496 (67*2π)/1552 weeks
68.06769 .31783 (68*2π)/1552 weeks
69-.46329 -.43975 (69*2π)/1552 weeks
70-.55328 .57108 (70*2π)/1552 weeks
71.38088 -.02771 (71*2π)/1552 weeks
72-.80564 .31964 (72*2π)/1552 weeks
73-.0948 .23319 (73*2π)/1552 weeks
74-.29928 .43457 (74*2π)/1552 weeks
75.03328 .22971 (75*2π)/1552 weeks
76.07388 -.28155 (76*2π)/1552 weeks
77.22948 -.0526 (77*2π)/1552 weeks
78.22948 .0526 (78*2π)/1552 weeks
79.07388 .28155 (79*2π)/1552 weeks
80.03328 -.22971 (80*2π)/1552 weeks
81-.29928 -.43457 (81*2π)/1552 weeks
82-.0948 -.23319 (82*2π)/1552 weeks
83-.80564 -.31964 (83*2π)/1552 weeks
84.38088 .02771 (84*2π)/1552 weeks
85-.55328 -.57108 (85*2π)/1552 weeks
86-.46329 .43975 (86*2π)/1552 weeks
87.06769 -.31783 (87*2π)/1552 weeks
88-.88693 .27496 (88*2π)/1552 weeks
89-.23511 -.35668 (89*2π)/1552 weeks
90-.5013 .45623 (90*2π)/1552 weeks
91.31316 -.28721 (91*2π)/1552 weeks
92-.08128 .0309 (92*2π)/1552 weeks
931.14023 .56679 (93*2π)/1552 weeks
94-.40217 -.69038 (94*2π)/1552 weeks
95.59753 .7778 (95*2π)/1552 weeks
96-.36372 -1.04789 (96*2π)/1552 weeks
97-.38133 -.29941 (97*2π)/1552 weeks
98-.14759 -.23416 (98*2π)/1552 weeks
99-.63604 -.0221 (99*2π)/1552 weeks
100-.32086 .07739 (100*2π)/1552 weeks
101-.76552 -.1432 (101*2π)/1552 weeks
102.17456 .7805 (102*2π)/1552 weeks
103-.97061 -.04401 (103*2π)/1552 weeks
104.65402 .05629 (104*2π)/1551 weeks
105.0143 -.25341 (105*2π)/1551 weeks
106.1192 -.09635 (106*2π)/1551 weeks
107.4492 -.04998 (107*2π)/1551 weeks
108.14497 .06117 (108*2π)/1551 weeks
109-.27808 .32973 (109*2π)/1551 weeks
110.20296 .55708 (110*2π)/1551 weeks
111.73793 .53652 (111*2π)/1551 weeks
112-.9139 .74601 (112*2π)/1551 weeks
113-.72309 1.2296 (113*2π)/1551 weeks
114-.33295 -.34109 (114*2π)/1551 weeks
115-1.2388 1.44776 (115*2π)/1551 weeks
116.20772 .46359 (116*2π)/1551 weeks
117-.9241 .68859 (117*2π)/1551 weeks
118.10449 .22895 (118*2π)/1551 weeks
119.3038 .59492 (119*2π)/1551 weeks
120-.46074 -.5335 (120*2π)/1551 weeks
121.27617 1.01426 (121*2π)/1551 weeks
122.35592 -.48861 (122*2π)/1551 weeks
123.38381 -.17805 (123*2π)/1551 weeks
124-.50436 -.06555 (124*2π)/1551 weeks
125-.30369 -.04227 (125*2π)/1551 weeks
126-.55708 .79809 (126*2π)/1551 weeks
127-.02802 .72222 (127*2π)/1551 weeks
128-.16384 .96379 (128*2π)/1551 weeks
129-1.03473 .6538 (129*2π)/1551 weeks
130-1.86207 .7375 (130*2π)/1551 weeks
131-.33344 1.27195 (131*2π)/1551 weeks
132-1.00024 .40331 (132*2π)/1551 weeks
133.69972 .93759 (133*2π)/1551 weeks
134-2.54232 1.01291 (134*2π)/1551 weeks
1351.92583 3.69032 (135*2π)/1551 weeks
136.05944 -1.59202 (136*2π)/1551 weeks
137.06429 1.39531 (137*2π)/1551 weeks
138-.20472 -.82144 (138*2π)/1551 weeks
139.08057 -.13804 (139*2π)/1551 weeks
140-.71795 .26796 (140*2π)/1551 weeks
141.40994 1.50799 (141*2π)/1551 weeks
142-1.01089 -1.06338 (142*2π)/1551 weeks
143-2.72584 2.09321 (143*2π)/1551 weeks
144-.99809 .12787 (144*2π)/1551 weeks
145-2.76632 -.61357 (145*2π)/1551 weeks
146-1.40524 3.27541 (146*2π)/1551 weeks
1473.37007 .80458 (147*2π)/1551 weeks
148-4.86738 -3.26045 (148*2π)/1551 weeks
1491.95426 1.25987 (149*2π)/1551 weeks
150.29449 1.24467 (150*2π)/1551 weeks
1513.89759 2.035 (151*2π)/1551 weeks
152-5.39017 8.72672 (152*2π)/1551 weeks
15315.19198 -2.30052 (153*2π)/1551 weeks

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