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# Fourier Analysis of ALFA (AlphaClone Alternative Alpha ETF)

ALFA (AlphaClone Alternative Alpha ETF) appears to have interesting cyclic behaviour every 28 weeks (.7029*sine), 31 weeks (.6003*sine), and 26 weeks (.3861*cosine).

ALFA (AlphaClone Alternative Alpha ETF) has an average price of 37.11 (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 5/31/2012 to 5/21/2018 for ALFA (AlphaClone Alternative Alpha ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
037.1054   0
1-3.144 -1.54924 (1*2π)/313313 weeks
22.03338 -4.85129 (2*2π)/313157 weeks
3-1.47885 -2.45915 (3*2π)/313104 weeks
41.22328 -1.56879 (4*2π)/31378 weeks
5-.76149 -1.30398 (5*2π)/31363 weeks
6.16047 -1.02154 (6*2π)/31352 weeks
7-.06915 -1.17151 (7*2π)/31345 weeks
8-.03566 -.67775 (8*2π)/31339 weeks
9-.48073 -.5503 (9*2π)/31335 weeks
10-.04944 -.6003 (10*2π)/31331 weeks
11-.1809 -.70287 (11*2π)/31328 weeks
12-.38609 -.32283 (12*2π)/31326 weeks
13-.10548 -.53331 (13*2π)/31324 weeks
14.00982 -.50047 (14*2π)/31322 weeks
15-.03895 -.38933 (15*2π)/31321 weeks
16-.18552 -.50993 (16*2π)/31320 weeks
17.23174 -.34891 (17*2π)/31318 weeks
18.05645 -.40155 (18*2π)/31317 weeks
19.12377 -.31819 (19*2π)/31316 weeks
20.07049 -.39499 (20*2π)/31316 weeks
21.04037 -.3492 (21*2π)/31315 weeks
22-.09125 -.202 (22*2π)/31314 weeks
23-.10661 -.48554 (23*2π)/31314 weeks
24.10226 -.25848 (24*2π)/31313 weeks
25-.20377 -.32065 (25*2π)/31313 weeks
26-.03875 -.35796 (26*2π)/31312 weeks
27.02375 -.09375 (27*2π)/31312 weeks
28-.20953 -.27319 (28*2π)/31311 weeks
29.03563 -.24934 (29*2π)/31311 weeks
30-.10604 -.41888 (30*2π)/31310 weeks
31-.03339 -.25928 (31*2π)/31310 weeks
32.01085 -.12069 (32*2π)/31310 weeks
33-.16545 -.17609 (33*2π)/3139 weeks
34-.06769 -.3675 (34*2π)/3139 weeks
35-.12113 -.18476 (35*2π)/3139 weeks
36-.06097 -.34498 (36*2π)/3139 weeks
37-.03139 -.27836 (37*2π)/3138 weeks
38-.11724 -.12787 (38*2π)/3138 weeks
39-.20649 -.16183 (39*2π)/3138 weeks
40-.10313 -.21712 (40*2π)/3138 weeks
41-.21904 -.20032 (41*2π)/3138 weeks
42-.04975 -.02306 (42*2π)/3137 weeks
43-.18889 -.18519 (43*2π)/3137 weeks
44-.05019 -.08405 (44*2π)/3137 weeks
45-.06231 -.08192 (45*2π)/3137 weeks
46-.11082 -.09804 (46*2π)/3137 weeks
47-.01927 -.0557 (47*2π)/3137 weeks
48.01041 -.11294 (48*2π)/3137 weeks
49-.02174 -.13492 (49*2π)/3136 weeks
50-.08281 -.10638 (50*2π)/3136 weeks
51.04987 -.20053 (51*2π)/3136 weeks
52-.06925 -.16852 (52*2π)/3136 weeks
53-.06869 -.12372 (53*2π)/3136 weeks
54-.07483 -.13926 (54*2π)/3136 weeks
55-.04807 -.16344 (55*2π)/3136 weeks
56-.05551 -.20008 (56*2π)/3136 weeks
57-.00498 -.12901 (57*2π)/3135 weeks
58-.11185 -.21037 (58*2π)/3135 weeks
59-.09104 -.16398 (59*2π)/3135 weeks
60-.01051 -.11523 (60*2π)/3135 weeks
61-.13624 -.04528 (61*2π)/3135 weeks
62-.07237 -.13462 (62*2π)/3135 weeks
63-.11241 -.08742 (63*2π)/3135 weeks
64-.07472 -.10631 (64*2π)/3135 weeks
65-.08506 -.08585 (65*2π)/3135 weeks
66-.1029 -.06289 (66*2π)/3135 weeks
67-.05383 -.1325 (67*2π)/3135 weeks
68-.16387 -.12208 (68*2π)/3135 weeks
69-.07178 -.13878 (69*2π)/3135 weeks
70-.0387 -.08027 (70*2π)/3134 weeks
71-.12673 -.03022 (71*2π)/3134 weeks
72-.06641 -.14803 (72*2π)/3134 weeks
73-.11471 -.02897 (73*2π)/3134 weeks
74-.14752 -.10971 (74*2π)/3134 weeks
75-.07618 -.12626 (75*2π)/3134 weeks
76-.19681 -.05689 (76*2π)/3134 weeks
77-.05954 -.07897 (77*2π)/3134 weeks
78-.13116 -.02015 (78*2π)/3134 weeks
79-.07478 -.06572 (79*2π)/3134 weeks
80-.15372 -.08217 (80*2π)/3134 weeks
81-.09172 .00429 (81*2π)/3134 weeks
82-.00655 -.03377 (82*2π)/3134 weeks
83-.08792 -.03427 (83*2π)/3134 weeks
84-.01401 -.08958 (84*2π)/3134 weeks
85-.05858 -.00365 (85*2π)/3134 weeks
86-.00354 -.05012 (86*2π)/3134 weeks
87-.05009 -.06684 (87*2π)/3134 weeks
88-.05862 -.02503 (88*2π)/3134 weeks
89-.02454 -.03759 (89*2π)/3134 weeks
90-.07126 -.06787 (90*2π)/3133 weeks
91-.06221 -.05772 (91*2π)/3133 weeks
92-.09016 -.09013 (92*2π)/3133 weeks
93-.10312 .02821 (93*2π)/3133 weeks
94-.08399 -.11377 (94*2π)/3133 weeks
95-.09496 -.06456 (95*2π)/3133 weeks
96-.09827 -.05331 (96*2π)/3133 weeks
97-.11935 -.07592 (97*2π)/3133 weeks
98-.07579 -.05458 (98*2π)/3133 weeks
99-.11482 -.03233 (99*2π)/3133 weeks
100-.07828 -.01118 (100*2π)/3133 weeks
101-.11786 .004 (101*2π)/3133 weeks
102-.09743 .00634 (102*2π)/3133 weeks
103-.02166 -.00738 (103*2π)/3133 weeks
104-.06239 .02876 (104*2π)/3133 weeks
105-.05705 -.04661 (105*2π)/3133 weeks
106-.08584 -.02872 (106*2π)/3133 weeks
107.00119 -.07512 (107*2π)/3133 weeks
108-.02966 -.0435 (108*2π)/3133 weeks
109-.03244 -.08755 (109*2π)/3133 weeks
110-.05733 -.07676 (110*2π)/3133 weeks
111-.02967 -.12285 (111*2π)/3133 weeks
112-.06038 -.05765 (112*2π)/3133 weeks
113-.07732 -.03055 (113*2π)/3133 weeks
114-.11327 -.08393 (114*2π)/3133 weeks
115-.12134 -.09513 (115*2π)/3133 weeks
116-.09308 -.0296 (116*2π)/3133 weeks
117-.13474 -.10462 (117*2π)/3133 weeks
118-.06917 -.02847 (118*2π)/3133 weeks
119-.10419 -.01882 (119*2π)/3133 weeks
120-.06864 -.01926 (120*2π)/3133 weeks
121-.14585 .00388 (121*2π)/3133 weeks
122-.07072 -.05737 (122*2π)/3133 weeks
123-.09437 .02459 (123*2π)/3133 weeks
124-.04885 -.00045 (124*2π)/3133 weeks
125-.07839 .01597 (125*2π)/3133 weeks
126-.07199 -.01199 (126*2π)/3132 weeks
127-.04202 .02278 (127*2π)/3132 weeks
128-.08885 .01127 (128*2π)/3132 weeks
129-.06015 -.00808 (129*2π)/3132 weeks
130-.09709 -.02115 (130*2π)/3132 weeks
131-.04301 -.04061 (131*2π)/3132 weeks
132-.12302 .0092 (132*2π)/3132 weeks
133-.05459 -.01861 (133*2π)/3132 weeks
134-.0816 .02737 (134*2π)/3132 weeks
135-.03517 .00655 (135*2π)/3132 weeks
136-.12103 -.07536 (136*2π)/3132 weeks
137-.04183 .02957 (137*2π)/3132 weeks
138-.03591 -.07517 (138*2π)/3132 weeks
139-.05278 -.00318 (139*2π)/3132 weeks
140-.04186 -.05821 (140*2π)/3132 weeks
141-.09787 .04067 (141*2π)/3132 weeks
142-.1162 -.02002 (142*2π)/3132 weeks
143-.04214 -.04701 (143*2π)/3132 weeks
144-.06344 .02798 (144*2π)/3132 weeks
145-.10596 -.04166 (145*2π)/3132 weeks
146-.02406 -.03492 (146*2π)/3132 weeks
147-.06942 -.03875 (147*2π)/3132 weeks
148-.09788 -.00378 (148*2π)/3132 weeks
149-.11757 -.07088 (149*2π)/3132 weeks
150-.05202 -.03332 (150*2π)/3132 weeks
151-.0836 -.06317 (151*2π)/3132 weeks
152-.05776 -.01374 (152*2π)/3132 weeks
153-.10396 -.00807 (153*2π)/3132 weeks
154-.06734 .01782 (154*2π)/3132 weeks
155-.11736 -.04804 (155*2π)/3132 weeks
156-.09597 -.00822 (156*2π)/3132 weeks
157-.09597 .00822 (157*2π)/3132 weeks
158-.11736 .04804 (158*2π)/3132 weeks
159-.06734 -.01782 (159*2π)/3132 weeks
160-.10396 .00807 (160*2π)/3132 weeks
161-.05776 .01374 (161*2π)/3132 weeks
162-.0836 .06317 (162*2π)/3132 weeks
163-.05202 .03332 (163*2π)/3132 weeks
164-.11757 .07088 (164*2π)/3132 weeks
165-.09788 .00378 (165*2π)/3132 weeks
166-.06942 .03875 (166*2π)/3132 weeks
167-.02406 .03492 (167*2π)/3132 weeks
168-.10596 .04166 (168*2π)/3132 weeks
169-.06344 -.02798 (169*2π)/3132 weeks
170-.04214 .04701 (170*2π)/3132 weeks
171-.1162 .02002 (171*2π)/3132 weeks
172-.09787 -.04067 (172*2π)/3132 weeks
173-.04186 .05821 (173*2π)/3132 weeks
174-.05278 .00318 (174*2π)/3132 weeks
175-.03591 .07517 (175*2π)/3132 weeks
176-.04183 -.02957 (176*2π)/3132 weeks
177-.12103 .07536 (177*2π)/3132 weeks
178-.03517 -.00655 (178*2π)/3132 weeks
179-.0816 -.02737 (179*2π)/3132 weeks
180-.05459 .01861 (180*2π)/3132 weeks
181-.12302 -.0092 (181*2π)/3132 weeks
182-.04301 .04061 (182*2π)/3132 weeks
183-.09709 .02115 (183*2π)/3132 weeks
184-.06015 .00808 (184*2π)/3132 weeks
185-.08885 -.01127 (185*2π)/3132 weeks
186-.04202 -.02278 (186*2π)/3132 weeks
187-.07199 .01199 (187*2π)/3132 weeks
188-.07839 -.01597 (188*2π)/3132 weeks
189-.04885 .00045 (189*2π)/3132 weeks
190-.09437 -.02459 (190*2π)/3132 weeks
191-.07072 .05737 (191*2π)/3132 weeks
192-.14585 -.00388 (192*2π)/3132 weeks
193-.06864 .01926 (193*2π)/3132 weeks
194-.10419 .01882 (194*2π)/3132 weeks
195-.06917 .02847 (195*2π)/3132 weeks
196-.13474 .10462 (196*2π)/3132 weeks
197-.09308 .0296 (197*2π)/3132 weeks
198-.12134 .09513 (198*2π)/3132 weeks
199-.11327 .08393 (199*2π)/3132 weeks
200-.07732 .03055 (200*2π)/3132 weeks
201-.06038 .05765 (201*2π)/3132 weeks
202-.02967 .12285 (202*2π)/3132 weeks
203-.05733 .07676 (203*2π)/3132 weeks
204-.03244 .08755 (204*2π)/3132 weeks
205-.02966 .0435 (205*2π)/3132 weeks
206.00119 .07512 (206*2π)/3132 weeks
207-.08584 .02872 (207*2π)/3132 weeks
208-.05705 .04661 (208*2π)/3132 weeks
209-.06239 -.02876 (209*2π)/3131 weeks
210-.02166 .00738 (210*2π)/3131 weeks
211-.09743 -.00634 (211*2π)/3131 weeks
212-.11786 -.004 (212*2π)/3131 weeks
213-.07828 .01118 (213*2π)/3131 weeks
214-.11482 .03233 (214*2π)/3131 weeks
215-.07579 .05458 (215*2π)/3131 weeks
216-.11935 .07592 (216*2π)/3131 weeks
217-.09827 .05331 (217*2π)/3131 weeks
218-.09496 .06456 (218*2π)/3131 weeks
219-.08399 .11377 (219*2π)/3131 weeks
220-.10312 -.02821 (220*2π)/3131 weeks
221-.09016 .09013 (221*2π)/3131 weeks
222-.06221 .05772 (222*2π)/3131 weeks
223-.07126 .06787 (223*2π)/3131 weeks
224-.02454 .03759 (224*2π)/3131 weeks
225-.05862 .02503 (225*2π)/3131 weeks
226-.05009 .06684 (226*2π)/3131 weeks
227-.00354 .05012 (227*2π)/3131 weeks
228-.05858 .00365 (228*2π)/3131 weeks
229-.01401 .08958 (229*2π)/3131 weeks
230-.08792 .03427 (230*2π)/3131 weeks
231-.00655 .03377 (231*2π)/3131 weeks
232-.09172 -.00429 (232*2π)/3131 weeks
233-.15372 .08217 (233*2π)/3131 weeks
234-.07478 .06572 (234*2π)/3131 weeks
235-.13116 .02015 (235*2π)/3131 weeks
236-.05954 .07897 (236*2π)/3131 weeks
237-.19681 .05689 (237*2π)/3131 weeks
238-.07618 .12626 (238*2π)/3131 weeks
239-.14752 .10971 (239*2π)/3131 weeks
240-.11471 .02897 (240*2π)/3131 weeks
241-.06641 .14803 (241*2π)/3131 weeks
242-.12673 .03022 (242*2π)/3131 weeks
243-.0387 .08027 (243*2π)/3131 weeks
244-.07178 .13878 (244*2π)/3131 weeks
245-.16387 .12208 (245*2π)/3131 weeks
246-.05383 .1325 (246*2π)/3131 weeks
247-.1029 .06289 (247*2π)/3131 weeks
248-.08506 .08585 (248*2π)/3131 weeks
249-.07472 .10631 (249*2π)/3131 weeks
250-.11241 .08742 (250*2π)/3131 weeks
251-.07237 .13462 (251*2π)/3131 weeks
252-.13624 .04528 (252*2π)/3131 weeks
253-.01051 .11523 (253*2π)/3131 weeks
254-.09104 .16398 (254*2π)/3131 weeks
255-.11185 .21037 (255*2π)/3131 weeks
256-.00498 .12901 (256*2π)/3131 weeks
257-.05551 .20008 (257*2π)/3131 weeks
258-.04807 .16344 (258*2π)/3131 weeks
259-.07483 .13926 (259*2π)/3131 weeks
260-.06869 .12372 (260*2π)/3131 weeks
261-.06925 .16852 (261*2π)/3131 weeks
262.04987 .20053 (262*2π)/3131 weeks
263-.08281 .10638 (263*2π)/3131 weeks
264-.02174 .13492 (264*2π)/3131 weeks
265.01041 .11294 (265*2π)/3131 weeks
266-.01927 .0557 (266*2π)/3131 weeks
267-.11082 .09804 (267*2π)/3131 weeks
268-.06231 .08192 (268*2π)/3131 weeks
269-.05019 .08405 (269*2π)/3131 weeks
270-.18889 .18519 (270*2π)/3131 weeks
271-.04975 .02306 (271*2π)/3131 weeks
272-.21904 .20032 (272*2π)/3131 weeks
273-.10313 .21712 (273*2π)/3131 weeks
274-.20649 .16183 (274*2π)/3131 weeks
275-.11724 .12787 (275*2π)/3131 weeks
276-.03139 .27836 (276*2π)/3131 weeks
277-.06097 .34498 (277*2π)/3131 weeks
278-.12113 .18476 (278*2π)/3131 weeks
279-.06769 .3675 (279*2π)/3131 weeks
280-.16545 .17609 (280*2π)/3131 weeks
281.01085 .12069 (281*2π)/3131 weeks
282-.03339 .25928 (282*2π)/3131 weeks
283-.10604 .41888 (283*2π)/3131 weeks
284.03563 .24934 (284*2π)/3131 weeks
285-.20953 .27319 (285*2π)/3131 weeks
286.02375 .09375 (286*2π)/3131 weeks
287-.03875 .35796 (287*2π)/3131 weeks
288-.20377 .32065 (288*2π)/3131 weeks
289.10226 .25848 (289*2π)/3131 weeks
290-.10661 .48554 (290*2π)/3131 weeks
291-.09125 .202 (291*2π)/3131 weeks
292.04037 .3492 (292*2π)/3131 weeks
293.07049 .39499 (293*2π)/3131 weeks
294.12377 .31819 (294*2π)/3131 weeks
295.05645 .40155 (295*2π)/3131 weeks
296.23174 .34891 (296*2π)/3131 weeks
297-.18552 .50993 (297*2π)/3131 weeks
298-.03895 .38933 (298*2π)/3131 weeks
299.00982 .50047 (299*2π)/3131 weeks
300-.10548 .53331 (300*2π)/3131 weeks
301-.38609 .32283 (301*2π)/3131 weeks
302-.1809 .70287 (302*2π)/3131 weeks
303-.04944 .6003 (303*2π)/3131 weeks
304-.48073 .5503 (304*2π)/3131 weeks
305-.03566 .67775 (305*2π)/3131 weeks
306-.06915 1.17151 (306*2π)/3131 weeks
307.16047 1.02154 (307*2π)/3131 weeks
308-.76149 1.30398 (308*2π)/3131 weeks
3091.22328 1.56879 (309*2π)/3131 weeks
310-1.47885 2.45915 (310*2π)/3131 weeks
3112.03338 4.85129 (311*2π)/3131 weeks