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# Fourier Analysis of SBGL (Sibanye Gold Limited)

SBGL (Sibanye Gold Limited) appears to have interesting cyclic behaviour every 25 weeks (.6046*cosine), 27 weeks (.5793*cosine), and 18 weeks (.367*cosine).

SBGL (Sibanye Gold Limited) has an average price of 7.32 (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 2/11/2013 to 4/16/2018 for SBGL (Sibanye Gold Limited), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
07.32032   0
1-2.54488 -1.41961 (1*2π)/271271 weeks
2-2.01567 1.06661 (2*2π)/271136 weeks
31.80765 -.85828 (3*2π)/27190 weeks
4-.67984 -.69561 (4*2π)/27168 weeks
5.66478 .81684 (5*2π)/27154 weeks
6-.211 -.25051 (6*2π)/27145 weeks
7-.06011 -.51846 (7*2π)/27139 weeks
8-.01072 .32112 (8*2π)/27134 weeks
9.27671 .62797 (9*2π)/27130 weeks
10.57925 -.29055 (10*2π)/27127 weeks
11-.60464 .12745 (11*2π)/27125 weeks
12.05323 .34101 (12*2π)/27123 weeks
13.00464 -.34234 (13*2π)/27121 weeks
14-.04761 .46671 (14*2π)/27119 weeks
15.36705 -.03294 (15*2π)/27118 weeks
16.05749 -.06041 (16*2π)/27117 weeks
17-.11728 .13573 (17*2π)/27116 weeks
18.02961 -.0413 (18*2π)/27115 weeks
19-.1018 -.03342 (19*2π)/27114 weeks
20-.13721 .3151 (20*2π)/27114 weeks
21.32784 -.0567 (21*2π)/27113 weeks
22-.04746 -.02033 (22*2π)/27112 weeks
23-.20457 .04916 (23*2π)/27112 weeks
24.18239 .08527 (24*2π)/27111 weeks
25-.02822 -.08058 (25*2π)/27111 weeks
26.04045 -.05223 (26*2π)/27110 weeks
27-.10251 -.01848 (27*2π)/27110 weeks
28-.12508 .00061 (28*2π)/27110 weeks
29.04463 .02821 (29*2π)/2719 weeks
30.03678 .08513 (30*2π)/2719 weeks
31.07662 .01453 (31*2π)/2719 weeks
32-.0876 .01229 (32*2π)/2718 weeks
33.05058 .00753 (33*2π)/2718 weeks
34.03991 -.07321 (34*2π)/2718 weeks
35.07573 .09405 (35*2π)/2718 weeks
36-.02595 .01142 (36*2π)/2718 weeks
37.09077 .01266 (37*2π)/2717 weeks
38-.05525 .01314 (38*2π)/2717 weeks
39.05982 .09343 (39*2π)/2717 weeks
40.02156 -.09553 (40*2π)/2717 weeks
41-.01102 .0461 (41*2π)/2717 weeks
42-.01434 .01539 (42*2π)/2716 weeks
43.02203 -.00446 (43*2π)/2716 weeks
44-.02001 -.002 (44*2π)/2716 weeks
45.00881 .0134 (45*2π)/2716 weeks
46-.02415 -.00161 (46*2π)/2716 weeks
47-.02707 .05224 (47*2π)/2716 weeks
48-.00355 .00084 (48*2π)/2716 weeks
49.11957 .03219 (49*2π)/2716 weeks
50.0279 -.05882 (50*2π)/2715 weeks
51-.0462 .07801 (51*2π)/2715 weeks
52.06035 .03951 (52*2π)/2715 weeks
53-.00687 -.02544 (53*2π)/2715 weeks
54.00188 .08149 (54*2π)/2715 weeks
55.02598 .08776 (55*2π)/2715 weeks
56.00065 -.09693 (56*2π)/2715 weeks
57-.03726 .02085 (57*2π)/2715 weeks
58-.01596 .01354 (58*2π)/2715 weeks
59.04971 -.01147 (59*2π)/2715 weeks
60.00173 .02734 (60*2π)/2715 weeks
61-.01565 -.07248 (61*2π)/2714 weeks
62.0026 -.02385 (62*2π)/2714 weeks
63.01438 .08696 (63*2π)/2714 weeks
64.0034 -.04558 (64*2π)/2714 weeks
65.00887 .06783 (65*2π)/2714 weeks
66.08726 -.06346 (66*2π)/2714 weeks
67-.02544 -.06901 (67*2π)/2714 weeks
68.01199 .01799 (68*2π)/2714 weeks
69.01352 .03966 (69*2π)/2714 weeks
70.02369 -.00556 (70*2π)/2714 weeks
71.03583 -.01445 (71*2π)/2714 weeks
72.0012 -.02128 (72*2π)/2714 weeks
73.0242 .00488 (73*2π)/2714 weeks
74.02121 .0541 (74*2π)/2714 weeks
75.01079 .07258 (75*2π)/2714 weeks
76.05955 -.07727 (76*2π)/2714 weeks
77.06037 .00993 (77*2π)/2714 weeks
78-.03729 .02529 (78*2π)/2713 weeks
79.04183 .05846 (79*2π)/2713 weeks
80.04032 -.01178 (80*2π)/2713 weeks
81-.00771 .00281 (81*2π)/2713 weeks
82.0773 -.035 (82*2π)/2713 weeks
83-.02523 -.01459 (83*2π)/2713 weeks
84.00387 .04792 (84*2π)/2713 weeks
85.07651 .06612 (85*2π)/2713 weeks
86.00093 -.03053 (86*2π)/2713 weeks
87.06101 -.0449 (87*2π)/2713 weeks
88-.00244 .03208 (88*2π)/2713 weeks
89.05955 .0065 (89*2π)/2713 weeks
90-.06362 -.03534 (90*2π)/2713 weeks
91.03244 .00582 (91*2π)/2713 weeks
92.07443 -.00563 (92*2π)/2713 weeks
93-.01316 .01851 (93*2π)/2713 weeks
94-.00994 -.03331 (94*2π)/2713 weeks
95.00739 .02873 (95*2π)/2713 weeks
96.04489 -.00534 (96*2π)/2713 weeks
97-.04358 -.00068 (97*2π)/2713 weeks
98.0046 .04651 (98*2π)/2713 weeks
99.05458 -.0276 (99*2π)/2713 weeks
100-.03857 .01718 (100*2π)/2713 weeks
101.00239 .02795 (101*2π)/2713 weeks
102.05811 .02082 (102*2π)/2713 weeks
103.00555 -.0115 (103*2π)/2713 weeks
104.01399 .01568 (104*2π)/2713 weeks
105.01945 -.00495 (105*2π)/2713 weeks
106.01103 -.01203 (106*2π)/2713 weeks
107.01215 .02149 (107*2π)/2713 weeks
108.05209 .0245 (108*2π)/2713 weeks
109.01756 -.00091 (109*2π)/2712 weeks
110.01309 .00178 (110*2π)/2712 weeks
111.00647 -.02575 (111*2π)/2712 weeks
112.0394 .03484 (112*2π)/2712 weeks
113.0612 -.00907 (113*2π)/2712 weeks
114-.00877 -.01361 (114*2π)/2712 weeks
115.02696 .01569 (115*2π)/2712 weeks
116.00035 .005 (116*2π)/2712 weeks
117-.00449 .00835 (117*2π)/2712 weeks
118.00752 .04016 (118*2π)/2712 weeks
119-.01357 -.0027 (119*2π)/2712 weeks
120.08877 -.02005 (120*2π)/2712 weeks
121-.06519 -.02234 (121*2π)/2712 weeks
122-.05319 .01672 (122*2π)/2712 weeks
123.05853 -.00369 (123*2π)/2712 weeks
124-.00112 -.0076 (124*2π)/2712 weeks
125.0326 .00441 (125*2π)/2712 weeks
126.00654 -.01216 (126*2π)/2712 weeks
127.01626 -.05539 (127*2π)/2712 weeks
128-.01533 .03552 (128*2π)/2712 weeks
129.00547 .0119 (129*2π)/2712 weeks
130.08558 -.00569 (130*2π)/2712 weeks
131.01133 -.03618 (131*2π)/2712 weeks
132-.00157 -.01791 (132*2π)/2712 weeks
133.00186 .02944 (133*2π)/2712 weeks
134-.00056 .00303 (134*2π)/2712 weeks
135.04928 -.00047 (135*2π)/2712 weeks
136.04928 .00047 (136*2π)/2712 weeks
137-.00056 -.00303 (137*2π)/2712 weeks
138.00186 -.02944 (138*2π)/2712 weeks
139-.00157 .01791 (139*2π)/2712 weeks
140.01133 .03618 (140*2π)/2712 weeks
141.08558 .00569 (141*2π)/2712 weeks
142.00547 -.0119 (142*2π)/2712 weeks
143-.01533 -.03552 (143*2π)/2712 weeks
144.01626 .05539 (144*2π)/2712 weeks
145.00654 .01216 (145*2π)/2712 weeks
146.0326 -.00441 (146*2π)/2712 weeks
147-.00112 .0076 (147*2π)/2712 weeks
148.05853 .00369 (148*2π)/2712 weeks
149-.05319 -.01672 (149*2π)/2712 weeks
150-.06519 .02234 (150*2π)/2712 weeks
151.08877 .02005 (151*2π)/2712 weeks
152-.01357 .0027 (152*2π)/2712 weeks
153.00752 -.04016 (153*2π)/2712 weeks
154-.00449 -.00835 (154*2π)/2712 weeks
155.00035 -.005 (155*2π)/2712 weeks
156.02696 -.01569 (156*2π)/2712 weeks
157-.00877 .01361 (157*2π)/2712 weeks
158.0612 .00907 (158*2π)/2712 weeks
159.0394 -.03484 (159*2π)/2712 weeks
160.00647 .02575 (160*2π)/2712 weeks
161.01309 -.00178 (161*2π)/2712 weeks
162.01756 .00091 (162*2π)/2712 weeks
163.05209 -.0245 (163*2π)/2712 weeks
164.01215 -.02149 (164*2π)/2712 weeks
165.01103 .01203 (165*2π)/2712 weeks
166.01945 .00495 (166*2π)/2712 weeks
167.01399 -.01568 (167*2π)/2712 weeks
168.00555 .0115 (168*2π)/2712 weeks
169.05811 -.02082 (169*2π)/2712 weeks
170.00239 -.02795 (170*2π)/2712 weeks
171-.03857 -.01718 (171*2π)/2712 weeks
172.05458 .0276 (172*2π)/2712 weeks
173.0046 -.04651 (173*2π)/2712 weeks
174-.04358 .00068 (174*2π)/2712 weeks
175.04489 .00534 (175*2π)/2712 weeks
176.00739 -.02873 (176*2π)/2712 weeks
177-.00994 .03331 (177*2π)/2712 weeks
178-.01316 -.01851 (178*2π)/2712 weeks
179.07443 .00563 (179*2π)/2712 weeks
180.03244 -.00582 (180*2π)/2712 weeks
181-.06362 .03534 (181*2π)/2711 weeks
182.05955 -.0065 (182*2π)/2711 weeks
183-.00244 -.03208 (183*2π)/2711 weeks
184.06101 .0449 (184*2π)/2711 weeks
185.00093 .03053 (185*2π)/2711 weeks
186.07651 -.06612 (186*2π)/2711 weeks
187.00387 -.04792 (187*2π)/2711 weeks
188-.02523 .01459 (188*2π)/2711 weeks
189.0773 .035 (189*2π)/2711 weeks
190-.00771 -.00281 (190*2π)/2711 weeks
191.04032 .01178 (191*2π)/2711 weeks
192.04183 -.05846 (192*2π)/2711 weeks
193-.03729 -.02529 (193*2π)/2711 weeks
194.06037 -.00993 (194*2π)/2711 weeks
195.05955 .07727 (195*2π)/2711 weeks
196.01079 -.07258 (196*2π)/2711 weeks
197.02121 -.0541 (197*2π)/2711 weeks
198.0242 -.00488 (198*2π)/2711 weeks
199.0012 .02128 (199*2π)/2711 weeks
200.03583 .01445 (200*2π)/2711 weeks
201.02369 .00556 (201*2π)/2711 weeks
202.01352 -.03966 (202*2π)/2711 weeks
203.01199 -.01799 (203*2π)/2711 weeks
204-.02544 .06901 (204*2π)/2711 weeks
205.08726 .06346 (205*2π)/2711 weeks
206.00887 -.06783 (206*2π)/2711 weeks
207.0034 .04558 (207*2π)/2711 weeks
208.01438 -.08696 (208*2π)/2711 weeks
209.0026 .02385 (209*2π)/2711 weeks
210-.01565 .07248 (210*2π)/2711 weeks
211.00173 -.02734 (211*2π)/2711 weeks
212.04971 .01147 (212*2π)/2711 weeks
213-.01596 -.01354 (213*2π)/2711 weeks
214-.03726 -.02085 (214*2π)/2711 weeks
215.00065 .09693 (215*2π)/2711 weeks
216.02598 -.08776 (216*2π)/2711 weeks
217.00188 -.08149 (217*2π)/2711 weeks
218-.00687 .02544 (218*2π)/2711 weeks
219.06035 -.03951 (219*2π)/2711 weeks
220-.0462 -.07801 (220*2π)/2711 weeks
221.0279 .05882 (221*2π)/2711 weeks
222.11957 -.03219 (222*2π)/2711 weeks
223-.00355 -.00084 (223*2π)/2711 weeks
224-.02707 -.05224 (224*2π)/2711 weeks
225-.02415 .00161 (225*2π)/2711 weeks
226.00881 -.0134 (226*2π)/2711 weeks
227-.02001 .002 (227*2π)/2711 weeks
228.02203 .00446 (228*2π)/2711 weeks
229-.01434 -.01539 (229*2π)/2711 weeks
230-.01102 -.0461 (230*2π)/2711 weeks
231.02156 .09553 (231*2π)/2711 weeks
232.05982 -.09343 (232*2π)/2711 weeks
233-.05525 -.01314 (233*2π)/2711 weeks
234.09077 -.01266 (234*2π)/2711 weeks
235-.02595 -.01142 (235*2π)/2711 weeks
236.07573 -.09405 (236*2π)/2711 weeks
237.03991 .07321 (237*2π)/2711 weeks
238.05058 -.00753 (238*2π)/2711 weeks
239-.0876 -.01229 (239*2π)/2711 weeks
240.07662 -.01453 (240*2π)/2711 weeks
241.03678 -.08513 (241*2π)/2711 weeks
242.04463 -.02821 (242*2π)/2711 weeks
243-.12508 -.00061 (243*2π)/2711 weeks
244-.10251 .01848 (244*2π)/2711 weeks
245.04045 .05223 (245*2π)/2711 weeks
246-.02822 .08058 (246*2π)/2711 weeks
247.18239 -.08527 (247*2π)/2711 weeks
248-.20457 -.04916 (248*2π)/2711 weeks
249-.04746 .02033 (249*2π)/2711 weeks
250.32784 .0567 (250*2π)/2711 weeks
251-.13721 -.3151 (251*2π)/2711 weeks
252-.1018 .03342 (252*2π)/2711 weeks
253.02961 .0413 (253*2π)/2711 weeks
254-.11728 -.13573 (254*2π)/2711 weeks
255.05749 .06041 (255*2π)/2711 weeks
256.36705 .03294 (256*2π)/2711 weeks
257-.04761 -.46671 (257*2π)/2711 weeks
258.00464 .34234 (258*2π)/2711 weeks
259.05323 -.34101 (259*2π)/2711 weeks
260-.60464 -.12745 (260*2π)/2711 weeks
261.57925 .29055 (261*2π)/2711 weeks
262.27671 -.62797 (262*2π)/2711 weeks
263-.01072 -.32112 (263*2π)/2711 weeks
264-.06011 .51846 (264*2π)/2711 weeks
265-.211 .25051 (265*2π)/2711 weeks
266.66478 -.81684 (266*2π)/2711 weeks
267-.67984 .69561 (267*2π)/2711 weeks
2681.80765 .85828 (268*2π)/2711 weeks
269-2.01567 -1.06661 (269*2π)/2711 weeks