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


ASA (ASA Gold and Precious Metals L) appears to have interesting cyclic behaviour every 203 weeks (.9378*cosine), 107 weeks (.8134*sine), and 203 weeks (.6172*sine).

ASA (ASA Gold and Precious Metals L) has an average price of 9.8 (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 1/3/1978 to 11/21/2016 for ASA (ASA Gold and Precious Metals L), this program was able to calculate the following Fourier Series:
<
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
09.79708   0 
12.0418 -6.02322 (1*2π)/20292,029 weeks
2-2.85796 -5.02227 (2*2π)/20291,015 weeks
3-2.27228 .37763 (3*2π)/2029676 weeks
4-1.11387 -.22538 (4*2π)/2029507 weeks
5-.57144 .793 (5*2π)/2029406 weeks
6.53286 -.01375 (6*2π)/2029338 weeks
7.69122 .25524 (7*2π)/2029290 weeks
8.82198 -.56154 (8*2π)/2029254 weeks
9.13275 -1.12171 (9*2π)/2029225 weeks
10-.93784 -.61719 (10*2π)/2029203 weeks
11-.27006 -.0557 (11*2π)/2029184 weeks
12.56272 -.21864 (12*2π)/2029169 weeks
13.40692 -.03826 (13*2π)/2029156 weeks
14.33667 -.3603 (14*2π)/2029145 weeks
15.03431 -.28765 (15*2π)/2029135 weeks
16.11973 -.05437 (16*2π)/2029127 weeks
17.37559 .35853 (17*2π)/2029119 weeks
18.25399 -.15615 (18*2π)/2029113 weeks
19.09648 -.81338 (19*2π)/2029107 weeks
20-.12683 -.28415 (20*2π)/2029101 weeks
21.05949 -.04845 (21*2π)/202997 weeks
22.37713 -.46255 (22*2π)/202992 weeks
23.0317 -.58337 (23*2π)/202988 weeks
24-.42294 -.38791 (24*2π)/202985 weeks
25-.15519 .0411 (25*2π)/202981 weeks
26.04537 .15384 (26*2π)/202978 weeks
27.17891 -.32708 (27*2π)/202975 weeks
28.07578 -.4429 (28*2π)/202972 weeks
29-.04414 -.26704 (29*2π)/202970 weeks
30.03708 -.10734 (30*2π)/202968 weeks
31-.04781 -.02459 (31*2π)/202965 weeks
32.36951 -.20485 (32*2π)/202963 weeks
33-.00201 -.44933 (33*2π)/202961 weeks
34-.45052 -.31653 (34*2π)/202960 weeks
35-.3198 -.0741 (35*2π)/202958 weeks
36-.03384 -.10185 (36*2π)/202956 weeks
37-.05862 -.25105 (37*2π)/202955 weeks
38-.06538 -.09953 (38*2π)/202953 weeks
39.00177 .01382 (39*2π)/202952 weeks
40.08574 -.21987 (40*2π)/202951 weeks
41-.03866 -.24211 (41*2π)/202949 weeks
42-.05392 -.15023 (42*2π)/202948 weeks
43-.16277 -.05494 (43*2π)/202947 weeks
44-.199 .06324 (44*2π)/202946 weeks
45.03271 .05611 (45*2π)/202945 weeks
46.00743 -.04979 (46*2π)/202944 weeks
47-.11035 -.00274 (47*2π)/202943 weeks
48.01248 -.15251 (48*2π)/202942 weeks
49-.02159 -.06686 (49*2π)/202941 weeks
50-.03354 -.00211 (50*2π)/202941 weeks
51.06294 -.23557 (51*2π)/202940 weeks
52-.09571 -.1623 (52*2π)/202939 weeks
53-.07168 -.1477 (53*2π)/202938 weeks
54-.0728 -.01982 (54*2π)/202938 weeks
55.01222 -.12214 (55*2π)/202937 weeks
56.08016 -.02155 (56*2π)/202936 weeks
57-.09615 -.09895 (57*2π)/202936 weeks
58.02388 .04548 (58*2π)/202935 weeks
59-.0351 .08549 (59*2π)/202934 weeks
60-.05956 -.06413 (60*2π)/202934 weeks
61.01119 -.09934 (61*2π)/202933 weeks
62-.08741 -.0801 (62*2π)/202933 weeks
63-.09519 .04397 (63*2π)/202932 weeks
64.05627 .13883 (64*2π)/202932 weeks
65.05963 -.10812 (65*2π)/202931 weeks
66-.07152 -.11118 (66*2π)/202931 weeks
67-.05401 -.14897 (67*2π)/202930 weeks
68-.05082 -.0567 (68*2π)/202930 weeks
69-.01145 .06164 (69*2π)/202929 weeks
70.05965 -.07178 (70*2π)/202929 weeks
71.04441 -.04216 (71*2π)/202929 weeks
72-.02172 -.01054 (72*2π)/202928 weeks
73.03989 -.02752 (73*2π)/202928 weeks
74-.04892 -.09598 (74*2π)/202927 weeks
75.04771 -.03918 (75*2π)/202927 weeks
76-.08987 -.08134 (76*2π)/202927 weeks
77-.03219 -.03869 (77*2π)/202926 weeks
78-.08022 -.0732 (78*2π)/202926 weeks
79-.09533 -.05901 (79*2π)/202926 weeks
80-.08066 -.02364 (80*2π)/202925 weeks
81-.00304 .11185 (81*2π)/202925 weeks
82-.01125 .05609 (82*2π)/202925 weeks
83.10168 -.02859 (83*2π)/202924 weeks
84.10232 -.08841 (84*2π)/202924 weeks
85-.03421 -.11265 (85*2π)/202924 weeks
86-.05207 -.07117 (86*2π)/202924 weeks
87-.14326 -.02264 (87*2π)/202923 weeks
88-.03852 .02526 (88*2π)/202923 weeks
89.03469 -.0188 (89*2π)/202923 weeks
90-.00758 -.11509 (90*2π)/202923 weeks
91-.12744 -.12987 (91*2π)/202922 weeks
92-.10301 .00159 (92*2π)/202922 weeks
93.03771 .07813 (93*2π)/202922 weeks
94-.0006 -.006 (94*2π)/202922 weeks
95-.00878 -.02199 (95*2π)/202921 weeks
96-.03213 -.00849 (96*2π)/202921 weeks
97.03683 .03432 (97*2π)/202921 weeks
98.05009 .03459 (98*2π)/202921 weeks
99.00548 -.0644 (99*2π)/202920 weeks
100-.05032 -.03382 (100*2π)/202920 weeks
101.00071 .04011 (101*2π)/202920 weeks
102.02115 .0637 (102*2π)/202920 weeks
103.05213 -.03214 (103*2π)/202920 weeks
104.04032 -.1133 (104*2π)/202920 weeks
105-.03174 -.06679 (105*2π)/202919 weeks
106-.05146 -.04304 (106*2π)/202919 weeks
107.00484 -.08189 (107*2π)/202919 weeks
108-.01712 -.02998 (108*2π)/202919 weeks
109.04284 .01337 (109*2π)/202919 weeks
110.0475 -.02262 (110*2π)/202918 weeks
111-.02821 -.03227 (111*2π)/202918 weeks
112-.00106 -.03994 (112*2π)/202918 weeks
113.00469 -.05013 (113*2π)/202918 weeks
114.01008 -.01969 (114*2π)/202918 weeks
115-.00077 -.03402 (115*2π)/202918 weeks
116.01994 -.06687 (116*2π)/202917 weeks
117-.02264 .01933 (117*2π)/202917 weeks
118.02506 -.01886 (118*2π)/202917 weeks
119-.07254 .00542 (119*2π)/202917 weeks
120-.02376 -.03273 (120*2π)/202917 weeks
121-.03793 -.04662 (121*2π)/202917 weeks
122-.06263 .03314 (122*2π)/202917 weeks
123.04337 .00139 (123*2π)/202916 weeks
124.04027 -.06458 (124*2π)/202916 weeks
125.02687 -.07627 (125*2π)/202916 weeks
126-.0195 -.06718 (126*2π)/202916 weeks
127-.12455 .02856 (127*2π)/202916 weeks
128.01377 .08136 (128*2π)/202916 weeks
129.10904 -.07436 (129*2π)/202916 weeks
130.0251 -.05909 (130*2π)/202916 weeks
131-.0107 .00223 (131*2π)/202915 weeks
132.07287 -.06179 (132*2π)/202915 weeks
133-.01212 -.08096 (133*2π)/202915 weeks
134-.06274 -.05154 (134*2π)/202915 weeks
135-.04981 -.02543 (135*2π)/202915 weeks
136-.02437 .02093 (136*2π)/202915 weeks
137-.03045 -.06937 (137*2π)/202915 weeks
138.0154 -.01824 (138*2π)/202915 weeks
139.02834 .02455 (139*2π)/202915 weeks
140.06912 -.05498 (140*2π)/202914 weeks
141-.0228 -.09324 (141*2π)/202914 weeks
142-.03654 -.03603 (142*2π)/202914 weeks
143-.06345 -.03986 (143*2π)/202914 weeks
144-.01362 -.02218 (144*2π)/202914 weeks
145-.02486 .02869 (145*2π)/202914 weeks
146.03752 .0106 (146*2π)/202914 weeks
147.01931 -.04587 (147*2π)/202914 weeks
148-.03475 -.04518 (148*2π)/202914 weeks
149-.05819 -.00996 (149*2π)/202914 weeks
150-.01528 -.0205 (150*2π)/202914 weeks
151.00065 -.05581 (151*2π)/202913 weeks
152-.00426 -.01373 (152*2π)/202913 weeks
153.02828 -.03459 (153*2π)/202913 weeks
154-.01457 -.06115 (154*2π)/202913 weeks
155-.00241 -.01798 (155*2π)/202913 weeks
156-.01589 -.01812 (156*2π)/202913 weeks
157.00565 -.02978 (157*2π)/202913 weeks
158-.02359 -.04639 (158*2π)/202913 weeks
159-.05236 -.0406 (159*2π)/202913 weeks
160-.05746 .02089 (160*2π)/202913 weeks
161.00932 .04827 (161*2π)/202913 weeks
162-.013 -.04264 (162*2π)/202913 weeks
163-.03223 -.0584 (163*2π)/202912 weeks
164-.06614 -.00462 (164*2π)/202912 weeks
165.0181 .06807 (165*2π)/202912 weeks
166-.00652 -.02796 (166*2π)/202912 weeks
167-.00749 -.04652 (167*2π)/202912 weeks
168-.02344 -.00193 (168*2π)/202912 weeks
169-.00789 -.02159 (169*2π)/202912 weeks
170.04012 -.03446 (170*2π)/202912 weeks
171.00011 -.0578 (171*2π)/202912 weeks
172-.0307 -.02276 (172*2π)/202912 weeks
173-.05265 .00393 (173*2π)/202912 weeks
174-.04994 -.00011 (174*2π)/202912 weeks
175-.00154 .03544 (175*2π)/202912 weeks
176.03194 -.01846 (176*2π)/202912 weeks
177-.00206 -.0047 (177*2π)/202911 weeks
178-.03563 -.01204 (178*2π)/202911 weeks
179-.02232 -.02793 (179*2π)/202911 weeks
180-.00043 -.02085 (180*2π)/202911 weeks
181-.0238 -.01037 (181*2π)/202911 weeks
182-.0133 -.04871 (182*2π)/202911 weeks
183-.02148 -.01901 (183*2π)/202911 weeks
184-.03216 -.01238 (184*2π)/202911 weeks
185-.02703 .0401 (185*2π)/202911 weeks
186-.00083 .02266 (186*2π)/202911 weeks
187.05382 -.03171 (187*2π)/202911 weeks
188-.02477 -.02763 (188*2π)/202911 weeks
189-.0422 .01006 (189*2π)/202911 weeks
190.0176 .04571 (190*2π)/202911 weeks
191.02903 -.03275 (191*2π)/202911 weeks
192-.00596 -.02966 (192*2π)/202911 weeks
193-.01227 .00837 (193*2π)/202911 weeks
194.02644 .00817 (194*2π)/202910 weeks
195.01451 -.05745 (195*2π)/202910 weeks
196-.04104 -.05777 (196*2π)/202910 weeks
197-.03313 -.01133 (197*2π)/202910 weeks
198-.02457 .01662 (198*2π)/202910 weeks
199.0129 .02824 (199*2π)/202910 weeks
200.04987 .00242 (200*2π)/202910 weeks
201.01426 -.00955 (201*2π)/202910 weeks
202.01287 -.04437 (202*2π)/202910 weeks
203.00808 -.04415 (203*2π)/202910 weeks
204-.02393 -.01701 (204*2π)/202910 weeks
205-.00963 -.00569 (205*2π)/202910 weeks
206-.01507 -.02904 (206*2π)/202910 weeks
207-.0145 .0262 (207*2π)/202910 weeks
208.01104 .01489 (208*2π)/202910 weeks
209.02434 -.03264 (209*2π)/202910 weeks
210.00099 -.04392 (210*2π)/202910 weeks
211-.01551 -.01635 (211*2π)/202910 weeks
212-.01404 -.01267 (212*2π)/202910 weeks
213.02278 -.00071 (213*2π)/202910 weeks
214.01066 -.03973 (214*2π)/20299 weeks
215.00563 -.05769 (215*2π)/20299 weeks
216-.00295 -.04057 (216*2π)/20299 weeks
217-.0466 -.01185 (217*2π)/20299 weeks
218-.01693 -.03386 (218*2π)/20299 weeks
219-.01626 -.02331 (219*2π)/20299 weeks
220-.05274 .00317 (220*2π)/20299 weeks
221-.04262 .01087 (221*2π)/20299 weeks
222.00292 .03811 (222*2π)/20299 weeks
223.03504 -.02344 (223*2π)/20299 weeks
224-.00428 -.0441 (224*2π)/20299 weeks
225-.06511 -.04593 (225*2π)/20299 weeks
226-.03745 .00392 (226*2π)/20299 weeks
227.00158 .01361 (227*2π)/20299 weeks
228.01137 -.01341 (228*2π)/20299 weeks
229-.01756 .00034 (229*2π)/20299 weeks
230-.01546 -.01608 (230*2π)/20299 weeks
231-.01723 .00554 (231*2π)/20299 weeks
232.0055 -.01095 (232*2π)/20299 weeks
233-.02203 .00864 (233*2π)/20299 weeks
234-.05847 -.02552 (234*2π)/20299 weeks
235-.00354 .00219 (235*2π)/20299 weeks
236.0059 .02948 (236*2π)/20299 weeks
237-.00145 -.00366 (237*2π)/20299 weeks
238-.01332 -.02192 (238*2π)/20299 weeks
239-.04231 .00335 (239*2π)/20298 weeks
240-.0034 .00795 (240*2π)/20298 weeks
241.01245 .01083 (241*2π)/20298 weeks
242.02614 -.0049 (242*2π)/20298 weeks
243.03412 -.01419 (243*2π)/20298 weeks
244-.02244 -.02867 (244*2π)/20298 weeks
245-.01983 -.0114 (245*2π)/20298 weeks
246.00286 .00397 (246*2π)/20298 weeks
247-.01558 -.02901 (247*2π)/20298 weeks
248.00791 .01001 (248*2π)/20298 weeks
249-.00989 -.00984 (249*2π)/20298 weeks
250-.00716 -.01576 (250*2π)/20298 weeks
251-.03102 -.03342 (251*2π)/20298 weeks
252-.00509 .04017 (252*2π)/20298 weeks
253.00621 .03018 (253*2π)/20298 weeks
254.08061 -.02494 (254*2π)/20298 weeks
255.00817 -.08279 (255*2π)/20298 weeks
256-.06303 -.02665 (256*2π)/20298 weeks
257-.01566 .00679 (257*2π)/20298 weeks
258-.00019 .00967 (258*2π)/20298 weeks
259-.00451 -.0032 (259*2π)/20298 weeks
260.00247 -.00375 (260*2π)/20298 weeks
261.00244 -.00128 (261*2π)/20298 weeks
262-.02455 -.03523 (262*2π)/20298 weeks
263-.04284 -.02851 (263*2π)/20298 weeks
264-.02673 .01896 (264*2π)/20298 weeks
265.03192 .00253 (265*2π)/20298 weeks
266.00035 -.0391 (266*2π)/20298 weeks
267-.02512 .01218 (267*2π)/20298 weeks
268.00587 .02042 (268*2π)/20298 weeks
269.00226 .02365 (269*2π)/20298 weeks
270.02144 -.01465 (270*2π)/20298 weeks
271.0178 -.04493 (271*2π)/20297 weeks
272-.03079 -.01136 (272*2π)/20297 weeks
273-.02221 .00285 (273*2π)/20297 weeks
274.0174 .01009 (274*2π)/20297 weeks
275.02032 -.01116 (275*2π)/20297 weeks
276.02262 -.03022 (276*2π)/20297 weeks
277-.00558 -.02915 (277*2π)/20297 weeks
278-.01613 -.00831 (278*2π)/20297 weeks
279-.01183 -.01743 (279*2π)/20297 weeks
280-.03203 -.02635 (280*2π)/20297 weeks
281-.0162 .00182 (281*2π)/20297 weeks
282.00129 -.00256 (282*2π)/20297 weeks
283.02212 -.03247 (283*2π)/20297 weeks
284.0043 -.02935 (284*2π)/20297 weeks
285-.04097 -.04134 (285*2π)/20297 weeks
286-.03396 -.00765 (286*2π)/20297 weeks
287-.02546 .04169 (287*2π)/20297 weeks
288.01957 .01101 (288*2π)/20297 weeks
289.02027 -.01977 (289*2π)/20297 weeks
290.00984 -.04153 (290*2π)/20297 weeks
291-.01069 -.01675 (291*2π)/20297 weeks
292-.03375 -.01598 (292*2π)/20297 weeks
293-.03764 -.01205 (293*2π)/20297 weeks
294-.01545 .03345 (294*2π)/20297 weeks
295.0121 .01059 (295*2π)/20297 weeks
296.02128 -.00828 (296*2π)/20297 weeks
297-.00943 -.00587 (297*2π)/20297 weeks
298-.01366 -.04682 (298*2π)/20297 weeks
299-.02204 -.03965 (299*2π)/20297 weeks
300-.04419 .00362 (300*2π)/20297 weeks
301-.02437 .01121 (301*2π)/20297 weeks
302.00514 -.00841 (302*2π)/20297 weeks
303.00091 .03231 (303*2π)/20297 weeks
304.00472 -.0025 (304*2π)/20297 weeks
305.00755 -.02702 (305*2π)/20297 weeks
306.00018 -.01517 (306*2π)/20297 weeks
307-.01644 -.02431 (307*2π)/20297 weeks
308-.04812 -.01497 (308*2π)/20297 weeks
309-.01486 .03134 (309*2π)/20297 weeks
310.02271 .014 (310*2π)/20297 weeks
311.01877 -.04081 (311*2π)/20297 weeks
312-.03207 -.00904 (312*2π)/20297 weeks
313-.02377 -.00913 (313*2π)/20296 weeks
314-.00121 -.00655 (314*2π)/20296 weeks
315-.00639 -.01354 (315*2π)/20296 weeks
316-.02705 -.02543 (316*2π)/20296 weeks
317-.01758 .00031 (317*2π)/20296 weeks
318-.01179 -.00058 (318*2π)/20296 weeks
319-.00249 .02065 (319*2π)/20296 weeks
320-.00767 -.01396 (320*2π)/20296 weeks
321-.0272 -.04162 (321*2π)/20296 weeks
322-.03635 .01898 (322*2π)/20296 weeks
323.00133 .0252 (323*2π)/20296 weeks
324.01234 -.00114 (324*2π)/20296 weeks
325-.00328 -.00898 (325*2π)/20296 weeks
326-.01073 -.00749 (326*2π)/20296 weeks
327-.01306 .00974 (327*2π)/20296 weeks
328.00893 .01991 (328*2π)/20296 weeks
329.02635 -.02737 (329*2π)/20296 weeks
330-.03932 -.0378 (330*2π)/20296 weeks
331-.03479