Back to list of Stocks    See Also: Seasonal Analysis of ASAGenetic Algorithms Stock Portfolio Generator, and Fourier Calculator

# Fourier Analysis of ASA (ASA Gold and Precious Metals L)

ASA (ASA Gold and Precious Metals L) appears to have interesting cyclic behaviour every 205 weeks (.9728*cosine), 108 weeks (.8017*sine), and 171 weeks (.6455*cosine).

ASA (ASA Gold and Precious Metals L) has an average price of 9.81 (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 1/3/1978 to 3/20/2017 for ASA (ASA Gold and Precious Metals L), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
09.814   0
11.87018 -6.10845 (1*2π)/20462,046 weeks
2-3.12073 -4.78298 (2*2π)/20461,023 weeks
3-2.13487 .66134 (3*2π)/2046682 weeks
4-.96028 -.06512 (4*2π)/2046512 weeks
5-.25016 .83577 (5*2π)/2046409 weeks
6.71775 -.18671 (6*2π)/2046341 weeks
7.8399 -.00404 (7*2π)/2046292 weeks
8.69744 -.86189 (8*2π)/2046256 weeks
9-.1734 -1.15311 (9*2π)/2046227 weeks
10-.9728 -.3182 (10*2π)/2046205 weeks
11-.04066 -.008 (11*2π)/2046186 weeks
12.64555 -.44132 (12*2π)/2046171 weeks
13.44077 -.22957 (13*2π)/2046157 weeks
14.20727 -.49973 (14*2π)/2046146 weeks
15-.03142 -.27851 (15*2π)/2046136 weeks
16.17102 -.11175 (16*2π)/2046128 weeks
17.48488 .0513 (17*2π)/2046120 weeks
18.03378 -.43234 (18*2π)/2046114 weeks
19-.37416 -.80169 (19*2π)/2046108 weeks
20-.21531 -.14406 (20*2π)/2046102 weeks
21.05721 -.13987 (21*2π)/204697 weeks
22.00441 -.62074 (22*2π)/204693 weeks
23-.36516 -.36562 (23*2π)/204689 weeks
24-.46341 .07635 (24*2π)/204685 weeks
25.08555 .13965 (25*2π)/204682 weeks
26.18978 -.03212 (26*2π)/204679 weeks
27-.10084 -.45833 (27*2π)/204676 weeks
28-.21557 -.32513 (28*2π)/204673 weeks
29-.12114 -.06969 (29*2π)/204671 weeks
30.03451 -.04497 (30*2π)/204668 weeks
31-.01606 -.00615 (31*2π)/204666 weeks
32.02283 -.37494 (32*2π)/204664 weeks
33-.41381 -.07416 (33*2π)/204662 weeks
34-.38514 .30533 (34*2π)/204660 weeks
35-.00589 .16509 (35*2π)/204658 weeks
36.07308 -.12328 (36*2π)/204657 weeks
37-.07181 -.11311 (37*2π)/204655 weeks
38.07539 -.00823 (38*2π)/204654 weeks
39.11983 -.0472 (39*2π)/204652 weeks
40-.07924 -.17915 (40*2π)/204651 weeks
41-.08147 .00214 (41*2π)/204650 weeks
42.04316 .05934 (42*2π)/204649 weeks
43.08324 .13942 (43*2π)/204648 weeks
44.14492 .08594 (44*2π)/204647 weeks
45.13426 -.15358 (45*2π)/204645 weeks
46-.01867 -.08696 (46*2π)/204644 weeks
47-.00682 .00678 (47*2π)/204644 weeks
48-.07308 -.15654 (48*2π)/204643 weeks
49.02774 -.04847 (49*2π)/204642 weeks
50.02201 -.05124 (50*2π)/204641 weeks
51-.14212 -.14111 (51*2π)/204640 weeks
52.00113 .05231 (52*2π)/204639 weeks
53.05384 -.03438 (53*2π)/204639 weeks
54.13707 -.04602 (54*2π)/204638 weeks
55.02796 -.13045 (55*2π)/204637 weeks
56.12443 -.09375 (56*2π)/204637 weeks
57.03193 .05025 (57*2π)/204636 weeks
58.15916 -.09513 (58*2π)/204635 weeks
59.06746 -.01275 (59*2π)/204635 weeks
60-.08 -.03212 (60*2π)/204634 weeks
61-.01938 -.08431 (61*2π)/204634 weeks
62.0526 -.00039 (62*2π)/204633 weeks
63.11698 -.08092 (63*2π)/204632 weeks
64.03576 -.17686 (64*2π)/204632 weeks
65-.18111 -.03821 (65*2π)/204631 weeks
66-.02754 .03956 (66*2π)/204631 weeks
67-.00518 -.05892 (67*2π)/204631 weeks
68.09368 -.09934 (68*2π)/204630 weeks
69.07913 -.13147 (69*2π)/204630 weeks
70-.07737 -.09491 (70*2π)/204629 weeks
71.02647 -.0415 (71*2π)/204629 weeks
72.03785 -.00603 (72*2π)/204628 weeks
73-.01851 -.04991 (73*2π)/204628 weeks
74-.00882 .02716 (74*2π)/204628 weeks
75.03211 -.08134 (75*2π)/204627 weeks
76.0395 .04151 (76*2π)/204627 weeks
77.03468 -.08684 (77*2π)/204627 weeks
78.0208 -.03776 (78*2π)/204626 weeks
79.03428 -.09585 (79*2π)/204626 weeks
80.0253 -.14377 (80*2π)/204626 weeks
81.01001 -.17418 (81*2π)/204625 weeks
82-.09804 -.04016 (82*2π)/204625 weeks
83-.13083 -.04304 (83*2π)/204625 weeks
84-.02103 .03347 (84*2π)/204624 weeks
85.07989 .05731 (85*2π)/204624 weeks
86.06908 -.05696 (86*2π)/204624 weeks
87.05182 -.07078 (87*2π)/204624 weeks
88-.06277 -.14582 (88*2π)/204623 weeks
89-.07938 -.05575 (89*2π)/204623 weeks
90-.01098 .0064 (90*2π)/204623 weeks
91.05971 -.06678 (91*2π)/204622 weeks
92.00945 -.20771 (92*2π)/204622 weeks
93-.08404 -.15365 (93*2π)/204622 weeks
94-.05357 .01787 (94*2π)/204622 weeks
95-.03004 -.03328 (95*2π)/204622 weeks
96-.02078 -.0525 (96*2π)/204621 weeks
97-.0521 -.06697 (97*2π)/204621 weeks
98-.02538 .01105 (98*2π)/204621 weeks
99-.0085 .04923 (99*2π)/204621 weeks
100.01819 -.05121 (100*2π)/204620 weeks
101-.04421 -.07589 (101*2π)/204620 weeks
102-.04614 .00959 (102*2π)/204620 weeks
103-.04724 .06477 (103*2π)/204620 weeks
104.02427 .01092 (104*2π)/204620 weeks
105.06565 -.07624 (105*2π)/204619 weeks
106-.01105 -.07586 (106*2π)/204619 weeks
107-.05052 -.06502 (107*2π)/204619 weeks
108.0111 -.0891 (108*2π)/204619 weeks
109-.02568 -.05285 (109*2π)/204619 weeks
110.01907 .01152 (110*2π)/204619 weeks
111.04132 -.015 (111*2π)/204618 weeks
112-.02921 -.04202 (112*2π)/204618 weeks
113-.0054 -.0453 (113*2π)/204618 weeks
114.00203 -.05633 (114*2π)/204618 weeks
115.00313 -.02581 (115*2π)/204618 weeks
116-.00601 -.04026 (116*2π)/204618 weeks
117.01776 -.07282 (117*2π)/204617 weeks
118-.03132 .00996 (118*2π)/204617 weeks
119.01814 -.02423 (119*2π)/204617 weeks
120-.07966 -.00142 (120*2π)/204617 weeks
121-.03145 -.03832 (121*2π)/204617 weeks
122-.04621 -.05003 (122*2π)/204617 weeks
123-.06343 .03112 (123*2π)/204617 weeks
124.04056 -.01236 (124*2π)/204617 weeks
125.02614 -.07789 (125*2π)/204616 weeks
126.00663 -.08342 (126*2π)/204616 weeks
127-.03999 -.06006 (127*2π)/204616 weeks
128-.11318 .05289 (128*2π)/204616 weeks
129.04206 .05885 (129*2π)/204616 weeks
130.08337 -.11679 (130*2π)/204616 weeks
131-.00379 -.06703 (131*2π)/204616 weeks
132-.01677 -.00266 (132*2π)/204616 weeks
133.03412 -.09047 (133*2π)/204615 weeks
134-.05977 -.06651 (134*2π)/204615 weeks
135-.08397 -.01551 (135*2π)/204615 weeks
136-.04954 .00077 (136*2π)/204615 weeks
137-.00779 .02026 (137*2π)/204615 weeks
138-.048 -.05903 (138*2π)/204615 weeks
139.01971 -.02555 (139*2π)/204615 weeks
140.03589 -.00522 (140*2π)/204615 weeks
141.00906 -.08992 (141*2π)/204615 weeks
142-.08587 -.04983 (142*2π)/204614 weeks
143-.04855 .00913 (143*2π)/204614 weeks
144-.05821 .0117 (144*2π)/204614 weeks
145.00114 -.00513 (145*2π)/204614 weeks
146.01578 .02962 (146*2π)/204614 weeks
147.03154 -.03431 (147*2π)/204614 weeks
148-.03373 -.04715 (148*2π)/204614 weeks
149-.05919 .00136 (149*2π)/204614 weeks
150-.03443 .0261 (150*2π)/204614 weeks
151-.01047 -.02548 (151*2π)/204614 weeks
152-.02403 -.04708 (152*2π)/204613 weeks
153.00308 -.01001 (153*2π)/204613 weeks
154-.00563 -.04269 (154*2π)/204613 weeks
155-.04447 -.01073 (155*2π)/204613 weeks
156.00463 .00514 (156*2π)/204613 weeks
157-.01173 .00825 (157*2π)/204613 weeks
158-.01245 -.01175 (158*2π)/204613 weeks
159-.03408 .0146 (159*2π)/204613 weeks
160-.01862 .03545 (160*2π)/204613 weeks
161.03613 .04021 (161*2π)/204613 weeks
162.04783 -.02127 (162*2π)/204613 weeks
163-.05387 -.0237 (163*2π)/204613 weeks
164-.03208 .00096 (164*2π)/204612 weeks
165.02512 .02926 (165*2π)/204612 weeks
166.07329 -.03859 (166*2π)/204612 weeks
167-.05241 -.03197 (167*2π)/204612 weeks
168-.03042 -.02318 (168*2π)/204612 weeks
169.01127 -.00112 (169*2π)/204612 weeks
170-.01238 -.03164 (170*2π)/204612 weeks
171-.01034 -.04899 (171*2π)/204612 weeks
172-.02268 .01278 (172*2π)/204612 weeks
173.02184 .03311 (173*2π)/204612 weeks
174.03041 .0232 (174*2π)/204612 weeks
175.01689 -.0124 (175*2π)/204612 weeks
176.0308 -.05348 (176*2π)/204612 weeks
177-.0301 -.04923 (177*2π)/204612 weeks
178-.00533 .00702 (178*2π)/204611 weeks
179-.01502 .01366 (179*2π)/204611 weeks
180-.01773 -.01953 (180*2π)/204611 weeks
181-.00103 -.02858 (181*2π)/204611 weeks
182.0028 -.00367 (182*2π)/204611 weeks
183-.01882 -.0201 (183*2π)/204611 weeks
184.02735 -.0164 (184*2π)/204611 weeks
185.02366 -.02065 (185*2π)/204611 weeks
186.03587 -.04206 (186*2π)/204611 weeks
187-.02441 -.05103 (187*2π)/204611 weeks
188-.0515 -.04435 (188*2π)/204611 weeks
189.00867 .02985 (189*2π)/204611 weeks
190.02346 -.01861 (190*2π)/204611 weeks
191-.00873 -.06324 (191*2π)/204611 weeks
192-.06584 -.00663 (192*2π)/204611 weeks
193-.00342 .01032 (193*2π)/204611 weeks
194.01144 -.01619 (194*2π)/204611 weeks
195-.02678 -.02374 (195*2π)/204610 weeks
196-.03882 .02531 (196*2π)/204610 weeks
197.02325 .01788 (197*2π)/204610 weeks
198.03371 -.04559 (198*2π)/204610 weeks
199.00737 -.04975 (199*2π)/204610 weeks
200-.02674 -.04753 (200*2π)/204610 weeks
201-.04385 -.01109 (201*2π)/204610 weeks
202-.00945 .03253 (202*2π)/204610 weeks
203-.01593 .01951 (203*2π)/204610 weeks
204.01721 .00125 (204*2π)/204610 weeks
205.03608 -.00644 (205*2π)/204610 weeks
206.00297 -.02404 (206*2π)/204610 weeks
207-.00557 -.00931 (207*2π)/204610 weeks
208.01208 -.03564 (208*2π)/204610 weeks
209-.03505 -.00479 (209*2π)/204610 weeks
210-.02877 .02041 (210*2π)/204610 weeks
211.01778 .00912 (211*2π)/204610 weeks
212.02559 -.01884 (212*2π)/204610 weeks
213-.00191 -.01782 (213*2π)/204610 weeks
214-.0122 -.01924 (214*2π)/204610 weeks
215.00417 .02095 (215*2π)/204610 weeks
216.0232 -.00762 (216*2π)/20469 weeks
217.04023 -.03166 (217*2π)/20469 weeks
218.03542 -.0298 (218*2π)/20469 weeks
219-.02172 -.03257 (219*2π)/20469 weeks
220.00738 -.0394 (220*2π)/20469 weeks
221.00872 -.03407 (221*2π)/20469 weeks
222-.03985 -.03056 (222*2π)/20469 weeks
223-.04803 -.02053 (223*2π)/20469 weeks
224-.02706 .03352 (224*2π)/20469 weeks
225.03505 .00207 (225*2π)/20469 weeks
226.01974 -.03458 (226*2π)/20469 weeks
227-.03918 -.06935 (227*2π)/20469 weeks
228-.04054 -.01859 (228*2π)/20469 weeks
229-.00894 .00885 (229*2π)/20469 weeks
230.01309 -.01093 (230*2π)/20469 weeks
231-.01636 -.00498 (231*2π)/20469 weeks
232-.01177 -.02063 (232*2π)/20469 weeks
233-.01901 .00029 (233*2π)/20469 weeks
234.00762 -.01072 (234*2π)/20469 weeks
235-.021 .00511 (235*2π)/20469 weeks
236-.05537 -.03326 (236*2π)/20469 weeks
237-.00552 -.00032 (237*2π)/20469 weeks
238.00371 .02911 (238*2π)/20469 weeks
239-.0003 -.00356 (239*2π)/20469 weeks
240-.01141 -.0225 (240*2π)/20469 weeks
241-.04016 .00304 (241*2π)/20468 weeks
242-.00017 .00715 (242*2π)/20468 weeks
243.01651 .00835 (243*2π)/20468 weeks
244.02861 -.0096 (244*2π)/20468 weeks
245.03303 -.02039 (245*2π)/20468 weeks
246-.02541 -.02663 (246*2π)/20468 weeks
247-.01758 -.00873 (247*2π)/20468 weeks
248.00737 .00088 (248*2π)/20468 weeks
249-.01688 -.02668 (249*2π)/20468 weeks
250.01448 .00602 (250*2π)/20468 weeks
251-.00916 -.0108 (251*2π)/20468 weeks
252-.00758 -.01617 (252*2π)/20468 weeks
253-.03057 -.02099 (253*2π)/20468 weeks
254.02156 .03595 (254*2π)/20468 weeks
255.02553 .0086 (255*2π)/20468 weeks
256.05882 -.06956 (256*2π)/20468 weeks
257-.03963 -.07345 (257*2π)/20468 weeks
258-.06291 .0151 (258*2π)/20468 weeks
259.00418 .01445 (259*2π)/20468 weeks
260.01297 .00368 (260*2π)/20468 weeks
261-.00065 -.00723 (261*2π)/20468 weeks
262.00311 -.01063 (262*2π)/20468 weeks
263-.00157 -.00865 (263*2π)/20468 weeks
264-.03941 -.01781 (264*2π)/20468 weeks
265-.03309 .00193 (265*2π)/20468 weeks
266.01551 .01841 (266*2π)/20468 weeks
267.03535 -.03478 (267*2π)/20468 weeks
268-.01944 -.02934 (268*2π)/20468 weeks
269.00638 .02346 (269*2π)/20468 weeks
270.02827 -.00533 (270*2π)/20468 weeks
271.01479 -.00815 (271*2π)/20468 weeks
272-.00655 -.04536 (272*2π)/20468 weeks
273-.02664 -.03994 (273*2π)/20467 weeks
274-.01966 .02009 (274*2π)/20467 weeks
275.00338 .0019 (275*2π)/20467 weeks
276.02109 -.02939 (276*2π)/20467 weeks
277-.00793 -.03446 (277*2π)/20467 weeks
278-.02174 -.03051 (278*2π)/20467 weeks
279-.0271 .00243 (279*2π)/20467 weeks
280-.01001 .01315 (280*2π)/20467 weeks
281-.01631 -.00122 (281*2π)/20467 weeks
282-.02168 .00754 (282*2π)/20467 weeks
283.01249 -.00443 (283*2π)/20467 weeks
284.00129 -.02343 (284*2π)/20467 weeks
285-.01899 -.03429 (285*2π)/20467 weeks
286-.01559 .00334 (286*2π)/20467 weeks
287-.02178 .03007 (287*2π)/20467 weeks
288.0267 .01203 (288*2π)/20467 weeks
289.04664 -.00228 (289*2π)/20467 weeks
290-.00101 -.04853 (290*2π)/20467 weeks
291-.02747 -.0269 (291*2π)/20467 weeks
292-.02684 -.00383 (292*2π)/20467 weeks
293.00573 .02046 (293*2π)/20467 weeks
294.00312 .0224 (294*2π)/20467 weeks
295.01366 .00299 (295*2π)/20467 weeks
296.0384 -.02281 (296*2π)/20467 weeks
297-.00891 -.03683 (297*2π)/20467 weeks
298-.02144 -.01838 (298*2π)/20467 weeks
299-.01579 .01587 (299*2π)/20467 weeks
300-.03337 .00628 (300*2π)/20467 weeks
301.00732 .00663 (301*2π)/20467 weeks
302.03949 .00421 (302*2π)/20467 weeks
303.0156 -.03095 (303*2π)/20467 weeks
304-.00601 -.04011 (304*2π)/20467 weeks
305.01896 -.01993 (305*2π)/20467 weeks
306-.0306 -.0114 (306*2π)/20467 weeks
307-.02507 -.00468 (307*2π)/20467 weeks
308.00399 .00272 (308*2π)/20467 weeks
309.00292 .01016 (309*2π)/20467 weeks
310.01928 .00234 (310*2π)/20467 weeks
311.01981 -.04831 (311*2π)/20467 weeks
312-.02904 -.03308 (312*2π)/20467 weeks
313-.03487 .01117 (313*2π)/20467 weeks
314.02744 .01922 (314*2π)/20467 weeks
315.00001 -.01598 (315*2π)/20466 weeks
316-.0049 -.02565 (316*2π)/20466 weeks
317-.00182 -.0058 (317*2π)/20466 weeks
318.00436 -.00264 (318*2π)/20466 weeks
319.01408 -.03239 (319*2π)/20466 weeks
320-.00191 -.02412 (320*2π)/20466 weeks
321-.00068 -.0227 (321*2π)/20466 weeks
322-.02268 .00467 (322*2π)/20466 weeks
323-.00297 -.0035 (323*2π)/20466 weeks
324.0264 -.04645 (324*2π)/20466 weeks
325-.02733 -.04036 (325*2π)/20466 weeks
326-.03017 -.00364 (326*2π)/20466 weeks
327-.00471 .00325 (327*2π)/20466 weeks
328-.00107 -.00911 (328*2π)/20466 weeks
329-.00288 -.01835