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# Fourier Analysis of PEIX (Pacific Ethanol)

PEIX (Pacific Ethanol) appears to have interesting cyclic behaviour every 49 weeks (93.2933*sine), 46 weeks (80.8478*sine), and 63 weeks (74.8072*cosine).

PEIX (Pacific Ethanol) has an average price of 358.44 (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 3/24/2005 to 6/11/2018 for PEIX (Pacific Ethanol), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0358.4427   0
1459.5755 424.3587 (1*2π)/691691 weeks
290.14568 477.5527 (2*2π)/691346 weeks
3-149.3085 324.9669 (3*2π)/691230 weeks
4-182.857 96.92653 (4*2π)/691173 weeks
5-89.11895 12.32989 (5*2π)/691138 weeks
6-54.82324 11.37942 (6*2π)/691115 weeks
7-38.08625 -11.13884 (7*2π)/69199 weeks
8-14.79302 -24.97973 (8*2π)/69186 weeks
99.51896 -31.70514 (9*2π)/69177 weeks
1040.48692 -33.47735 (10*2π)/69169 weeks
1174.80724 -7.62237 (11*2π)/69163 weeks
1274.17902 33.09579 (12*2π)/69158 weeks
1368.47109 59.68865 (13*2π)/69153 weeks
1434.14151 93.2933 (14*2π)/69149 weeks
15-9.58442 80.84782 (15*2π)/69146 weeks
16-24.60051 64.9026 (16*2π)/69143 weeks
17-44.20275 44.85795 (17*2π)/69141 weeks
18-43.3389 12.27338 (18*2π)/69138 weeks
19-29.83841 -2.15274 (19*2π)/69136 weeks
20-22.23462 -17.98594 (20*2π)/69135 weeks
217.70693 -30.37798 (21*2π)/69133 weeks
2231.80503 -12.4513 (22*2π)/69131 weeks
2336.94309 5.36666 (23*2π)/69130 weeks
2437.6546 26.939 (24*2π)/69129 weeks
2518.62654 40.11965 (25*2π)/69128 weeks
267.34234 35.12307 (26*2π)/69127 weeks
271.52972 38.97923 (27*2π)/69126 weeks
28-13.49078 35.62395 (28*2π)/69125 weeks
29-21.48029 23.17082 (29*2π)/69124 weeks
30-23.71948 10.91625 (30*2π)/69123 weeks
31-17.62881 -4.77929 (31*2π)/69122 weeks
32-1.50204 -9.69054 (32*2π)/69122 weeks
339.14999 -1.63917 (33*2π)/69121 weeks
3410.00863 6.85222 (34*2π)/69120 weeks
357.43649 10.27674 (35*2π)/69120 weeks
362.66218 11.34641 (36*2π)/69119 weeks
374.49928 5.90866 (37*2π)/69119 weeks
3812.69885 12.45387 (38*2π)/69118 weeks
393.47059 23.73474 (39*2π)/69118 weeks
40-8.17761 19.31668 (40*2π)/69117 weeks
41-11.46708 12.19263 (41*2π)/69117 weeks
42-12.3693 4.12477 (42*2π)/69116 weeks
43-7.64614 -.73804 (43*2π)/69116 weeks
44-6.43951 -3.37642 (44*2π)/69116 weeks
45-.13669 -11.19926 (45*2π)/69115 weeks
4612.48929 -9.08522 (46*2π)/69115 weeks
4719.40429 .45199 (47*2π)/69115 weeks
4818.7426 12.70168 (48*2π)/69114 weeks
499.77983 19.71935 (49*2π)/69114 weeks
50.76652 19.98792 (50*2π)/69114 weeks
51-6.28854 15.85684 (51*2π)/69114 weeks
52-9.30358 9.77741 (52*2π)/69113 weeks
53-10.10366 3.36524 (53*2π)/69113 weeks
54-8.51729 -3.27738 (54*2π)/69113 weeks
55-3.13543 -9.04938 (55*2π)/69113 weeks
565.68663 -12.32393 (56*2π)/69112 weeks
5716.94265 -8.37618 (57*2π)/69112 weeks
5820.96646 3.99515 (58*2π)/69112 weeks
5915.09285 11.95419 (59*2π)/69112 weeks
608.89098 11.35528 (60*2π)/69112 weeks
619.58446 8.73776 (61*2π)/69111 weeks
6213.55777 13.33908 (62*2π)/69111 weeks
639.6273 21.79219 (63*2π)/69111 weeks
64-1.88893 24.74628 (64*2π)/69111 weeks
65-11.49351 17.65492 (65*2π)/69111 weeks
66-12.41277 8.63612 (66*2π)/69110 weeks
67-11.2522 3.51948 (67*2π)/69110 weeks
68-9.83811 -1.99736 (68*2π)/69110 weeks
69-4.83931 -7.63897 (69*2π)/69110 weeks
703.403 -10.54555 (70*2π)/69110 weeks
7113.53629 -6.41934 (71*2π)/69110 weeks
7215.88762 4.25012 (72*2π)/69110 weeks
7311.47215 10.17351 (73*2π)/6919 weeks
746.70976 12.33009 (74*2π)/6919 weeks
752.46792 11.51064 (75*2π)/6919 weeks
761.07471 9.4604 (76*2π)/6919 weeks
77.46311 9.56474 (77*2π)/6919 weeks
78-3.33457 7.9705 (78*2π)/6919 weeks
79-3.08339 2.79081 (79*2π)/6919 weeks
80-.18103 .25596 (80*2π)/6919 weeks
814.77503 -1.63442 (81*2π)/6919 weeks
8210.00314 3.62121 (82*2π)/6918 weeks
837.40063 9.70131 (83*2π)/6918 weeks
843.60363 9.94105 (84*2π)/6918 weeks
852.78211 8.73443 (85*2π)/6918 weeks
863.20258 10.44946 (86*2π)/6918 weeks
87.0692 13.2488 (87*2π)/6918 weeks
88-6.55711 12.66244 (88*2π)/6918 weeks
89-12.1166 4.28349 (89*2π)/6918 weeks
90-5.92991 -6.46785 (90*2π)/6918 weeks
915.93906 -5.26433 (91*2π)/6918 weeks
929.68479 3.37737 (92*2π)/6918 weeks
936.24184 10.36551 (93*2π)/6917 weeks
94-1.46875 11.42031 (94*2π)/6917 weeks
95-4.03656 5.85103 (95*2π)/6917 weeks
96-2.51539 4.91296 (96*2π)/6917 weeks
97-5.1783 3.82045 (97*2π)/6917 weeks
98-4.8027 -1.3581 (98*2π)/6917 weeks
99-.65169 -3.92598 (99*2π)/6917 weeks
1003.19289 -4.56852 (100*2π)/6917 weeks
1018.21448 -1.76612 (101*2π)/6917 weeks
1028.15632 2.87225 (102*2π)/6917 weeks
1037.40429 3.829 (103*2π)/6917 weeks
1048.25733 6.22784 (104*2π)/6917 weeks
1057.03915 9.8185 (105*2π)/6917 weeks
1063.39642 12.47236 (106*2π)/6917 weeks
107-2.36767 12.47092 (107*2π)/6916 weeks
108-6.22427 7.01316 (108*2π)/6916 weeks
109-3.32102 1.84354 (109*2π)/6916 weeks
110.35157 2.86729 (110*2π)/6916 weeks
111-.22808 4.67362 (111*2π)/6916 weeks
112-1.51544 4.01055 (112*2π)/6916 weeks
113-2.08522 3.09648 (113*2π)/6916 weeks
114-2.06804 .7125 (114*2π)/6916 weeks
1151.28458 -.66748 (115*2π)/6916 weeks
1163.16379 1.74496 (116*2π)/6916 weeks
1172.64509 3.18822 (117*2π)/6916 weeks
1182.16992 3.65164 (118*2π)/6916 weeks
1191.61924 3.93833 (119*2π)/6916 weeks
1201.53092 3.93767 (120*2π)/6916 weeks
1211.09845 4.89058 (121*2π)/6916 weeks
122-.86793 3.97808 (122*2π)/6916 weeks
123-.08343 1.82134 (123*2π)/6916 weeks
1241.85941 2.37255 (124*2π)/6916 weeks
1251.36598 3.90481 (125*2π)/6916 weeks
126.51045 3.26025 (126*2π)/6915 weeks
127.85071 3.13456 (127*2π)/6915 weeks
1281.09375 2.85565 (128*2π)/6915 weeks
1292.01194 3.79 (129*2π)/6915 weeks
130.03756 5.09191 (130*2π)/6915 weeks
131-1.22341 2.85872 (131*2π)/6915 weeks
132.41937 2.40744 (132*2π)/6915 weeks
133-.19358 3.05016 (133*2π)/6915 weeks
134-.20911 1.92923 (134*2π)/6915 weeks
135.03391 1.9298 (135*2π)/6915 weeks
136.00054 .42103 (136*2π)/6915 weeks
1372.76029 -.24268 (137*2π)/6915 weeks
1384.29134 2.30086 (138*2π)/6915 weeks
1393.30487 3.94216 (139*2π)/6915 weeks
1402.46616 4.25472 (140*2π)/6915 weeks
1412.40812 4.05256 (141*2π)/6915 weeks
1423.17564 4.87304 (142*2π)/6915 weeks
1432.95514 7.09511 (143*2π)/6915 weeks
144.47501 9.09767 (144*2π)/6915 weeks
145-2.70725 8.82982 (145*2π)/6915 weeks
146-5.25175 7.87816 (146*2π)/6915 weeks
147-8.63867 4.98699 (147*2π)/6915 weeks
148-9.00292 -.19424 (148*2π)/6915 weeks
149-6.4332 -4.23945 (149*2π)/6915 weeks
150-2.09064 -6.7041 (150*2π)/6915 weeks
1512.86243 -5.61094 (151*2π)/6915 weeks
1525.26566 -2.19659 (152*2π)/6915 weeks
1535.6552 .52696 (153*2π)/6915 weeks
1545.45232 3.11345 (154*2π)/6914 weeks
1553.16493 5.31182 (155*2π)/6914 weeks
1561.71322 5.06761 (156*2π)/6914 weeks
157.75559 6.35195 (157*2π)/6914 weeks
158-2.65635 6.372 (158*2π)/6914 weeks
159-4.63392 4.09449 (159*2π)/6914 weeks
160-5.47928 1.3335 (160*2π)/6914 weeks
161-4.40085 -2.03011 (161*2π)/6914 weeks
162-1.36754 -3.1797 (162*2π)/6914 weeks
163.30407 -2.29798 (163*2π)/6914 weeks
164.53096 -2.39347 (164*2π)/6914 weeks
1652.43033 -3.36541 (165*2π)/6914 weeks
1666.26723 -2.17984 (166*2π)/6914 weeks
1678.17397 3.13828 (167*2π)/6914 weeks
1684.52349 8.532 (168*2π)/6914 weeks
169-1.96667 8.86306 (169*2π)/6914 weeks
170-5.77618 4.82143 (170*2π)/6914 weeks
171-5.68146 .71805 (171*2π)/6914 weeks
172-4.40283 -1.44675 (172*2π)/6914 weeks
173-3.46882 -3.1536 (173*2π)/6914 weeks
174-2.02922 -5.0829 (174*2π)/6914 weeks
1751.57595 -7.27761 (175*2π)/6914 weeks
1766.95323 -5.37872 (176*2π)/6914 weeks
1778.46825 -.3335 (177*2π)/6914 weeks
1787.31712 3.19936 (178*2π)/6914 weeks
1795.04304 5.81531 (179*2π)/6914 weeks
1801.54206 7.28989 (180*2π)/6914 weeks
181-2.89451 5.95133 (181*2π)/6914 weeks
182-4.39317 1.34149 (182*2π)/6914 weeks
183-2.49621 -1.26603 (183*2π)/6914 weeks
184-1.06237 -2.47024 (184*2π)/6914 weeks
1851.53077 -3.42956 (185*2π)/6914 weeks
1863.94924 -2.05101 (186*2π)/6914 weeks
1875.22371 -.1209 (187*2π)/6914 weeks
1885.24898 3.31023 (188*2π)/6914 weeks
1891.78734 5.13556 (189*2π)/6914 weeks
190-.63382 3.72023 (190*2π)/6914 weeks
191-1.30499 2.16159 (191*2π)/6914 weeks
192-1.1127 .97395 (192*2π)/6914 weeks
193-1.28679 .78091 (193*2π)/6914 weeks
194-2.19742 -1.08155 (194*2π)/6914 weeks
195-.11435 -3.48688 (195*2π)/6914 weeks
1962.37983 -2.80315 (196*2π)/6914 weeks
1973.20405 -1.86149 (197*2π)/6914 weeks
1983.90982 -1.11618 (198*2π)/6913 weeks
1994.23958 -.29855 (199*2π)/6913 weeks
2004.94677 .2304 (200*2π)/6913 weeks
2015.88961 2.2151 (201*2π)/6913 weeks
2024.44682 4.66462 (202*2π)/6913 weeks
2032.48395 5.06742 (203*2π)/6913 weeks
204.96685 5.32243 (204*2π)/6913 weeks
205-.91757 4.93833 (205*2π)/6913 weeks
206-2.37606 3.69876 (206*2π)/6913 weeks
207-3.30703 1.89707 (207*2π)/6913 weeks
208-3.34601 -.07178 (208*2π)/6913 weeks
209-2.61644 -1.89897 (209*2π)/6913 weeks
210-1.28358 -3.79918 (210*2π)/6913 weeks
2111.90356 -5.09989 (211*2π)/6913 weeks
2125.8411 -2.6952 (212*2π)/6913 weeks
2135.43076 1.43582 (213*2π)/6913 weeks
2143.21949 2.58667 (214*2π)/6913 weeks
2151.87467 2.66568 (215*2π)/6913 weeks
216.75355 2.21963 (216*2π)/6913 weeks
217.27926 1.19855 (217*2π)/6913 weeks
218.55204 .60398 (218*2π)/6913 weeks
219.73591 .15976 (219*2π)/6913 weeks
2201.23643 .06188 (220*2π)/6913 weeks
2211.40477 -.08322 (221*2π)/6913 weeks
2222.47574 -.31901 (222*2π)/6913 weeks
2233.35336 1.59182 (223*2π)/6913 weeks
2241.32748 3.05205 (224*2π)/6913 weeks
225-.15227 1.52186 (225*2π)/6913 weeks
226.52138 .53541 (226*2π)/6913 weeks
2271.12985 1.07495 (227*2π)/6913 weeks
228.19933 1.82648 (228*2π)/6913 weeks
229-1.60667 1.01113 (229*2π)/6913 weeks
230-1.66806 -1.75764 (230*2π)/6913 weeks
231.73202 -3.02539 (231*2π)/6913 weeks
2322.23153 -2.47286 (232*2π)/6913 weeks
2333.55365 -1.7086 (233*2π)/6913 weeks
2343.90049 -.37877 (234*2π)/6913 weeks
2354.05523 .29333 (235*2π)/6913 weeks
2364.23283 2.04723 (236*2π)/6913 weeks
2372.61514 3.63351 (237*2π)/6913 weeks
238-.22916 3.6824 (238*2π)/6913 weeks
239-2.17351 1.13008 (239*2π)/6913 weeks
240-1.42421 -1.70728 (240*2π)/6913 weeks
241.51444 -3.3218 (241*2π)/6913 weeks
2423.20618 -3.48281 (242*2π)/6913 weeks
2435.28648 -1.88611 (243*2π)/6913 weeks
2446.04756 .09835 (244*2π)/6913 weeks
2455.92463 2.42233 (245*2π)/6913 weeks
2464.41912 3.97427 (246*2π)/6913 weeks
2472.98574 4.79141 (247*2π)/6913 weeks
2481.08192 5.32045 (248*2π)/6913 weeks
249-1.17954 4.49283 (249*2π)/6913 weeks
250-2.12225 2.33641 (250*2π)/6913 weeks
251-1.85527 1.35061 (251*2π)/6913 weeks
252-2.45195 .2867 (252*2π)/6913 weeks
253-2.57229 -1.92651 (253*2π)/6913 weeks
254-.66314 -4.67652 (254*2π)/6913 weeks
2553.62414 -5.01635 (255*2π)/6913 weeks
2566.58286 -2.0738 (256*2π)/6913 weeks
2576.45227 1.72014 (257*2π)/6913 weeks
2584.37141 3.61836 (258*2π)/6913 weeks
2592.82586 3.89639 (259*2π)/6913 weeks
2601.66688 4.38278 (260*2π)/6913 weeks
261-.29319 4.26751 (261*2π)/6913 weeks
262-1.31529 3.00708 (262*2π)/6913 weeks
263-2.30755 2.23163 (263*2π)/6913 weeks
264-3.07256 .12939 (264*2π)/6913 weeks
265-1.90345 -1.87442 (265*2π)/6913 weeks
266-.44013 -2.59945 (266*2π)/6913 weeks
2671.1068 -2.85588 (267*2π)/6913 weeks
2682.31282 -2.13037 (268*2π)/6913 weeks
2693.16509 -1.85528 (269*2π)/6913 weeks
2704.50981 -.5252 (270*2π)/6913 weeks
2714.48164 1.67125 (271*2π)/6913 weeks
2723.05325 3.45718 (272*2π)/6913 weeks
273.83187 3.87966 (273*2π)/6913 weeks
274-1.04554 2.77065 (274*2π)/6913 weeks
275-1.3495 1.1002 (275*2π)/6913 weeks
276-1.21497 .74219 (276*2π)/6913 weeks
277-2.07414 -.34984 (277*2π)/6912 weeks
278-1.31665 -2.45267 (278*2π)/6912 weeks
279.45643 -2.9124 (279*2π)/6912 weeks
2801.91901 -2.65957 (280*2π)/6912 weeks
2812.90349 -1.3716 (281*2π)/6912 weeks
2822.18765 -.4293 (282*2π)/6912 weeks
2832.1265 -.86931 (283*2π)/6912 weeks
2843.15774 -.44342 (284*2π)/6912 weeks
2853.0666 1.31263 (285*2π)/6912 weeks
2861.26204 2.56264 (286*2π)/6912 weeks
287-1.71752 1.75992 (287*2π)/6912 weeks
288-2.60531 -2.35975 (288*2π)/6912 weeks
289.94535 -4.69653 (289*2π)/6912 weeks
2903.76766 -3.40008 (290*2π)/6912 weeks
2914.78033 -1.27102 (291*2π)/6912 weeks
2924.07704 .50194 (292*2π)/6912 weeks
2933.04391 .72735 (293*2π)/6912 weeks
2942.97476 .7646 (294*2π)/6912 weeks
2952.83625 1.27636 (295*2π)/6912 weeks
2962.26122 1.87779 (296*2π)/6912 weeks
297.97873 2.12276 (297*2π)/6912 weeks
298-.03875 1.17271 (298*2π)/6912 weeks
299.01045 .05729 (299*2π)/6912 weeks
300.28802 -.36052 (300*2π)/6912 weeks
301.34627 -.61319 (301*2π)/6912 weeks
302-.04437 -1.29508 (302*2π)/6912 weeks
303.6092 -3.23007 (303*2π)/6912 weeks
3043.40762 -3.67689 (304*2π)/6912 weeks
3055.29923 -1.66725 (305*2π)/6912 weeks
3065.42643 .7278 (306*2π)/6912 weeks
3073.75841 2.52463 (307*2π)/6912 weeks
3082.00964 2.06498 (308*2π)/6912 weeks
3091.76634 1.80185 (309*2π)/6912 weeks
310.9263 1.92868 (310*2π)/6912 weeks
311-.29445 1.15239 (311*2π)/6912 weeks
312-.72349 -.46236 (312*2π)/6912 weeks
313-.10651 -2.03551 (313*2π)/6912 weeks
3141.74583 -3.37338 (314*2π)/6912 weeks
3154.24822 -2.66202 (315*2π)/6912 weeks
3165.21261 -.76629 (316*2π)/6912 weeks
3175.57113 .99196 (317*2π)/6912 weeks
3184.61312 3.22225 (318*2π)/6912 weeks
3192.37165 4.16993 (319*2π)/6912 weeks
320.18856 3.86377 (320*2π)/6912 weeks
321-1.50995 1.89012 (321*2π)/6912 weeks
322-1.01132 -.37602 (322*2π)/6912 weeks
323.27506 -1.00249 (323*2π)/6912 weeks
3241.12014 -1.1595 (324*2π)/6912 weeks
3251.97731 -.66869 (325*2π)/6912 weeks
3261.6686 -.01113 (326*2π)/6912 weeks
3271.3592 -.54669 (327*2π)/6912 weeks
3282.03999 -1.03855 (328*2π)/6912 weeks
3293.24637 -.78764 (329*2π)/6912 weeks
3304.34736 .63295 (330*2π)/6912 weeks
3313.49849 3.30762 (331*2π)/6912 weeks
332.4083 4.0373 (332*2π)/6912 weeks
333-1.46665 2.25301 (333*2π)/6912 weeks
334-1.7622 .56896 (334*2π)/6912 weeks
335-2.0288 -.7286 (335*2π)/6912 weeks
336-1.55246 -2.50488 (336*2π)/6912 weeks
337-.4422 -4.13102 (337*2π)/6912 weeks
3382.46695 -5.61671 (338*2π)/6912 weeks
3395.90072 -3.49998 (339*2π)/6912 weeks
3406.30329 -.5971 (340*2π)/6912 weeks
3415.94444 1.56852 (341*2π)/6912 weeks
3424.35863 3.64556 (342*2π)/6912 weeks
3432.05454 4.28558 (343*2π)/6912 weeks
344-.36353 4.19857 (344*2π)/6912 weeks
345-3.23543 2.0797 (345*2π)/6912 weeks
346-3.23543 -2.0797 (346*2π)/6912 weeks
347-.36353 -4.19857 (347*2π)/6912 weeks
3482.05454 -4.28558 (348*2π)/6912 weeks
3494.35863 -3.64556 (349*2π)/6912 weeks
3505.94444 -1.56852 (350*2π)/6912 weeks
3516.30329 .5971 (351*2π)/6912 weeks
3525.90072 3.49998 (352*2π)/6912 weeks
3532.46695 5.61671 (353*2π)/6912 weeks
354-.4422 4.13102 (354*2π)/6912 weeks
355-1.55246 2.50488 (355*2π)/6912 weeks
356-2.0288 .7286 (356*2π)/6912 weeks
357-1.7622 -.56896 (357*2π)/6912 weeks
358-1.46665 -2.25301 (358*2π)/6912 weeks
359.4083 -4.0373 (359*2π)/6912 weeks
3603.49849 -3.30762 (360*2π)/6912 weeks
3614.34736 -.63295 (361*2π)/6912 weeks
3623.24637 .78764 (362*2π)/6912 weeks
3632.03999 1.03855 (363*2π)/6912 weeks
3641.3592 .54669 (364*2π)/6912 weeks
3651.6686 .01113 (365*2π)/6912 weeks
3661.97731 .66869 (366*2π)/6912 weeks
3671.12014 1.1595 (367*2π)/6912 weeks
368.27506 1.00249 (368*2π)/6912 weeks
369-1.01132 .37602 (369*2π)/6912 weeks
370-1.50995 -1.89012 (370*2π)/6912 weeks
371.18856 -3.86377 (371*2π)/6912 weeks
3722.37165 -4.16993 (372*2π)/6912 weeks
3734.61312 -3.22225 (373*2π)/6912 weeks
3745.57113 -.99196 (374*2π)/6912 weeks
3755.21261 .76629 (375*2π)/6912 weeks
3764.24822 2.66202 (376*2π)/6912 weeks
3771.74583 3.37338 (377*2π)/6912 weeks
378-.10651 2.03551 (378*2π)/6912 weeks
379-.72349 .46236 (379*2π)/6912 weeks
380-.29445 -1.15239 (380*2π)/6912 weeks
381.9263 -1.92868 (381*2π)/6912 weeks
3821.76634 -1.80185 (382*2π)/6912 weeks
3832.00964 -2.06498 (383*2π)/6912 weeks
3843.75841 -2.52463 (384*2π)/6912 weeks
3855.42643 -.7278 (385*2π)/6912 weeks
3865.29923 1.66725 (386*2π)/6912 weeks
3873.40762 3.67689 (387*2π)/6912 weeks
388.6092 3.23007 (388*2π)/6912 weeks
389-.04437 1.29508 (389*2π)/6912 weeks
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