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# Fourier Analysis of AMRS (Amyris)

AMRS (Amyris) appears to have interesting cyclic behaviour every 40 weeks (8.3178*sine), 17 weeks (7.3187*sine), and 33 weeks (6.9243*sine).

AMRS (Amyris) has an average price of 83.73 (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 9/28/2010 to 5/21/2018 for AMRS (Amyris), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
083.73138   0
175.88809 65.65116 (1*2π)/400400 weeks
253.61432 78.83384 (2*2π)/400200 weeks
36.93635 74.15294 (3*2π)/400133 weeks
4-11.87555 51.32257 (4*2π)/400100 weeks
5-20.85482 32.56141 (5*2π)/40080 weeks
6-12.24329 14.96994 (6*2π)/40067 weeks
7-8.10252 11.69508 (7*2π)/40057 weeks
8-6.85053 10.93813 (8*2π)/40050 weeks
9-5.88557 9.81945 (9*2π)/40044 weeks
10-5.25238 8.31779 (10*2π)/40040 weeks
11-4.30988 3.02449 (11*2π)/40036 weeks
12-1.36934 6.92431 (12*2π)/40033 weeks
13-3.83422 4.98201 (13*2π)/40031 weeks
14-3.48939 6.41959 (14*2π)/40029 weeks
15-5.12216 .27126 (15*2π)/40027 weeks
16-1.40473 -.3415 (16*2π)/40025 weeks
17-.01068 .98888 (17*2π)/40024 weeks
18-.08824 .07212 (18*2π)/40022 weeks
191.40726 .30342 (19*2π)/40021 weeks
203.1234 -.33945 (20*2π)/40020 weeks
214.72478 1.04309 (21*2π)/40019 weeks
224.92933 2.9833 (22*2π)/40018 weeks
234.86956 5.05174 (23*2π)/40017 weeks
242.79045 7.31873 (24*2π)/40017 weeks
25-.41292 6.46885 (25*2π)/40016 weeks
26-1.38591 5.12627 (26*2π)/40015 weeks
27-2.35023 2.52107 (27*2π)/40015 weeks
28-.88735 .798 (28*2π)/40014 weeks
291.82576 .05404 (29*2π)/40014 weeks
302.78107 1.43219 (30*2π)/40013 weeks
312.87164 4.74063 (31*2π)/40013 weeks
32-.36341 4.52089 (32*2π)/40013 weeks
33-.29135 3.32252 (33*2π)/40012 weeks
34-.90725 1.73286 (34*2π)/40012 weeks
351.49017 1.1521 (35*2π)/40011 weeks
36.59925 2.78195 (36*2π)/40011 weeks
37.76139 2.70589 (37*2π)/40011 weeks
38-.43623 2.81084 (38*2π)/40011 weeks
39-.74402 1.37325 (39*2π)/40010 weeks
40.43211 1.31743 (40*2π)/40010 weeks
41.18419 1.11597 (41*2π)/40010 weeks
42.80378 1.3568 (42*2π)/40010 weeks
43.48842 1.86772 (43*2π)/4009 weeks
44.38482 .70433 (44*2π)/4009 weeks
45.55901 1.02706 (45*2π)/4009 weeks
46.35834 .47947 (46*2π)/4009 weeks
471.95407 .80775 (47*2π)/4009 weeks
481.00818 .777 (48*2π)/4008 weeks
492.26022 .88504 (49*2π)/4008 weeks
501.8496 1.92617 (50*2π)/4008 weeks
511.47531 2.02096 (51*2π)/4008 weeks
521.32082 2.46728 (52*2π)/4008 weeks
53.41683 2.00108 (53*2π)/4008 weeks
54.7668 2.00227 (54*2π)/4007 weeks
55.33151 1.15717 (55*2π)/4007 weeks
561.09164 1.21385 (56*2π)/4007 weeks
571.75343 1.37974 (57*2π)/4007 weeks
581.41696 2.54698 (58*2π)/4007 weeks
59.28817 2.74003 (59*2π)/4007 weeks
60-.65222 2.00911 (60*2π)/4007 weeks
61.14495 1.26104 (61*2π)/4007 weeks
62.12752 .89262 (62*2π)/4006 weeks
63.70551 1.14167 (63*2π)/4006 weeks
64.59598 1.22201 (64*2π)/4006 weeks
65.2855 1.54424 (65*2π)/4006 weeks
66.06217 1.60422 (66*2π)/4006 weeks
67-.02636 .7678 (67*2π)/4006 weeks
68-.43042 .45276 (68*2π)/4006 weeks
69.58787 -.18328 (69*2π)/4006 weeks
701.31662 .1235 (70*2π)/4006 weeks
711.75113 1.01822 (71*2π)/4006 weeks
721.20325 1.51444 (72*2π)/4006 weeks
73.98695 1.30531 (73*2π)/4005 weeks
74.63851 1.90179 (74*2π)/4005 weeks
75-.43925 1.39647 (75*2π)/4005 weeks
76-.25017 .48257 (76*2π)/4005 weeks
77.67404 -.35619 (77*2π)/4005 weeks
781.7985 .17645 (78*2π)/4005 weeks
791.3422 1.35859 (79*2π)/4005 weeks
80.89565 1.37137 (80*2π)/4005 weeks
81.83354 1.67831 (81*2π)/4005 weeks
82-.1222 .73297 (82*2π)/4005 weeks
83.83596 .50665 (83*2π)/4005 weeks
84.68873 .43222 (84*2π)/4005 weeks
851.70684 .65684 (85*2π)/4005 weeks
861.30654 1.40119 (86*2π)/4005 weeks
871.36185 1.71954 (87*2π)/4005 weeks
88.394 2.36596 (88*2π)/4005 weeks
89-.78994 1.49221 (89*2π)/4004 weeks
90-.22628 .43259 (90*2π)/4004 weeks
91.10171 .16086 (91*2π)/4004 weeks
921.25888 .17331 (92*2π)/4004 weeks
93.90445 .95384 (93*2π)/4004 weeks
94.90853 1.33372 (94*2π)/4004 weeks
95.08503 1.74953 (95*2π)/4004 weeks
96-.0917 .35955 (96*2π)/4004 weeks
97.27158 .8054 (97*2π)/4004 weeks
98.3452 .81379 (98*2π)/4004 weeks
99.09896 .55196 (99*2π)/4004 weeks
100.26088 .30492 (100*2π)/4004 weeks
101.90278 .74341 (101*2π)/4004 weeks
102.31248 .81726 (102*2π)/4004 weeks
103-.18288 .86335 (103*2π)/4004 weeks
104-.06847 .38024 (104*2π)/4004 weeks
105-.07967 .0098 (105*2π)/4004 weeks
106.34625 -.29075 (106*2π)/4004 weeks
107.85803 -.17044 (107*2π)/4004 weeks
1081.04378 .09525 (108*2π)/4004 weeks
1091.39667 .61646 (109*2π)/4004 weeks
110.44991 1.01085 (110*2π)/4004 weeks
111.35058 .64721 (111*2π)/4004 weeks
112-.24224 .43701 (112*2π)/4004 weeks
113.26657 -.58534 (113*2π)/4004 weeks
1141.23175 -.12377 (114*2π)/4004 weeks
1151.32822 .19107 (115*2π)/4003 weeks
1161.24566 .93613 (116*2π)/4003 weeks
117.18524 1.03086 (117*2π)/4003 weeks
118.14607 .61663 (118*2π)/4003 weeks
119-.05356 .1092 (119*2π)/4003 weeks
120.44723 -.5055 (120*2π)/4003 weeks
121.9856 -.02516 (121*2π)/4003 weeks
122.86601 .01819 (122*2π)/4003 weeks
123.8948 .22787 (123*2π)/4003 weeks
124.71982 .36302 (124*2π)/4003 weeks
125.66076 .16942 (125*2π)/4003 weeks
126.43302 -.09262 (126*2π)/4003 weeks
127.80764 -.43216 (127*2π)/4003 weeks
1281.59508 -.26909 (128*2π)/4003 weeks
1291.48607 .27443 (129*2π)/4003 weeks
1301.78505 .22431 (130*2π)/4003 weeks
1311.56469 .94821 (131*2π)/4003 weeks
1321.31293 1.23451 (132*2π)/4003 weeks
133.43937 1.38968 (133*2π)/4003 weeks
134.32154 .2553 (134*2π)/4003 weeks
1351.2021 .38236 (135*2π)/4003 weeks
1361.19832 .84183 (136*2π)/4003 weeks
1371.08528 1.13707 (137*2π)/4003 weeks
138.76226 1.62816 (138*2π)/4003 weeks
139-.15537 1.50495 (139*2π)/4003 weeks
140-.61986 .89109 (140*2π)/4003 weeks
141-.53244 .11936 (141*2π)/4003 weeks
142.20653 -.0962 (142*2π)/4003 weeks
143.16988 -.00448 (143*2π)/4003 weeks
144.62987 -.04272 (144*2π)/4003 weeks
145.22555 .29924 (145*2π)/4003 weeks
146.01854 .04216 (146*2π)/4003 weeks
147-.0459 -.49242 (147*2π)/4003 weeks
148.94763 -.78718 (148*2π)/4003 weeks
1491.36993 -.35229 (149*2π)/4003 weeks
1501.28033 .28689 (150*2π)/4003 weeks
1511.01952 .40626 (151*2π)/4003 weeks
152.67786 .45471 (152*2π)/4003 weeks
153.69063 .25257 (153*2π)/4003 weeks
154.67638 .21845 (154*2π)/4003 weeks
155.76294 .19484 (155*2π)/4003 weeks
156.77599 .21528 (156*2π)/4003 weeks
157.76482 .0947 (157*2π)/4003 weeks
1581.02011 .01624 (158*2π)/4003 weeks
1591.20363 .47227 (159*2π)/4003 weeks
160.87728 .85751 (160*2π)/4003 weeks
161.47181 .701 (161*2π)/4002 weeks
162.30801 .55565 (162*2π)/4002 weeks
163.49792 .21543 (163*2π)/4002 weeks
164.32693 .42906 (164*2π)/4002 weeks
165.58423 .00448 (165*2π)/4002 weeks
166.488 .20779 (166*2π)/4002 weeks
167.55792 .3999 (167*2π)/4002 weeks
168.3506 .08435 (168*2π)/4002 weeks
169.43788 .15821 (169*2π)/4002 weeks
170.82343 -.25447 (170*2π)/4002 weeks
171.85689 .58351 (171*2π)/4002 weeks
172.56261 .25099 (172*2π)/4002 weeks
173.27198 .66415 (173*2π)/4002 weeks
174-.13486 -.10675 (174*2π)/4002 weeks
175.52275 -.19338 (175*2π)/4002 weeks
176.46643 -.06082 (176*2π)/4002 weeks
177.8364 -.36703 (177*2π)/4002 weeks
178.72831 .31195 (178*2π)/4002 weeks
179.6141 .09877 (179*2π)/4002 weeks
180.39992 .28799 (180*2π)/4002 weeks
181.25751 -.02987 (181*2π)/4002 weeks
182.47153 .00937 (182*2π)/4002 weeks
183.20436 -.1879 (183*2π)/4002 weeks
184.56293 -.44173 (184*2π)/4002 weeks
185.656 -.23419 (185*2π)/4002 weeks
186.77004 -.13906 (186*2π)/4002 weeks
187.46407 -.15372 (187*2π)/4002 weeks
188.61746 -.24371 (188*2π)/4002 weeks
189.70341 -.46437 (189*2π)/4002 weeks
190.90237 -.3595 (190*2π)/4002 weeks
1911.00399 -.12272 (191*2π)/4002 weeks
192.90352 -.14294 (192*2π)/4002 weeks
1931.05774 -.06852 (193*2π)/4002 weeks
194.92571 .24156 (194*2π)/4002 weeks
195.63416 .19423 (195*2π)/4002 weeks
196.41851 -.01729 (196*2π)/4002 weeks
197.5037 -.31892 (197*2π)/4002 weeks
198.77736 -.76977 (198*2π)/4002 weeks
1991.37642 -.55248 (199*2π)/4002 weeks
2001.66489   (200*2π)/4002 weeks
2011.37642 .55248 (201*2π)/4002 weeks
202.77736 .76977 (202*2π)/4002 weeks
203.5037 .31892 (203*2π)/4002 weeks
204.41851 .01729 (204*2π)/4002 weeks
205.63416 -.19423 (205*2π)/4002 weeks
206.92571 -.24156 (206*2π)/4002 weeks
2071.05774 .06852 (207*2π)/4002 weeks
208.90352 .14294 (208*2π)/4002 weeks
2091.00399 .12272 (209*2π)/4002 weeks
210.90237 .3595 (210*2π)/4002 weeks
211.70341 .46437 (211*2π)/4002 weeks
212.61746 .24371 (212*2π)/4002 weeks
213.46407 .15372 (213*2π)/4002 weeks
214.77004 .13906 (214*2π)/4002 weeks
215.656 .23419 (215*2π)/4002 weeks
216.56293 .44173 (216*2π)/4002 weeks
217.20436 .1879 (217*2π)/4002 weeks
218.47153 -.00937 (218*2π)/4002 weeks
219.25751 .02987 (219*2π)/4002 weeks
220.39992 -.28799 (220*2π)/4002 weeks
221.6141 -.09877 (221*2π)/4002 weeks
222.72831 -.31195 (222*2π)/4002 weeks
223.8364 .36703 (223*2π)/4002 weeks
224.46643 .06082 (224*2π)/4002 weeks
225.52275 .19338 (225*2π)/4002 weeks
226-.13486 .10675 (226*2π)/4002 weeks
227.27198 -.66415 (227*2π)/4002 weeks
228.56261 -.25099 (228*2π)/4002 weeks
229.85689 -.58351 (229*2π)/4002 weeks
230.82343 .25447 (230*2π)/4002 weeks
231.43788 -.15821 (231*2π)/4002 weeks
232.3506 -.08435 (232*2π)/4002 weeks
233.55792 -.3999 (233*2π)/4002 weeks
234.488 -.20779 (234*2π)/4002 weeks
235.58423 -.00448 (235*2π)/4002 weeks
236.32693 -.42906 (236*2π)/4002 weeks
237.49792 -.21543 (237*2π)/4002 weeks
238.30801 -.55565 (238*2π)/4002 weeks
239.47181 -.701 (239*2π)/4002 weeks
240.87728 -.85751 (240*2π)/4002 weeks
2411.20363 -.47227 (241*2π)/4002 weeks
2421.02011 -.01624 (242*2π)/4002 weeks
243.76482 -.0947 (243*2π)/4002 weeks
244.77599 -.21528 (244*2π)/4002 weeks
245.76294 -.19484 (245*2π)/4002 weeks
246.67638 -.21845 (246*2π)/4002 weeks
247.69063 -.25257 (247*2π)/4002 weeks
248.67786 -.45471 (248*2π)/4002 weeks
2491.01952 -.40626 (249*2π)/4002 weeks
2501.28033 -.28689 (250*2π)/4002 weeks
2511.36993 .35229 (251*2π)/4002 weeks
252.94763 .78718 (252*2π)/4002 weeks
253-.0459 .49242 (253*2π)/4002 weeks
254.01854 -.04216 (254*2π)/4002 weeks
255.22555 -.29924 (255*2π)/4002 weeks
256.62987 .04272 (256*2π)/4002 weeks
257.16988 .00448 (257*2π)/4002 weeks
258.20653 .0962 (258*2π)/4002 weeks
259-.53244 -.11936 (259*2π)/4002 weeks
260-.61986 -.89109 (260*2π)/4002 weeks
261-.15537 -1.50495 (261*2π)/4002 weeks
262.76226 -1.62816 (262*2π)/4002 weeks
2631.08528 -1.13707 (263*2π)/4002 weeks
2641.19832 -.84183 (264*2π)/4002 weeks
2651.2021 -.38236 (265*2π)/4002 weeks
266.32154 -.2553 (266*2π)/4002 weeks
267.43937 -1.38968 (267*2π)/4001 weeks
2681.31293 -1.23451 (268*2π)/4001 weeks
2691.56469 -.94821 (269*2π)/4001 weeks
2701.78505 -.22431 (270*2π)/4001 weeks
2711.48607 -.27443 (271*2π)/4001 weeks
2721.59508 .26909 (272*2π)/4001 weeks
273.80764 .43216 (273*2π)/4001 weeks
274.43302 .09262 (274*2π)/4001 weeks
275.66076 -.16942 (275*2π)/4001 weeks
276.71982 -.36302 (276*2π)/4001 weeks
277.8948 -.22787 (277*2π)/4001 weeks
278.86601 -.01819 (278*2π)/4001 weeks
279.9856 .02516 (279*2π)/4001 weeks
280.44723 .5055 (280*2π)/4001 weeks
281-.05356 -.1092 (281*2π)/4001 weeks
282.14607 -.61663 (282*2π)/4001 weeks
283.18524 -1.03086 (283*2π)/4001 weeks
2841.24566 -.93613 (284*2π)/4001 weeks
2851.32822 -.19107 (285*2π)/4001 weeks
2861.23175 .12377 (286*2π)/4001 weeks
287.26657 .58534 (287*2π)/4001 weeks
288-.24224 -.43701 (288*2π)/4001 weeks
289.35058 -.64721 (289*2π)/4001 weeks
290.44991 -1.01085 (290*2π)/4001 weeks
2911.39667 -.61646 (291*2π)/4001 weeks
2921.04378 -.09525 (292*2π)/4001 weeks
293.85803 .17044 (293*2π)/4001 weeks
294.34625 .29075 (294*2π)/4001 weeks
295-.07967 -.0098 (295*2π)/4001 weeks
296-.06847 -.38024 (296*2π)/4001 weeks
297-.18288 -.86335 (297*2π)/4001 weeks
298.31248 -.81726 (298*2π)/4001 weeks
299.90278 -.74341 (299*2π)/4001 weeks
300.26088 -.30492 (300*2π)/4001 weeks
301.09896 -.55196 (301*2π)/4001 weeks
302.3452 -.81379 (302*2π)/4001 weeks
303.27158 -.8054 (303*2π)/4001 weeks
304-.0917 -.35955 (304*2π)/4001 weeks
305.08503 -1.74953 (305*2π)/4001 weeks
306.90853 -1.33372 (306*2π)/4001 weeks
307.90445 -.95384 (307*2π)/4001 weeks
3081.25888 -.17331 (308*2π)/4001 weeks
309.10171 -.16086 (309*2π)/4001 weeks
310-.22628 -.43259 (310*2π)/4001 weeks
311-.78994 -1.49221 (311*2π)/4001 weeks
312.394 -2.36596 (312*2π)/4001 weeks
3131.36185 -1.71954 (313*2π)/4001 weeks
3141.30654 -1.40119 (314*2π)/4001 weeks
3151.70684 -.65684 (315*2π)/4001 weeks
316.68873 -.43222 (316*2π)/4001 weeks
317.83596 -.50665 (317*2π)/4001 weeks
318-.1222 -.73297 (318*2π)/4001 weeks
319.83354 -1.67831 (319*2π)/4001 weeks
320.89565 -1.37137 (320*2π)/4001 weeks
3211.3422 -1.35859 (321*2π)/4001 weeks
3221.7985 -.17645 (322*2π)/4001 weeks
323.67404 .35619 (323*2π)/4001 weeks
324-.25017 -.48257 (324*2π)/4001 weeks
325-.43925 -1.39647 (325*2π)/4001 weeks
326.63851 -1.90179 (326*2π)/4001 weeks
327.98695 -1.30531 (327*2π)/4001 weeks
3281.20325 -1.51444 (328*2π)/4001 weeks
3291.75113 -1.01822 (329*2π)/4001 weeks
3301.31662 -.1235 (330*2π)/4001 weeks
331.58787 .18328 (331*2π)/4001 weeks
332-.43042 -.45276 (332*2π)/4001 weeks
333-.02636 -.7678 (333*2π)/4001 weeks
334.06217 -1.60422 (334*2π)/4001 weeks
335.2855 -1.54424 (335*2π)/4001 weeks
336.59598 -1.22201 (336*2π)/4001 weeks
337.70551 -1.14167 (337*2π)/4001 weeks
338.12752 -.89262 (338*2π)/4001 weeks
339.14495 -1.26104 (339*2π)/4001 weeks
340-.65222 -2.00911 (340*2π)/4001 weeks
341.28817 -2.74003 (341*2π)/4001 weeks
3421.41696 -2.54698 (342*2π)/4001 weeks
3431.75343 -1.37974 (343*2π)/4001 weeks
3441.09164 -1.21385 (344*2π)/4001 weeks
345.33151 -1.15717 (345*2π)/4001 weeks
346.7668 -2.00227 (346*2π)/4001 weeks
347.41683 -2.00108 (347*2π)/4001 weeks
3481.32082 -2.46728 (348*2π)/4001 weeks
3491.47531 -2.02096 (349*2π)/4001 weeks
3501.8496 -1.92617 (350*2π)/4001 weeks
3512.26022 -.88504 (351*2π)/4001 weeks
3521.00818 -.777 (352*2π)/4001 weeks
3531.95407 -.80775 (353*2π)/4001 weeks
354.35834 -.47947 (354*2π)/4001 weeks
355.55901 -1.02706 (355*2π)/4001 weeks
356.38482 -.70433 (356*2π)/4001 weeks
357.48842 -1.86772 (357*2π)/4001 weeks
358.80378 -1.3568 (358*2π)/4001 weeks
359.18419 -1.11597 (359*2π)/4001 weeks
360.43211 -1.31743 (360*2π)/4001 weeks
361-.74402 -1.37325 (361*2π)/4001 weeks
362-.43623 -2.81084 (362*2π)/4001 weeks
363.76139 -2.70589 (363*2π)/4001 weeks
364.59925 -2.78195 (364*2π)/4001 weeks
3651.49017 -1.1521 (365*2π)/4001 weeks
366-.90725 -1.73286 (366*2π)/4001 weeks
367-.29135 -3.32252 (367*2π)/4001 weeks
368-.36341 -4.52089 (368*2π)/4001 weeks
3692.87164 -4.74063 (369*2π)/4001 weeks
3702.78107 -1.43219 (370*2π)/4001 weeks
3711.82576 -.05404 (371*2π)/4001 weeks
372-.88735 -.798 (372*2π)/4001 weeks
373-2.35023 -2.52107 (373*2π)/4001 weeks
374-1.38591 -5.12627 (374*2π)/4001 weeks
375-.41292 -6.46885 (375*2π)/4001 weeks
3762.79045 -7.31873 (376*2π)/4001 weeks
3774.86956 -5.05174 (377*2π)/4001 weeks
3784.92933 -2.9833 (378*2π)/4001 weeks
3794.72478 -1.04309 (379*2π)/4001 weeks
3803.1234 .33945 (380*2π)/4001 weeks
3811.40726 -.30342 (381*2π)/4001 weeks
382-.08824 -.07212 (382*2π)/4001 weeks
383-.01068 -.98888 (383*2π)/4001 weeks
384-1.40473 .3415 (384*2π)/4001 weeks
385-5.12216 -.27126 (385*2π)/4001 weeks
386-3.48939 -6.41959 (386*2π)/4001 weeks
387-3.83422 -4.98201 (387*2π)/4001 weeks
388-1.36934 -6.92431 (388*2π)/4001 weeks
389-4.30988 -3.02449 (389*2π)/4001 weeks
390-5.25238 -8.31779 (390*2π)/4001 weeks
391-5.88557 -9.81945 (391*2π)/4001 weeks
392-6.85053 -10.93813 (392*2π)/4001 weeks
393-8.10252 -11.69508 (393*2π)/4001 weeks
394-12.24329 -14.96994 (394*2π)/4001 weeks
395-20.85482 -32.56141 (395*2π)/4001 weeks
396-11.87555 -51.32257 (396*2π)/4001 weeks
3976.93635 -74.15294 (397*2π)/4001 weeks
39853.61432 -78.83384 (398*2π)/4001 weeks