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Fourier Analysis of AMPH (Amphastar Pharmaceuticals, Inc.)


AMPH (Amphastar Pharmaceuticals, Inc.) appears to have interesting cyclic behaviour every 13 weeks (.6374*sine), 13 weeks (.464*cosine), and 6 weeks (.3322*cosine).

AMPH (Amphastar Pharmaceuticals, Inc.) has an average price of 14.06 (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 12/5/2016 for AMPH (Amphastar Pharmaceuticals, Inc.), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
014.05651   0 
1.25696 -.94898 (1*2π)/129129 weeks
2.55118 -3.15279 (2*2π)/12965 weeks
3.031 -1.07031 (3*2π)/12943 weeks
4-.66619 -.49206 (4*2π)/12932 weeks
5.35249 -.47454 (5*2π)/12926 weeks
6-.7182 -.79123 (6*2π)/12922 weeks
7.26467 -.36033 (7*2π)/12918 weeks
8-.2982 -.5558 (8*2π)/12916 weeks
9-.02533 -.59126 (9*2π)/12914 weeks
10.46401 -.63744 (10*2π)/12913 weeks
11-.09626 -.38013 (11*2π)/12912 weeks
12.00296 -.43072 (12*2π)/12911 weeks
13-.19151 -.16361 (13*2π)/12910 weeks
14.05437 -.37215 (14*2π)/1299 weeks
15-.21075 -.26861 (15*2π)/1299 weeks
16-.12114 -.22189 (16*2π)/1298 weeks
17-.16393 -.08389 (17*2π)/1298 weeks
18-.0031 -.21526 (18*2π)/1297 weeks
19-.27384 -.20623 (19*2π)/1297 weeks
20-.33223 -.12692 (20*2π)/1296 weeks
21-.12312 .11386 (21*2π)/1296 weeks
22.00716 .00737 (22*2π)/1296 weeks
23.0136 -.04683 (23*2π)/1296 weeks
24-.06607 -.29202 (24*2π)/1295 weeks
25-.06766 -.02931 (25*2π)/1295 weeks
26-.09485 -.19254 (26*2π)/1295 weeks
27-.09515 -.03223 (27*2π)/1295 weeks
28.00704 -.05741 (28*2π)/1295 weeks
29-.07051 .1017 (29*2π)/1294 weeks
30.03059 -.03051 (30*2π)/1294 weeks
31.03072 -.10851 (31*2π)/1294 weeks
32-.07316 -.22903 (32*2π)/1294 weeks
33-.03229 -.03158 (33*2π)/1294 weeks
34-.10138 -.19643 (34*2π)/1294 weeks
35-.08703 -.09585 (35*2π)/1294 weeks
36-.05041 -.21687 (36*2π)/1294 weeks
37-.09238 -.05342 (37*2π)/1293 weeks
38-.02639 -.13955 (38*2π)/1293 weeks
39-.01116 -.15407 (39*2π)/1293 weeks
40-.08498 -.10212 (40*2π)/1293 weeks
41-.12874 .00916 (41*2π)/1293 weeks
42-.01937 -.06069 (42*2π)/1293 weeks
43-.04256 -.01786 (43*2π)/1293 weeks
44-.1155 -.10011 (44*2π)/1293 weeks
45-.02434 .02171 (45*2π)/1293 weeks
46-.17059 .05587 (46*2π)/1293 weeks
47-.03952 .03323 (47*2π)/1293 weeks
48-.08077 .02032 (48*2π)/1293 weeks
49-.06771 .02761 (49*2π)/1293 weeks
50.00455 -.02193 (50*2π)/1293 weeks
51-.02844 .09731 (51*2π)/1293 weeks
52-.02089 -.0731 (52*2π)/1292 weeks
53-.00405 -.01273 (53*2π)/1292 weeks
54-.09525 -.11476 (54*2π)/1292 weeks
55-.06111 -.0879 (55*2π)/1292 weeks
56-.00201 -.07582 (56*2π)/1292 weeks
57-.01496 -.00326 (57*2π)/1292 weeks
58-.1238 -.07879 (58*2π)/1292 weeks
59-.03896 -.00373 (59*2π)/1292 weeks
60-.10146 -.01606 (60*2π)/1292 weeks
61-.06316 .04468 (61*2π)/1292 weeks
62-.05299 -.00779 (62*2π)/1292 weeks
63-.05089 .0759 (63*2π)/1292 weeks
64-.10355 .01767 (64*2π)/1292 weeks
65-.10355 -.01767 (65*2π)/1292 weeks
66-.05089 -.0759 (66*2π)/1292 weeks
67-.05299 .00779 (67*2π)/1292 weeks
68-.06316 -.04468 (68*2π)/1292 weeks
69-.10146 .01606 (69*2π)/1292 weeks
70-.03896 .00373 (70*2π)/1292 weeks
71-.1238 .07879 (71*2π)/1292 weeks
72-.01496 .00326 (72*2π)/1292 weeks
73-.00201 .07582 (73*2π)/1292 weeks
74-.06111 .0879 (74*2π)/1292 weeks
75-.09525 .11476 (75*2π)/1292 weeks
76-.00405 .01273 (76*2π)/1292 weeks
77-.02089 .0731 (77*2π)/1292 weeks
78-.02844 -.09731 (78*2π)/1292 weeks
79.00455 .02193 (79*2π)/1292 weeks
80-.06771 -.02761 (80*2π)/1292 weeks
81-.08077 -.02032 (81*2π)/1292 weeks
82-.03952 -.03323 (82*2π)/1292 weeks
83-.17059 -.05587 (83*2π)/1292 weeks
84-.02434 -.02171 (84*2π)/1292 weeks
85-.1155 .10011 (85*2π)/1292 weeks
86-.04256 .01786 (86*2π)/1292 weeks
87-.01937 .06069 (87*2π)/1291 weeks
88-.12874 -.00916 (88*2π)/1291 weeks
89-.08498 .10212 (89*2π)/1291 weeks
90-.01116 .15407 (90*2π)/1291 weeks
91-.02639 .13955 (91*2π)/1291 weeks
92-.09238 .05342 (92*2π)/1291 weeks
93-.05041 .21687 (93*2π)/1291 weeks
94-.08703 .09585 (94*2π)/1291 weeks
95-.10138 .19643 (95*2π)/1291 weeks
96-.03229 .03158 (96*2π)/1291 weeks
97-.07316 .22903 (97*2π)/1291 weeks
98.03072 .10851 (98*2π)/1291 weeks
99.03059 .03051 (99*2π)/1291 weeks
100-.07051 -.1017 (100*2π)/1291 weeks
101.00704 .05741 (101*2π)/1291 weeks
102-.09515 .03223 (102*2π)/1291 weeks
103-.09485 .19254 (103*2π)/1291 weeks
104-.06766 .02931 (104*2π)/1291 weeks
105-.06607 .29202 (105*2π)/1291 weeks
106.0136 .04683 (106*2π)/1291 weeks
107.00716 -.00737 (107*2π)/1291 weeks
108-.12312 -.11386 (108*2π)/1291 weeks
109-.33223 .12692 (109*2π)/1291 weeks
110-.27384 .20623 (110*2π)/1291 weeks
111-.0031 .21526 (111*2π)/1291 weeks
112-.16393 .08389 (112*2π)/1291 weeks
113-.12114 .22189 (113*2π)/1291 weeks
114-.21075 .26861 (114*2π)/1291 weeks
115.05437 .37215 (115*2π)/1291 weeks
116-.19151 .16361 (116*2π)/1291 weeks
117.00296 .43072 (117*2π)/1291 weeks
118-.09626 .38013 (118*2π)/1291 weeks
119.46401 .63744 (119*2π)/1291 weeks
120-.02533 .59126 (120*2π)/1291 weeks
121-.2982 .5558 (121*2π)/1291 weeks
122.26467 .36033 (122*2π)/1291 weeks
123-.7182 .79123 (123*2π)/1291 weeks
124.35249 .47454 (124*2π)/1291 weeks
125-.66619 .49206 (125*2π)/1291 weeks
126.031 1.07031 (126*2π)/1291 weeks
127.55118 3.15279 (127*2π)/1291 weeks

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