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Fourier Analysis of AMLP (Alerian MLP ETF)


AMLP (Alerian MLP ETF) appears to have interesting cyclic behaviour every 33 weeks (.1287*sine), 27 weeks (.1227*sine), and 27 weeks (.1147*cosine).

AMLP (Alerian MLP ETF) has an average price of 12.72 (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 8/25/2010 to 11/28/2016 for AMLP (Alerian MLP ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
012.71873   0 
1-1.82312 -1.04694 (1*2π)/328328 weeks
2-.10955 .67253 (2*2π)/328164 weeks
3.52756 .07437 (3*2π)/328109 weeks
4.3049 -.41452 (4*2π)/32882 weeks
5.11575 -.20949 (5*2π)/32866 weeks
6-.27994 -.42871 (6*2π)/32855 weeks
7-.34242 -.13695 (7*2π)/32847 weeks
8-.0995 -.01964 (8*2π)/32841 weeks
9.02337 -.02804 (9*2π)/32836 weeks
10-.02292 .12868 (10*2π)/32833 weeks
11.01674 -.01306 (11*2π)/32830 weeks
12.11465 -.12274 (12*2π)/32827 weeks
13-.00533 -.09771 (13*2π)/32825 weeks
14-.1001 -.06501 (14*2π)/32823 weeks
15-.02687 -.03998 (15*2π)/32822 weeks
16-.0044 .01882 (16*2π)/32821 weeks
17-.00917 -.03572 (17*2π)/32819 weeks
18-.02137 -.05054 (18*2π)/32818 weeks
19-.05191 -.04461 (19*2π)/32817 weeks
20.02401 -.03393 (20*2π)/32816 weeks
21.00223 -.04251 (21*2π)/32816 weeks
22-.00755 -.02778 (22*2π)/32815 weeks
23-.01515 -.04581 (23*2π)/32814 weeks
24-.01 .00677 (24*2π)/32814 weeks
25-.05157 -.08717 (25*2π)/32813 weeks
26-.00387 -.01658 (26*2π)/32813 weeks
27.01507 .01727 (27*2π)/32812 weeks
28.04932 -.06275 (28*2π)/32812 weeks
29-.02786 -.07997 (29*2π)/32811 weeks
30-.02582 .01178 (30*2π)/32811 weeks
31-.00675 .01404 (31*2π)/32811 weeks
32-.04522 .00261 (32*2π)/32810 weeks
33.04193 .02759 (33*2π)/32810 weeks
34.05081 -.03654 (34*2π)/32810 weeks
35-.00604 -.05254 (35*2π)/3289 weeks
36-.01081 -.08664 (36*2π)/3289 weeks
37-.02283 -.03331 (37*2π)/3289 weeks
38-.03871 .03997 (38*2π)/3289 weeks
39.02927 .0302 (39*2π)/3288 weeks
40.00535 -.00788 (40*2π)/3288 weeks
41.02048 -.04082 (41*2π)/3288 weeks
42.03335 -.02895 (42*2π)/3288 weeks
43-.0175 -.04916 (43*2π)/3288 weeks
44-.02409 -.00608 (44*2π)/3287 weeks
45-.01978 -.01115 (45*2π)/3287 weeks
46-.02116 -.03328 (46*2π)/3287 weeks
47-.02084 -.02703 (47*2π)/3287 weeks
48.00244 -.01062 (48*2π)/3287 weeks
49.03276 -.01993 (49*2π)/3287 weeks
50-.00767 -.04893 (50*2π)/3287 weeks
51-.01516 .01112 (51*2π)/3286 weeks
52.00039 -.02413 (52*2π)/3286 weeks
53.00123 -.0254 (53*2π)/3286 weeks
54-.01596 -.02199 (54*2π)/3286 weeks
55-.00546 -.03546 (55*2π)/3286 weeks
56-.04052 -.02355 (56*2π)/3286 weeks
57-.04898 .02217 (57*2π)/3286 weeks
58-.00025 .01933 (58*2π)/3286 weeks
59.02174 .01118 (59*2π)/3286 weeks
60.03375 -.02625 (60*2π)/3285 weeks
61.00252 -.04543 (61*2π)/3285 weeks
62-.04076 -.03337 (62*2π)/3285 weeks
63-.04563 -.02617 (63*2π)/3285 weeks
64-.00838 .02356 (64*2π)/3285 weeks
65.00321 .01091 (65*2π)/3285 weeks
66.0212 -.01165 (66*2π)/3285 weeks
67.00091 -.01329 (67*2π)/3285 weeks
68-.00143 -.00368 (68*2π)/3285 weeks
69-.03272 -.03724 (69*2π)/3285 weeks
70-.03899 .02067 (70*2π)/3285 weeks
71-.00198 -.00414 (71*2π)/3285 weeks
72-.0093 .00199 (72*2π)/3285 weeks
73.00086 -.00138 (73*2π)/3284 weeks
74.02652 -.02149 (74*2π)/3284 weeks
75-.01318 -.04704 (75*2π)/3284 weeks
76-.04707 .00947 (76*2π)/3284 weeks
77-.02533 .0099 (77*2π)/3284 weeks
78-.03195 .01691 (78*2π)/3284 weeks
79-.00885 .02909 (79*2π)/3284 weeks
80.02145 .00795 (80*2π)/3284 weeks
81.00914 -.03259 (81*2π)/3284 weeks
82-.03143 -.03718 (82*2π)/3284 weeks
83-.03402 -.02516 (83*2π)/3284 weeks
84-.02938 .02228 (84*2π)/3284 weeks
85-.00422 .0108 (85*2π)/3284 weeks
86.00927 .01754 (86*2π)/3284 weeks
87.00991 -.00544 (87*2π)/3284 weeks
88-.00952 -.01377 (88*2π)/3284 weeks
89-.01389 -.00234 (89*2π)/3284 weeks
90-.00534 .0054 (90*2π)/3284 weeks
91-.01709 .01694 (91*2π)/3284 weeks
92.01732 -.00611 (92*2π)/3284 weeks
93.00492 -.00192 (93*2π)/3284 weeks
94-.00853 -.01141 (94*2π)/3283 weeks
95-.00403 .00055 (95*2π)/3283 weeks
96-.01119 .00898 (96*2π)/3283 weeks
97.02265 -.00372 (97*2π)/3283 weeks
98.01633 -.01905 (98*2π)/3283 weeks
99-.02065 -.00871 (99*2π)/3283 weeks
100-.00183 .00591 (100*2π)/3283 weeks
101-.00377 -.00305 (101*2π)/3283 weeks
102.0086 .00652 (102*2π)/3283 weeks
103.02744 -.03014 (103*2π)/3283 weeks
104-.00646 -.0336 (104*2π)/3283 weeks
105-.02334 -.01282 (105*2π)/3283 weeks
106-.017 -.00449 (106*2π)/3283 weeks
107-.0251 .00267 (107*2π)/3283 weeks
108-.01683 .0046 (108*2π)/3283 weeks
109.00402 -.00098 (109*2π)/3283 weeks
110-.00651 -.01065 (110*2π)/3283 weeks
111-.00043 -.01736 (111*2π)/3283 weeks
112.00087 .00028 (112*2π)/3283 weeks
113.00139 .00226 (113*2π)/3283 weeks
114-.00725 -.01492 (114*2π)/3283 weeks
115-.01547 -.00506 (115*2π)/3283 weeks
116-.02016 -.00985 (116*2π)/3283 weeks
117-.01596 -.00284 (117*2π)/3283 weeks
118-.01248 .01003 (118*2π)/3283 weeks
119.00967 -.00496 (119*2π)/3283 weeks
120.00171 .0157 (120*2π)/3283 weeks
121-.01074 -.01732 (121*2π)/3283 weeks
122-.00875 -.0097 (122*2π)/3283 weeks
123-.01313 .00714 (123*2π)/3283 weeks
124.00378 -.00035 (124*2π)/3283 weeks
125-.00669 -.01843 (125*2π)/3283 weeks
126-.01525 -.01109 (126*2π)/3283 weeks
127-.01052 .00129 (127*2π)/3283 weeks
128-.00493 -.01457 (128*2π)/3283 weeks
129-.00677 -.00684 (129*2π)/3283 weeks
130-.00301 -.01022 (130*2π)/3283 weeks
131-.00916 .00112 (131*2π)/3283 weeks
132-.00933 .00778 (132*2π)/3282 weeks
133.01365 -.00937 (133*2π)/3282 weeks
134-.01361 -.00825 (134*2π)/3282 weeks
135-.02512 -.00406 (135*2π)/3282 weeks
136-.03206 .00125 (136*2π)/3282 weeks
137-.00279 .01923 (137*2π)/3282 weeks
138.0104 .01152 (138*2π)/3282 weeks
139-.0063 -.01332 (139*2π)/3282 weeks
140-.01104 .00606 (140*2π)/3282 weeks
141-.01374 -.00848 (141*2π)/3282 weeks
142-.02937 -.00203 (142*2π)/3282 weeks
143-.0032 -.00424 (143*2π)/3282 weeks
144.01169 -.01173 (144*2π)/3282 weeks
145-.02642 .01352 (145*2π)/3282 weeks
146-.0147 .02362 (146*2π)/3282 weeks
147.01865 .01448 (147*2π)/3282 weeks
148-.00555 -.01706 (148*2π)/3282 weeks
149.00581 .00014 (149*2π)/3282 weeks
150-.00572 -.01033 (150*2π)/3282 weeks
151-.01835 -.0135 (151*2π)/3282 weeks
152-.0094 .01532 (152*2π)/3282 weeks
153-.00175 -.00396 (153*2π)/3282 weeks
154-.02252 -.00526 (154*2π)/3282 weeks
155-.01645 .01187 (155*2π)/3282 weeks
156.00653 .0237 (156*2π)/3282 weeks
157.0123 -.01177 (157*2π)/3282 weeks
158.00414 -.00924 (158*2π)/3282 weeks
159-.01027 -.01293 (159*2π)/3282 weeks
160-.00983 -.00705 (160*2π)/3282 weeks
161-.02455 .00789 (161*2π)/3282 weeks
162-.00011 .00197 (162*2π)/3282 weeks
163-.00313 .00744 (163*2π)/3282 weeks
164-.00656   (164*2π)/3282 weeks
165-.00313 -.00744 (165*2π)/3282 weeks
166-.00011 -.00197 (166*2π)/3282 weeks
167-.02455 -.00789 (167*2π)/3282 weeks
168-.00983 .00705 (168*2π)/3282 weeks
169-.01027 .01293 (169*2π)/3282 weeks
170.00414 .00924 (170*2π)/3282 weeks
171.0123 .01177 (171*2π)/3282 weeks
172.00653 -.0237 (172*2π)/3282 weeks
173-.01645 -.01187 (173*2π)/3282 weeks
174-.02252 .00526 (174*2π)/3282 weeks
175-.00175 .00396 (175*2π)/3282 weeks
176-.0094 -.01532 (176*2π)/3282 weeks
177-.01835 .0135 (177*2π)/3282 weeks
178-.00572 .01033 (178*2π)/3282 weeks
179.00581 -.00014 (179*2π)/3282 weeks
180-.00555 .01706 (180*2π)/3282 weeks
181.01865 -.01448 (181*2π)/3282 weeks
182-.0147 -.02362 (182*2π)/3282 weeks
183-.02642 -.01352 (183*2π)/3282 weeks
184.01169 .01173 (184*2π)/3282 weeks
185-.0032 .00424 (185*2π)/3282 weeks
186-.02937 .00203 (186*2π)/3282 weeks
187-.01374 .00848 (187*2π)/3282 weeks
188-.01104 -.00606 (188*2π)/3282 weeks
189-.0063 .01332 (189*2π)/3282 weeks
190.0104 -.01152 (190*2π)/3282 weeks
191-.00279 -.01923 (191*2π)/3282 weeks
192-.03206 -.00125 (192*2π)/3282 weeks
193-.02512 .00406 (193*2π)/3282 weeks
194-.01361 .00825 (194*2π)/3282 weeks
195.01365 .00937 (195*2π)/3282 weeks
196-.00933 -.00778 (196*2π)/3282 weeks
197-.00916 -.00112 (197*2π)/3282 weeks
198-.00301 .01022 (198*2π)/3282 weeks
199-.00677 .00684 (199*2π)/3282 weeks
200-.00493 .01457 (200*2π)/3282 weeks
201-.01052 -.00129 (201*2π)/3282 weeks
202-.01525 .01109 (202*2π)/3282 weeks
203-.00669 .01843 (203*2π)/3282 weeks
204.00378 .00035 (204*2π)/3282 weeks
205-.01313 -.00714 (205*2π)/3282 weeks
206-.00875 .0097 (206*2π)/3282 weeks
207-.01074 .01732 (207*2π)/3282 weeks
208.00171 -.0157 (208*2π)/3282 weeks
209.00967 .00496 (209*2π)/3282 weeks
210-.01248 -.01003 (210*2π)/3282 weeks
211-.01596 .00284 (211*2π)/3282 weeks
212-.02016 .00985 (212*2π)/3282 weeks
213-.01547 .00506 (213*2π)/3282 weeks
214-.00725 .01492 (214*2π)/3282 weeks
215.00139 -.00226 (215*2π)/3282 weeks
216.00087 -.00028 (216*2π)/3282 weeks
217-.00043 .01736 (217*2π)/3282 weeks
218-.00651 .01065 (218*2π)/3282 weeks
219.00402 .00098 (219*2π)/3281 weeks
220-.01683 -.0046 (220*2π)/3281 weeks
221-.0251 -.00267 (221*2π)/3281 weeks
222-.017 .00449 (222*2π)/3281 weeks
223-.02334 .01282 (223*2π)/3281 weeks
224-.00646 .0336 (224*2π)/3281 weeks
225.02744 .03014 (225*2π)/3281 weeks
226.0086 -.00652 (226*2π)/3281 weeks
227-.00377 .00305 (227*2π)/3281 weeks
228-.00183 -.00591 (228*2π)/3281 weeks
229-.02065 .00871 (229*2π)/3281 weeks
230.01633 .01905 (230*2π)/3281 weeks
231.02265 .00372 (231*2π)/3281 weeks
232-.01119 -.00898 (232*2π)/3281 weeks
233-.00403 -.00055 (233*2π)/3281 weeks
234-.00853 .01141 (234*2π)/3281 weeks
235.00492 .00192 (235*2π)/3281 weeks
236.01732 .00611 (236*2π)/3281 weeks
237-.01709 -.01694 (237*2π)/3281 weeks
238-.00534 -.0054 (238*2π)/3281 weeks
239-.01389 .00234 (239*2π)/3281 weeks
240-.00952 .01377 (240*2π)/3281 weeks
241.00991 .00544 (241*2π)/3281 weeks
242.00927 -.01754 (242*2π)/3281 weeks
243-.00422 -.0108 (243*2π)/3281 weeks
244-.02938 -.02228 (244*2π)/3281 weeks
245-.03402 .02516 (245*2π)/3281 weeks
246-.03143 .03718 (246*2π)/3281 weeks
247.00914 .03259 (247*2π)/3281 weeks
248.02145 -.00795 (248*2π)/3281 weeks
249-.00885 -.02909 (249*2π)/3281 weeks
250-.03195 -.01691 (250*2π)/3281 weeks
251-.02533 -.0099 (251*2π)/3281 weeks
252-.04707 -.00947 (252*2π)/3281 weeks
253-.01318 .04704 (253*2π)/3281 weeks
254.02652 .02149 (254*2π)/3281 weeks
255.00086 .00138 (255*2π)/3281 weeks
256-.0093 -.00199 (256*2π)/3281 weeks
257-.00198 .00414 (257*2π)/3281 weeks
258-.03899 -.02067 (258*2π)/3281 weeks
259-.03272 .03724 (259*2π)/3281 weeks
260-.00143 .00368 (260*2π)/3281 weeks
261.00091 .01329 (261*2π)/3281 weeks
262.0212 .01165 (262*2π)/3281 weeks
263.00321 -.01091 (263*2π)/3281 weeks
264-.00838 -.02356 (264*2π)/3281 weeks
265-.04563 .02617 (265*2π)/3281 weeks
266-.04076 .03337 (266*2π)/3281 weeks
267.00252 .04543 (267*2π)/3281 weeks
268.03375 .02625 (268*2π)/3281 weeks
269.02174 -.01118 (269*2π)/3281 weeks
270-.00025 -.01933 (270*2π)/3281 weeks
271-.04898 -.02217 (271*2π)/3281 weeks
272-.04052 .02355 (272*2π)/3281 weeks
273-.00546 .03546 (273*2π)/3281 weeks
274-.01596 .02199 (274*2π)/3281 weeks
275.00123 .0254 (275*2π)/3281 weeks
276.00039 .02413 (276*2π)/3281 weeks
277-.01516 -.01112 (277*2π)/3281 weeks
278-.00767 .04893 (278*2π)/3281 weeks
279.03276 .01993 (279*2π)/3281 weeks
280.00244 .01062 (280*2π)/3281 weeks
281-.02084 .02703 (281*2π)/3281 weeks
282-.02116 .03328 (282*2π)/3281 weeks
283-.01978 .01115 (283*2π)/3281 weeks
284-.02409 .00608 (284*2π)/3281 weeks
285-.0175 .04916 (285*2π)/3281 weeks
286.03335 .02895 (286*2π)/3281 weeks
287.02048 .04082 (287*2π)/3281 weeks
288.00535 .00788 (288*2π)/3281 weeks
289.02927 -.0302 (289*2π)/3281 weeks
290-.03871 -.03997 (290*2π)/3281 weeks
291-.02283 .03331 (291*2π)/3281 weeks
292-.01081 .08664 (292*2π)/3281 weeks
293-.00604 .05254 (293*2π)/3281 weeks
294.05081 .03654 (294*2π)/3281 weeks
295.04193 -.02759 (295*2π)/3281 weeks
296-.04522 -.00261 (296*2π)/3281 weeks
297-.00675 -.01404 (297*2π)/3281 weeks
298-.02582 -.01178 (298*2π)/3281 weeks
299-.02786 .07997 (299*2π)/3281 weeks
300.04932 .06275 (300*2π)/3281 weeks
301.01507 -.01727 (301*2π)/3281 weeks
302-.00387 .01658 (302*2π)/3281 weeks
303-.05157 .08717 (303*2π)/3281 weeks
304-.01 -.00677 (304*2π)/3281 weeks
305-.01515 .04581 (305*2π)/3281 weeks
306-.00755 .02778 (306*2π)/3281 weeks
307.00223 .04251 (307*2π)/3281 weeks
308.02401 .03393 (308*2π)/3281 weeks
309-.05191 .04461 (309*2π)/3281 weeks
310-.02137 .05054 (310*2π)/3281 weeks
311-.00917 .03572 (311*2π)/3281 weeks
312-.0044 -.01882 (312*2π)/3281 weeks
313-.02687 .03998 (313*2π)/3281 weeks
314-.1001 .06501 (314*2π)/3281 weeks
315-.00533 .09771 (315*2π)/3281 weeks
316.11465 .12274 (316*2π)/3281 weeks
317.01674 .01306 (317*2π)/3281 weeks
318-.02292 -.12868 (318*2π)/3281 weeks
319.02337 .02804 (319*2π)/3281 weeks
320-.0995 .01964 (320*2π)/3281 weeks
321-.34242 .13695 (321*2π)/3281 weeks
322-.27994 .42871 (322*2π)/3281 weeks
323.11575 .20949 (323*2π)/3281 weeks
324.3049 .41452 (324*2π)/3281 weeks
325.52756 -.07437 (325*2π)/3281 weeks
326-.10955 -.67253 (326*2π)/3281 weeks

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