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# Fourier Analysis of MLPS (UBS ETRACS 1xM Shrt Alrn MLP Infr TR ETN)

MLPS (UBS ETRACS 1xM Shrt Alrn MLP Infr TR ETN) appears to have interesting cyclic behaviour every 40 weeks (.5195*sine), 36 weeks (.2987*sine), and 28 weeks (.2938*cosine).

MLPS (UBS ETRACS 1xM Shrt Alrn MLP Infr TR ETN) has an average price of 14.64 (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 9/29/2010 to 4/16/2018 for MLPS (UBS ETRACS 1xM Shrt Alrn MLP Infr TR ETN), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
014.63673   0
12.82794 2.67099 (1*2π)/395395 weeks
2-.50016 2.43142 (2*2π)/395198 weeks
3.89074 1.62851 (3*2π)/395132 weeks
4.33181 .22507 (4*2π)/39599 weeks
5-.32124 .69632 (5*2π)/39579 weeks
6-.02736 .52416 (6*2π)/39566 weeks
7.55118 .19964 (7*2π)/39556 weeks
8-.02687 .31585 (8*2π)/39549 weeks
9.13675 .78704 (9*2π)/39544 weeks
10.27858 .5195 (10*2π)/39540 weeks
11.02931 .29868 (11*2π)/39536 weeks
12-.16385 .12513 (12*2π)/39533 weeks
13.09901 .29599 (13*2π)/39530 weeks
14.29384 .29127 (14*2π)/39528 weeks
15-.0187 .24655 (15*2π)/39526 weeks
16.0215 .28252 (16*2π)/39525 weeks
17.22529 .10677 (17*2π)/39523 weeks
18.07509 .13367 (18*2π)/39522 weeks
19-.05141 .19051 (19*2π)/39521 weeks
20.05301 .08392 (20*2π)/39520 weeks
21.06031 .05218 (21*2π)/39519 weeks
22.06351 .08403 (22*2π)/39518 weeks
23.0657 .09126 (23*2π)/39517 weeks
24.01662 .1718 (24*2π)/39516 weeks
25-.04042 .13243 (25*2π)/39516 weeks
26-.02543 .09012 (26*2π)/39515 weeks
27.03851 .05669 (27*2π)/39515 weeks
28.08289 .10574 (28*2π)/39514 weeks
29-.01515 .13247 (29*2π)/39514 weeks
30-.02293 .03358 (30*2π)/39513 weeks
31.03448 .11799 (31*2π)/39513 weeks
32.03539 .10081 (32*2π)/39512 weeks
33-.01053 .07307 (33*2π)/39512 weeks
34.1072 .15241 (34*2π)/39512 weeks
35.08209 .08012 (35*2π)/39511 weeks
36.00723 .16957 (36*2π)/39511 weeks
37.02957 .15449 (37*2π)/39511 weeks
38-.0174 .10237 (38*2π)/39510 weeks
39-.04328 .04374 (39*2π)/39510 weeks
40.00715 .1543 (40*2π)/39510 weeks
41.09426 .07107 (41*2π)/39510 weeks
42-.0041 .02812 (42*2π)/3959 weeks
43-.02027 .06285 (43*2π)/3959 weeks
44.09894 .08836 (44*2π)/3959 weeks
45.0657 .04919 (45*2π)/3959 weeks
46-.05746 .10998 (46*2π)/3959 weeks
47.07824 .10568 (47*2π)/3958 weeks
48.05553 .06801 (48*2π)/3958 weeks
49-.01245 .04023 (49*2π)/3958 weeks
50.01823 .09626 (50*2π)/3958 weeks
51.05766 .14846 (51*2π)/3958 weeks
52-.00788 .04443 (52*2π)/3958 weeks
53-.01915 .06924 (53*2π)/3957 weeks
54.00088 .06571 (54*2π)/3957 weeks
55.0339 .06568 (55*2π)/3957 weeks
56.02206 .05549 (56*2π)/3957 weeks
57-.0258 .07909 (57*2π)/3957 weeks
58-.01525 .09864 (58*2π)/3957 weeks
59-.01854 .0142 (59*2π)/3957 weeks
60-.02618 .0565 (60*2π)/3957 weeks
61.06323 .02607 (61*2π)/3956 weeks
62.06232 .06235 (62*2π)/3956 weeks
63.04215 .06667 (63*2π)/3956 weeks
64.01903 .07342 (64*2π)/3956 weeks
65.02805 .10422 (65*2π)/3956 weeks
66.02222 .09091 (66*2π)/3956 weeks
67.03451 .00263 (67*2π)/3956 weeks
68-.01984 .0119 (68*2π)/3956 weeks
69.02933 .10698 (69*2π)/3956 weeks
70.08964 .03702 (70*2π)/3956 weeks
71.01775 .01756 (71*2π)/3956 weeks
72.00363 .10215 (72*2π)/3955 weeks
73.05749 .06662 (73*2π)/3955 weeks
74.00363 -.00568 (74*2π)/3955 weeks
75.0024 .05697 (75*2π)/3955 weeks
76.08292 .07239 (76*2π)/3955 weeks
77.06203 .00431 (77*2π)/3955 weeks
78.04224 .06391 (78*2π)/3955 weeks
79.03336 .0764 (79*2π)/3955 weeks
80-.00576 .01846 (80*2π)/3955 weeks
81-.00098 .00525 (81*2π)/3955 weeks
82.03288 .00858 (82*2π)/3955 weeks
83.08004 .00645 (83*2π)/3955 weeks
84.02117 .01129 (84*2π)/3955 weeks
85.04009 .07275 (85*2π)/3955 weeks
86.01845 .06608 (86*2π)/3955 weeks
87.00269 .04792 (87*2π)/3955 weeks
88.00937 .04718 (88*2π)/3954 weeks
89.04239 .04591 (89*2π)/3954 weeks
90.05007 -.01012 (90*2π)/3954 weeks
91-.00995 .04553 (91*2π)/3954 weeks
92.05437 .08271 (92*2π)/3954 weeks
93.03883 .04884 (93*2π)/3954 weeks
94.01017 .00668 (94*2π)/3954 weeks
95-.01305 .02692 (95*2π)/3954 weeks
96.06284 .0405 (96*2π)/3954 weeks
97.05914 -.03262 (97*2π)/3954 weeks
98.01701 .03548 (98*2π)/3954 weeks
99.08052 .07261 (99*2π)/3954 weeks
100.05711 .03514 (100*2π)/3954 weeks
101-.02035 .04716 (101*2π)/3954 weeks
102.02595 .05554 (102*2π)/3954 weeks
103.05764 .01046 (103*2π)/3954 weeks
104.04603 -.00121 (104*2π)/3954 weeks
105.05468 .05133 (105*2π)/3954 weeks
106.06346 .03341 (106*2π)/3954 weeks
107.03055 .057 (107*2π)/3954 weeks
108.01815 .03207 (108*2π)/3954 weeks
109.01699 .00195 (109*2π)/3954 weeks
110.04389 -.01901 (110*2π)/3954 weeks
111.06876 .02803 (111*2π)/3954 weeks
112.04379 .0402 (112*2π)/3954 weeks
113.01337 .05514 (113*2π)/3953 weeks
114.04405 .03367 (114*2π)/3953 weeks
115.01562 .00936 (115*2π)/3953 weeks
116-.01479 .01334 (116*2π)/3953 weeks
117.04355 .02983 (117*2π)/3953 weeks
118.0744 .00712 (118*2π)/3953 weeks
119.01951 .02221 (119*2π)/3953 weeks
120.05198 .03647 (120*2π)/3953 weeks
121.01788 .04012 (121*2π)/3953 weeks
122-.00043 .04244 (122*2π)/3953 weeks
123.01495 .03896 (123*2π)/3953 weeks
124.03251 -.03575 (124*2π)/3953 weeks
125.00552 .01786 (125*2π)/3953 weeks
126.06676 .06256 (126*2π)/3953 weeks
127.06514 .02372 (127*2π)/3953 weeks
128.02144 .03882 (128*2π)/3953 weeks
129-.00106 .06105 (129*2π)/3953 weeks
130.00224 .03667 (130*2π)/3953 weeks
131.02357 .00951 (131*2π)/3953 weeks
132.0155 .02722 (132*2π)/3953 weeks
133.02943 .03131 (133*2π)/3953 weeks
134.04924 .00777 (134*2π)/3953 weeks
135.04065 .00636 (135*2π)/3953 weeks
136.05276 .02004 (136*2π)/3953 weeks
137.04497 .02667 (137*2π)/3953 weeks
138.06166 .00284 (138*2π)/3953 weeks
139.04746 .02882 (139*2π)/3953 weeks
140.03715 .02472 (140*2π)/3953 weeks
141.0412 .00708 (141*2π)/3953 weeks
142.04451 .02091 (142*2π)/3953 weeks
143.00502 .01393 (143*2π)/3953 weeks
144.03463 -.00793 (144*2π)/3953 weeks
145.04834 .00685 (145*2π)/3953 weeks
146.01256 .00706 (146*2π)/3953 weeks
147.02719 .00828 (147*2π)/3953 weeks
148.04751 .00132 (148*2π)/3953 weeks
149.03302 .02404 (149*2π)/3953 weeks
150.03301 .03876 (150*2π)/3953 weeks
151.03248 -.00536 (151*2π)/3953 weeks
152.02118 -.00854 (152*2π)/3953 weeks
153.05536 .00127 (153*2π)/3953 weeks
154.07008 .01978 (154*2π)/3953 weeks
155.03757 .03545 (155*2π)/3953 weeks
156.02356 .01489 (156*2π)/3953 weeks
157.00725 .01962 (157*2π)/3953 weeks
158.00529 .00807 (158*2π)/3953 weeks
159.03407 -.00745 (159*2π)/3952 weeks
160.02948 .00312 (160*2π)/3952 weeks
161.03415 -.01513 (161*2π)/3952 weeks
162.03183 -.004 (162*2π)/3952 weeks
163.03555 .03838 (163*2π)/3952 weeks
164.04679 .00815 (164*2π)/3952 weeks
165.00596 -.00497 (165*2π)/3952 weeks
166.02191 .00716 (166*2π)/3952 weeks
167.06746 -.01238 (167*2π)/3952 weeks
168.04601 -.0044 (168*2π)/3952 weeks
169.04362 -.0142 (169*2π)/3952 weeks
170.05201 .02277 (170*2π)/3952 weeks
171.03338 -.00622 (171*2π)/3952 weeks
172.02421 .02931 (172*2π)/3952 weeks
173.04016 .02356 (173*2π)/3952 weeks
174.01175 .02196 (174*2π)/3952 weeks
175.04719 -.0034 (175*2π)/3952 weeks
176.02703 -.00544 (176*2π)/3952 weeks
177.01506 .0476 (177*2π)/3952 weeks
178.05438 .00138 (178*2π)/3952 weeks
179.0377 .00137 (179*2π)/3952 weeks
180.01674 .00154 (180*2π)/3952 weeks
181.0496 .00988 (181*2π)/3952 weeks
182.05677 .00553 (182*2π)/3952 weeks
183.01914 .01822 (183*2π)/3952 weeks
184.02585 -.00468 (184*2π)/3952 weeks
185.0162 -.00659 (185*2π)/3952 weeks
186.05531 .00321 (186*2π)/3952 weeks
187.02603 -.02329 (187*2π)/3952 weeks
188.00626 .03112 (188*2π)/3952 weeks
189.07107 -.00076 (189*2π)/3952 weeks
190.01775 -.03436 (190*2π)/3952 weeks
191.01945 .01562 (191*2π)/3952 weeks
192.05569 .01857 (192*2π)/3952 weeks
193.04698 .00324 (193*2π)/3952 weeks
194.00017 .01347 (194*2π)/3952 weeks
195.04754 .00751 (195*2π)/3952 weeks
196.04524 -.00526 (196*2π)/3952 weeks
197.01156 .0085 (197*2π)/3952 weeks
198.01156 -.0085 (198*2π)/3952 weeks
199.04524 .00526 (199*2π)/3952 weeks
200.04754 -.00751 (200*2π)/3952 weeks
201.00017 -.01347 (201*2π)/3952 weeks
202.04698 -.00324 (202*2π)/3952 weeks
203.05569 -.01857 (203*2π)/3952 weeks
204.01945 -.01562 (204*2π)/3952 weeks
205.01775 .03436 (205*2π)/3952 weeks
206.07107 .00076 (206*2π)/3952 weeks
207.00626 -.03112 (207*2π)/3952 weeks
208.02603 .02329 (208*2π)/3952 weeks
209.05531 -.00321 (209*2π)/3952 weeks
210.0162 .00659 (210*2π)/3952 weeks
211.02585 .00468 (211*2π)/3952 weeks
212.01914 -.01822 (212*2π)/3952 weeks
213.05677 -.00553 (213*2π)/3952 weeks
214.0496 -.00988 (214*2π)/3952 weeks
215.01674 -.00154 (215*2π)/3952 weeks
216.0377 -.00137 (216*2π)/3952 weeks
217.05438 -.00138 (217*2π)/3952 weeks
218.01506 -.0476 (218*2π)/3952 weeks
219.02703 .00544 (219*2π)/3952 weeks
220.04719 .0034 (220*2π)/3952 weeks
221.01175 -.02196 (221*2π)/3952 weeks
222.04016 -.02356 (222*2π)/3952 weeks
223.02421 -.02931 (223*2π)/3952 weeks
224.03338 .00622 (224*2π)/3952 weeks
225.05201 -.02277 (225*2π)/3952 weeks
226.04362 .0142 (226*2π)/3952 weeks
227.04601 .0044 (227*2π)/3952 weeks
228.06746 .01238 (228*2π)/3952 weeks
229.02191 -.00716 (229*2π)/3952 weeks
230.00596 .00497 (230*2π)/3952 weeks
231.04679 -.00815 (231*2π)/3952 weeks
232.03555 -.03838 (232*2π)/3952 weeks
233.03183 .004 (233*2π)/3952 weeks
234.03415 .01513 (234*2π)/3952 weeks
235.02948 -.00312 (235*2π)/3952 weeks
236.03407 .00745 (236*2π)/3952 weeks
237.00529 -.00807 (237*2π)/3952 weeks
238.00725 -.01962 (238*2π)/3952 weeks
239.02356 -.01489 (239*2π)/3952 weeks
240.03757 -.03545 (240*2π)/3952 weeks
241.07008 -.01978 (241*2π)/3952 weeks
242.05536 -.00127 (242*2π)/3952 weeks
243.02118 .00854 (243*2π)/3952 weeks
244.03248 .00536 (244*2π)/3952 weeks
245.03301 -.03876 (245*2π)/3952 weeks
246.03302 -.02404 (246*2π)/3952 weeks
247.04751 -.00132 (247*2π)/3952 weeks
248.02719 -.00828 (248*2π)/3952 weeks
249.01256 -.00706 (249*2π)/3952 weeks
250.04834 -.00685 (250*2π)/3952 weeks
251.03463 .00793 (251*2π)/3952 weeks
252.00502 -.01393 (252*2π)/3952 weeks
253.04451 -.02091 (253*2π)/3952 weeks
254.0412 -.00708 (254*2π)/3952 weeks
255.03715 -.02472 (255*2π)/3952 weeks
256.04746 -.02882 (256*2π)/3952 weeks
257.06166 -.00284 (257*2π)/3952 weeks
258.04497 -.02667 (258*2π)/3952 weeks
259.05276 -.02004 (259*2π)/3952 weeks
260.04065 -.00636 (260*2π)/3952 weeks
261.04924 -.00777 (261*2π)/3952 weeks
262.02943 -.03131 (262*2π)/3952 weeks
263.0155 -.02722 (263*2π)/3952 weeks
264.02357 -.00951 (264*2π)/3951 weeks
265.00224 -.03667 (265*2π)/3951 weeks
266-.00106 -.06105 (266*2π)/3951 weeks
267.02144 -.03882 (267*2π)/3951 weeks
268.06514 -.02372 (268*2π)/3951 weeks
269.06676 -.06256 (269*2π)/3951 weeks
270.00552 -.01786 (270*2π)/3951 weeks
271.03251 .03575 (271*2π)/3951 weeks
272.01495 -.03896 (272*2π)/3951 weeks
273-.00043 -.04244 (273*2π)/3951 weeks
274.01788 -.04012 (274*2π)/3951 weeks
275.05198 -.03647 (275*2π)/3951 weeks
276.01951 -.02221 (276*2π)/3951 weeks
277.0744 -.00712 (277*2π)/3951 weeks
278.04355 -.02983 (278*2π)/3951 weeks
279-.01479 -.01334 (279*2π)/3951 weeks
280.01562 -.00936 (280*2π)/3951 weeks
281.04405 -.03367 (281*2π)/3951 weeks
282.01337 -.05514 (282*2π)/3951 weeks
283.04379 -.0402 (283*2π)/3951 weeks
284.06876 -.02803 (284*2π)/3951 weeks
285.04389 .01901 (285*2π)/3951 weeks
286.01699 -.00195 (286*2π)/3951 weeks
287.01815 -.03207 (287*2π)/3951 weeks
288.03055 -.057 (288*2π)/3951 weeks
289.06346 -.03341 (289*2π)/3951 weeks
290.05468 -.05133 (290*2π)/3951 weeks
291.04603 .00121 (291*2π)/3951 weeks
292.05764 -.01046 (292*2π)/3951 weeks
293.02595 -.05554 (293*2π)/3951 weeks
294-.02035 -.04716 (294*2π)/3951 weeks
295.05711 -.03514 (295*2π)/3951 weeks
296.08052 -.07261 (296*2π)/3951 weeks
297.01701 -.03548 (297*2π)/3951 weeks
298.05914 .03262 (298*2π)/3951 weeks
299.06284 -.0405 (299*2π)/3951 weeks
300-.01305 -.02692 (300*2π)/3951 weeks
301.01017 -.00668 (301*2π)/3951 weeks
302.03883 -.04884 (302*2π)/3951 weeks
303.05437 -.08271 (303*2π)/3951 weeks
304-.00995 -.04553 (304*2π)/3951 weeks
305.05007 .01012 (305*2π)/3951 weeks
306.04239 -.04591 (306*2π)/3951 weeks
307.00937 -.04718 (307*2π)/3951 weeks
308.00269 -.04792 (308*2π)/3951 weeks
309.01845 -.06608 (309*2π)/3951 weeks
310.04009 -.07275 (310*2π)/3951 weeks
311.02117 -.01129 (311*2π)/3951 weeks
312.08004 -.00645 (312*2π)/3951 weeks
313.03288 -.00858 (313*2π)/3951 weeks
314-.00098 -.00525 (314*2π)/3951 weeks
315-.00576 -.01846 (315*2π)/3951 weeks
316.03336 -.0764 (316*2π)/3951 weeks
317.04224 -.06391 (317*2π)/3951 weeks
318.06203 -.00431 (318*2π)/3951 weeks
319.08292 -.07239 (319*2π)/3951 weeks
320.0024 -.05697 (320*2π)/3951 weeks
321.00363 .00568 (321*2π)/3951 weeks
322.05749 -.06662 (322*2π)/3951 weeks
323.00363 -.10215 (323*2π)/3951 weeks
324.01775 -.01756 (324*2π)/3951 weeks
325.08964 -.03702 (325*2π)/3951 weeks
326.02933 -.10698 (326*2π)/3951 weeks
327-.01984 -.0119 (327*2π)/3951 weeks
328.03451 -.00263 (328*2π)/3951 weeks
329.02222 -.09091 (329*2π)/3951 weeks
330.02805 -.10422 (330*2π)/3951 weeks
331.01903 -.07342 (331*2π)/3951 weeks
332.04215 -.06667 (332*2π)/3951 weeks
333.06232 -.06235 (333*2π)/3951 weeks
334.06323 -.02607 (334*2π)/3951 weeks
335-.02618 -.0565 (335*2π)/3951 weeks
336-.01854 -.0142 (336*2π)/3951 weeks
337-.01525 -.09864 (337*2π)/3951 weeks
338-.0258 -.07909 (338*2π)/3951 weeks
339.02206 -.05549 (339*2π)/3951 weeks
340.0339 -.06568 (340*2π)/3951 weeks
341.00088 -.06571 (341*2π)/3951 weeks
342-.01915 -.06924 (342*2π)/3951 weeks
343-.00788 -.04443 (343*2π)/3951 weeks
344.05766 -.14846 (344*2π)/3951 weeks
345.01823 -.09626 (345*2π)/3951 weeks
346-.01245 -.04023 (346*2π)/3951 weeks
347.05553 -.06801 (347*2π)/3951 weeks
348.07824 -.10568 (348*2π)/3951 weeks
349-.05746 -.10998 (349*2π)/3951 weeks
350.0657 -.04919 (350*2π)/3951 weeks
351.09894 -.08836 (351*2π)/3951 weeks
352-.02027 -.06285 (352*2π)/3951 weeks
353-.0041 -.02812 (353*2π)/3951 weeks
354.09426 -.07107 (354*2π)/3951 weeks
355.00715 -.1543 (355*2π)/3951 weeks
356-.04328 -.04374 (356*2π)/3951 weeks
357-.0174 -.10237 (357*2π)/3951 weeks
358.02957 -.15449 (358*2π)/3951 weeks
359.00723 -.16957 (359*2π)/3951 weeks
360.08209 -.08012 (360*2π)/3951 weeks
361.1072 -.15241 (361*2π)/3951 weeks
362-.01053 -.07307 (362*2π)/3951 weeks
363.03539 -.10081 (363*2π)/3951 weeks
364.03448 -.11799 (364*2π)/3951 weeks
365-.02293 -.03358 (365*2π)/3951 weeks
366-.01515 -.13247 (366*2π)/3951 weeks
367.08289 -.10574 (367*2π)/3951 weeks
368.03851 -.05669 (368*2π)/3951 weeks
369-.02543 -.09012 (369*2π)/3951 weeks
370-.04042 -.13243 (370*2π)/3951 weeks
371.01662 -.1718 (371*2π)/3951 weeks
372.0657 -.09126 (372*2π)/3951 weeks
373.06351 -.08403 (373*2π)/3951 weeks
374.06031 -.05218 (374*2π)/3951 weeks
375.05301 -.08392 (375*2π)/3951 weeks
376-.05141 -.19051 (376*2π)/3951 weeks
377.07509 -.13367 (377*2π)/3951 weeks
378.22529 -.10677 (378*2π)/3951 weeks
379.0215 -.28252 (379*2π)/3951 weeks
380-.0187 -.24655 (380*2π)/3951 weeks
381.29384 -.29127 (381*2π)/3951 weeks
382.09901 -.29599 (382*2π)/3951 weeks
383-.16385 -.12513 (383*2π)/3951 weeks
384.02931 -.29868 (384*2π)/3951 weeks
385.27858 -.5195 (385*2π)/3951 weeks
386.13675 -.78704 (386*2π)/3951 weeks
387-.02687 -.31585 (387*2π)/3951 weeks
388.55118 -.19964 (388*2π)/3951 weeks
389-.02736 -.52416 (389*2π)/3951 weeks
390-.32124 -.69632 (390*2π)/3951 weeks
391.33181 -.22507 (391*2π)/3951 weeks
392.89074 -1.62851 (392*2π)/3951 weeks
393-.50016 -2.43142 (393*2π)/3951 weeks