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Fourier Analysis of AMPH (Amphastar Pharmaceuticals, Inc.)


AMPH (Amphastar Pharmaceuticals, Inc.) appears to have interesting cyclic behaviour every 15 weeks (.4534*sine), 14 weeks (.4221*sine), and 12 weeks (.2865*cosine).

AMPH (Amphastar Pharmaceuticals, Inc.) has an average price of 14.34 (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 6/25/2014 to 4/24/2017 for AMPH (Amphastar Pharmaceuticals, Inc.), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
014.3447   0 
1.00996 -1.87271 (1*2π)/149149 weeks
2-1.92342 -2.70593 (2*2π)/14975 weeks
3-.32742 -.0479 (3*2π)/14950 weeks
4-.05708 .28662 (4*2π)/14937 weeks
5-.47754 -.31683 (5*2π)/14930 weeks
6.25614 .33848 (6*2π)/14925 weeks
7-.40337 -.47675 (7*2π)/14921 weeks
8.3932 -.2507 (8*2π)/14919 weeks
9-.2719 -.30559 (9*2π)/14917 weeks
10-.15195 -.45339 (10*2π)/14915 weeks
11-.12619 -.4221 (11*2π)/14914 weeks
12.28652 .21937 (12*2π)/14912 weeks
13.15953 -.0751 (13*2π)/14911 weeks
14.25817 -.21693 (14*2π)/14911 weeks
15.00299 -.08787 (15*2π)/14910 weeks
16.08398 -.35497 (16*2π)/1499 weeks
17-.10023 -.0843 (17*2π)/1499 weeks
18-.01434 -.16101 (18*2π)/1498 weeks
19-.00943 -.13758 (19*2π)/1498 weeks
20-.19841 -.10599 (20*2π)/1497 weeks
21.00176 -.01581 (21*2π)/1497 weeks
22-.21419 -.07186 (22*2π)/1497 weeks
23-.19817 .10377 (23*2π)/1496 weeks
24.20495 .11877 (24*2π)/1496 weeks
25.09597 -.17721 (25*2π)/1496 weeks
26-.0776 -.12944 (26*2π)/1496 weeks
27-.13295 .01783 (27*2π)/1496 weeks
28.07698 -.1588 (28*2π)/1495 weeks
29-.03256 -.00398 (29*2π)/1495 weeks
30-.03994 -.14675 (30*2π)/1495 weeks
31.00986 -.01448 (31*2π)/1495 weeks
32.0319 -.12425 (32*2π)/1495 weeks
33.01518 -.03967 (33*2π)/1495 weeks
34-.21017 -.0546 (34*2π)/1494 weeks
35-.11736 .10877 (35*2π)/1494 weeks
36.05374 .08803 (36*2π)/1494 weeks
37.03413 -.12915 (37*2π)/1494 weeks
38.06452 -.01468 (38*2π)/1494 weeks
39-.09181 -.12833 (39*2π)/1494 weeks
40-.01228 -.077 (40*2π)/1494 weeks
41-.08799 -.0947 (41*2π)/1494 weeks
42.05776 -.093 (42*2π)/1494 weeks
43-.06773 -.05955 (43*2π)/1493 weeks
44.015 -.09168 (44*2π)/1493 weeks
45.00772 -.12296 (45*2π)/1493 weeks
46-.05857 -.02841 (46*2π)/1493 weeks
47.00849 .04173 (47*2π)/1493 weeks
48-.04253 -.08503 (48*2π)/1493 weeks
49-.0209 -.00099 (49*2π)/1493 weeks
50-.03593 .04994 (50*2π)/1493 weeks
51-.02748 -.04741 (51*2π)/1493 weeks
52.04074 .08113 (52*2π)/1493 weeks
53-.02067 .11793 (53*2π)/1493 weeks
54.10022 -.03126 (54*2π)/1493 weeks
55.02673 -.05765 (55*2π)/1493 weeks
56-.02659 -.09812 (56*2π)/1493 weeks
57-.1025 -.07516 (57*2π)/1493 weeks
58-.02344 -.01254 (58*2π)/1493 weeks
59-.05059 .09702 (59*2π)/1493 weeks
60-.01669 -.07361 (60*2π)/1492 weeks
61-.02177 -.04507 (61*2π)/1492 weeks
62-.14989 -.01986 (62*2π)/1492 weeks
63-.05543 -.01351 (63*2π)/1492 weeks
64-.01683 -.01979 (64*2π)/1492 weeks
65.04762 .01123 (65*2π)/1492 weeks
66.03743 .04436 (66*2π)/1492 weeks
67-.05037 -.05232 (67*2π)/1492 weeks
68.0302 .00374 (68*2π)/1492 weeks
69-.01218 .01521 (69*2π)/1492 weeks
70.04329 -.02692 (70*2π)/1492 weeks
71-.03699 -.04116 (71*2π)/1492 weeks
72-.01508 -.03726 (72*2π)/1492 weeks
73-.07469 .04264 (73*2π)/1492 weeks
74-.0962 .00808 (74*2π)/1492 weeks
75-.0962 -.00808 (75*2π)/1492 weeks
76-.07469 -.04264 (76*2π)/1492 weeks
77-.01508 .03726 (77*2π)/1492 weeks
78-.03699 .04116 (78*2π)/1492 weeks
79.04329 .02692 (79*2π)/1492 weeks
80-.01218 -.01521 (80*2π)/1492 weeks
81.0302 -.00374 (81*2π)/1492 weeks
82-.05037 .05232 (82*2π)/1492 weeks
83.03743 -.04436 (83*2π)/1492 weeks
84.04762 -.01123 (84*2π)/1492 weeks
85-.01683 .01979 (85*2π)/1492 weeks
86-.05543 .01351 (86*2π)/1492 weeks
87-.14989 .01986 (87*2π)/1492 weeks
88-.02177 .04507 (88*2π)/1492 weeks
89-.01669 .07361 (89*2π)/1492 weeks
90-.05059 -.09702 (90*2π)/1492 weeks
91-.02344 .01254 (91*2π)/1492 weeks
92-.1025 .07516 (92*2π)/1492 weeks
93-.02659 .09812 (93*2π)/1492 weeks
94.02673 .05765 (94*2π)/1492 weeks
95.10022 .03126 (95*2π)/1492 weeks
96-.02067 -.11793 (96*2π)/1492 weeks
97.04074 -.08113 (97*2π)/1492 weeks
98-.02748 .04741 (98*2π)/1492 weeks
99-.03593 -.04994 (99*2π)/1492 weeks
100-.0209 .00099 (100*2π)/1491 weeks
101-.04253 .08503 (101*2π)/1491 weeks
102.00849 -.04173 (102*2π)/1491 weeks
103-.05857 .02841 (103*2π)/1491 weeks
104.00772 .12296 (104*2π)/1491 weeks
105.015 .09168 (105*2π)/1491 weeks
106-.06773 .05955 (106*2π)/1491 weeks
107.05776 .093 (107*2π)/1491 weeks
108-.08799 .0947 (108*2π)/1491 weeks
109-.01228 .077 (109*2π)/1491 weeks
110-.09181 .12833 (110*2π)/1491 weeks
111.06452 .01468 (111*2π)/1491 weeks
112.03413 .12915 (112*2π)/1491 weeks
113.05374 -.08803 (113*2π)/1491 weeks
114-.11736 -.10877 (114*2π)/1491 weeks
115-.21017 .0546 (115*2π)/1491 weeks
116.01518 .03967 (116*2π)/1491 weeks
117.0319 .12425 (117*2π)/1491 weeks
118.00986 .01448 (118*2π)/1491 weeks
119-.03994 .14675 (119*2π)/1491 weeks
120-.03256 .00398 (120*2π)/1491 weeks
121.07698 .1588 (121*2π)/1491 weeks
122-.13295 -.01783 (122*2π)/1491 weeks
123-.0776 .12944 (123*2π)/1491 weeks
124.09597 .17721 (124*2π)/1491 weeks
125.20495 -.11877 (125*2π)/1491 weeks
126-.19817 -.10377 (126*2π)/1491 weeks
127-.21419 .07186 (127*2π)/1491 weeks
128.00176 .01581 (128*2π)/1491 weeks
129-.19841 .10599 (129*2π)/1491 weeks
130-.00943 .13758 (130*2π)/1491 weeks
131-.01434 .16101 (131*2π)/1491 weeks
132-.10023 .0843 (132*2π)/1491 weeks
133.08398 .35497 (133*2π)/1491 weeks
134.00299 .08787 (134*2π)/1491 weeks
135.25817 .21693 (135*2π)/1491 weeks
136.15953 .0751 (136*2π)/1491 weeks
137.28652 -.21937 (137*2π)/1491 weeks
138-.12619 .4221 (138*2π)/1491 weeks
139-.15195 .45339 (139*2π)/1491 weeks
140-.2719 .30559 (140*2π)/1491 weeks
141.3932 .2507 (141*2π)/1491 weeks
142-.40337 .47675 (142*2π)/1491 weeks
143.25614 -.33848 (143*2π)/1491 weeks
144-.47754 .31683 (144*2π)/1491 weeks
145-.05708 -.28662 (145*2π)/1491 weeks
146-.32742 .0479 (146*2π)/1491 weeks
147-1.92342 2.70593 (147*2π)/1491 weeks



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