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# Fourier Analysis of BEEIX (BlackRock Emerging Markets All Portfolio)

BEEIX (BlackRock Emerging Markets All Portfolio) appears to have interesting cyclic behaviour every 25 weeks (.172*sine), 35 weeks (.1686*sine), and 32 weeks (.0907*sine).

BEEIX (BlackRock Emerging Markets All Portfolio) has an average price of 8.45 (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 6/25/2013 to 2/24/2020 for BEEIX (BlackRock Emerging Markets All Portfolio), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
08.44556   0
1.14155 -.81751 (1*2π)/349349 weeks
2-.12903 .1916 (2*2π)/349175 weeks
3.10935 -.433 (3*2π)/349116 weeks
4.08796 -.38313 (4*2π)/34987 weeks
5-.12291 .01316 (5*2π)/34970 weeks
6.06518 -.13886 (6*2π)/34958 weeks
7.1437 .00483 (7*2π)/34950 weeks
8.00481 -.11417 (8*2π)/34944 weeks
9-.04138 -.07767 (9*2π)/34939 weeks
10-.05572 -.16864 (10*2π)/34935 weeks
11.02424 -.0907 (11*2π)/34932 weeks
12-.01385 -.05525 (12*2π)/34929 weeks
13-.0037 -.05636 (13*2π)/34927 weeks
14.01164 -.17203 (14*2π)/34925 weeks
15-.0367 -.01111 (15*2π)/34923 weeks
16-.06151 -.10313 (16*2π)/34922 weeks
17.03215 -.0463 (17*2π)/34921 weeks
18-.02677 .00118 (18*2π)/34919 weeks
19.02583 -.03335 (19*2π)/34918 weeks
20.00889 -.03052 (20*2π)/34917 weeks
21-.01662 -.03225 (21*2π)/34917 weeks
22.03789 -.04412 (22*2π)/34916 weeks
23-.03587 -.03669 (23*2π)/34915 weeks
24.00039 -.04534 (24*2π)/34915 weeks
25-.02414 -.01998 (25*2π)/34914 weeks
26-.02745 -.02323 (26*2π)/34913 weeks
27-.04516 .01799 (27*2π)/34913 weeks
28-.01504 -.01419 (28*2π)/34912 weeks
29.02358 -.00282 (29*2π)/34912 weeks
30-.00247 .02258 (30*2π)/34912 weeks
31-.0103 -.01111 (31*2π)/34911 weeks
32-.00186 -.05271 (32*2π)/34911 weeks
33-.01868 -.02457 (33*2π)/34911 weeks
34-.02191 -.02198 (34*2π)/34910 weeks
35-.03027 -.00194 (35*2π)/34910 weeks
36-.0273 -.00477 (36*2π)/34910 weeks
37.00267 -.00373 (37*2π)/3499 weeks
38.01013 -.03232 (38*2π)/3499 weeks
39-.01844 -.02199 (39*2π)/3499 weeks
40-.00952 -.01195 (40*2π)/3499 weeks
41.01792 -.00897 (41*2π)/3499 weeks
42-.01041 -.03278 (42*2π)/3498 weeks
43-.00382 -.02196 (43*2π)/3498 weeks
44-.00785 -.0294 (44*2π)/3498 weeks
45-.01527 -.00441 (45*2π)/3498 weeks
46-.00035 -.01625 (46*2π)/3498 weeks
47-.00735 -.02665 (47*2π)/3497 weeks
48-.0249 -.03201 (48*2π)/3497 weeks
49-.02351 -.01888 (49*2π)/3497 weeks
50-.0043 -.02083 (50*2π)/3497 weeks
51-.0038 -.02773 (51*2π)/3497 weeks
52-.01028 -.00994 (52*2π)/3497 weeks
53-.00103 .01386 (53*2π)/3497 weeks
54-.00675 -.01833 (54*2π)/3496 weeks
55-.01992 -.01677 (55*2π)/3496 weeks
56.00574 -.01893 (56*2π)/3496 weeks
57.0063 -.02213 (57*2π)/3496 weeks
58-.0219 -.01306 (58*2π)/3496 weeks
59-.00418 -.021 (59*2π)/3496 weeks
60-.00912 -.01776 (60*2π)/3496 weeks
61.00088 -.01815 (61*2π)/3496 weeks
62-.00317 -.0027 (62*2π)/3496 weeks
63-.03006 -.00662 (63*2π)/3496 weeks
64.01493 -.01023 (64*2π)/3495 weeks
65-.02255 .00655 (65*2π)/3495 weeks
66.00235 -.02199 (66*2π)/3495 weeks
67-.01103 -.00725 (67*2π)/3495 weeks
68-.02442 -.01255 (68*2π)/3495 weeks
69-.01113 -.00981 (69*2π)/3495 weeks
70.015 -.00088 (70*2π)/3495 weeks
71-.02559 -.01281 (71*2π)/3495 weeks
72-.01256 -.00863 (72*2π)/3495 weeks
73-.01633 -.00288 (73*2π)/3495 weeks
74-.02216 -.01442 (74*2π)/3495 weeks
75-.01013 -.01418 (75*2π)/3495 weeks
76-.01368 -.00477 (76*2π)/3495 weeks
77-.01545 -.01183 (77*2π)/3495 weeks
78-.01509 .00697 (78*2π)/3494 weeks
79-.00905 -.01086 (79*2π)/3494 weeks
80-.00226 -.01673 (80*2π)/3494 weeks
81-.00874 -.00049 (81*2π)/3494 weeks
82-.00767 -.00198 (82*2π)/3494 weeks
83-.01793 -.00393 (83*2π)/3494 weeks
84-.00369 -.00963 (84*2π)/3494 weeks
85-.00234 -.0064 (85*2π)/3494 weeks
86-.00321 .00439 (86*2π)/3494 weeks
87-.01301 -.00564 (87*2π)/3494 weeks
88.00089 -.00638 (88*2π)/3494 weeks
89-.00519 -.006 (89*2π)/3494 weeks
90-.01606 -.00928 (90*2π)/3494 weeks
91-.00372 .00795 (91*2π)/3494 weeks
92-.00472 .00031 (92*2π)/3494 weeks
93-.00417 -.01484 (93*2π)/3494 weeks
94-.01068 .00329 (94*2π)/3494 weeks
95.00283 .00604 (95*2π)/3494 weeks
96.00125 -.00424 (96*2π)/3494 weeks
97.00459 -.00461 (97*2π)/3494 weeks
98.00092 -.01547 (98*2π)/3494 weeks
99-.00095 -.00636 (99*2π)/3494 weeks
100-.0122 -.00394 (100*2π)/3493 weeks
101-.00577 .00912 (101*2π)/3493 weeks
102-.00267 -.01177 (102*2π)/3493 weeks
103-.01181 .00047 (103*2π)/3493 weeks
104-.00235 -.001 (104*2π)/3493 weeks
105.00117 -.003 (105*2π)/3493 weeks
106-.00433 -.01496 (106*2π)/3493 weeks
107-.00868 -.00677 (107*2π)/3493 weeks
108-.00213 .00277 (108*2π)/3493 weeks
109-.00296 -.00388 (109*2π)/3493 weeks
110-.01507 -.00147 (110*2π)/3493 weeks
111.00845 -.00554 (111*2π)/3493 weeks
112-.00525 -.0099 (112*2π)/3493 weeks
113-.01628 -.00419 (113*2π)/3493 weeks
114.002 .0084 (114*2π)/3493 weeks
115-.00273 -.0106 (115*2π)/3493 weeks
116-.00999 -.00519 (116*2π)/3493 weeks
117.00445 .00069 (117*2π)/3493 weeks
118.001 -.0046 (118*2π)/3493 weeks
119-.01097 -.00794 (119*2π)/3493 weeks
120-.00402 .00017 (120*2π)/3493 weeks
121-.00124 .00453 (121*2π)/3493 weeks
122-.0107 -.00842 (122*2π)/3493 weeks
123-.01501 -.00724 (123*2π)/3493 weeks
124.0059 .00221 (124*2π)/3493 weeks
125-.00949 -.00531 (125*2π)/3493 weeks
126-.01102 -.00251 (126*2π)/3493 weeks
127-.00924 -.00004 (127*2π)/3493 weeks
128-.00732 .00317 (128*2π)/3493 weeks
129-.0034 -.00419 (129*2π)/3493 weeks
130-.00844 .00089 (130*2π)/3493 weeks
131-.00412 -.00558 (131*2π)/3493 weeks
132-.00547 -.00576 (132*2π)/3493 weeks
133-.01211 -.00144 (133*2π)/3493 weeks
134-.00886 -.00171 (134*2π)/3493 weeks
135-.00619 -.00772 (135*2π)/3493 weeks
136-.00073 .00133 (136*2π)/3493 weeks
137-.00806 .00537 (137*2π)/3493 weeks
138-.00999 -.00221 (138*2π)/3493 weeks
139-.00631 -.00354 (139*2π)/3493 weeks
140.00024 .00266 (140*2π)/3492 weeks
141-.01009 -.00088 (141*2π)/3492 weeks
142-.00229 -.00302 (142*2π)/3492 weeks
143-.00597 -.00038 (143*2π)/3492 weeks
144-.00237 -.00535 (144*2π)/3492 weeks
145.00031 -.00109 (145*2π)/3492 weeks
146-.01644 -.00068 (146*2π)/3492 weeks
147-.00347 -.00507 (147*2π)/3492 weeks
148-.00938 .00424 (148*2π)/3492 weeks
149.00005 .00544 (149*2π)/3492 weeks
150-.00299 -.00382 (150*2π)/3492 weeks
151-.00026 .00008 (151*2π)/3492 weeks
152-.00965 .00382 (152*2π)/3492 weeks
153-.00059 -.00697 (153*2π)/3492 weeks
154-.00508 .00051 (154*2π)/3492 weeks
155-.00748 -.00415 (155*2π)/3492 weeks
156-.01659 -.00366 (156*2π)/3492 weeks
157-.00352 .00344 (157*2π)/3492 weeks
158-.00518 .00685 (158*2π)/3492 weeks
159.00207 -.00206 (159*2π)/3492 weeks
160-.00417 .00406 (160*2π)/3492 weeks
161-.01212 -.00088 (161*2π)/3492 weeks
162-.00209 -.00508 (162*2π)/3492 weeks
163-.00358 .00568 (163*2π)/3492 weeks
164-.00692 -.00368 (164*2π)/3492 weeks
165-.00311 .00167 (165*2π)/3492 weeks
166-.01337 -.00355 (166*2π)/3492 weeks
167-.00191 -.0068 (167*2π)/3492 weeks
168-.01477 .00981 (168*2π)/3492 weeks
169.00059 -.0091 (169*2π)/3492 weeks
170.00228 .00214 (170*2π)/3492 weeks
171-.01231 -.00106 (171*2π)/3492 weeks
172-.00795 .00026 (172*2π)/3492 weeks
173.00329 -.00126 (173*2π)/3492 weeks
174-.0037 .00024 (174*2π)/3492 weeks
175-.0037 -.00024 (175*2π)/3492 weeks
176.00329 .00126 (176*2π)/3492 weeks
177-.00795 -.00026 (177*2π)/3492 weeks
178-.01231 .00106 (178*2π)/3492 weeks
179.00228 -.00214 (179*2π)/3492 weeks
180.00059 .0091 (180*2π)/3492 weeks
181-.01477 -.00981 (181*2π)/3492 weeks
182-.00191 .0068 (182*2π)/3492 weeks
183-.01337 .00355 (183*2π)/3492 weeks
184-.00311 -.00167 (184*2π)/3492 weeks
185-.00692 .00368 (185*2π)/3492 weeks
186-.00358 -.00568 (186*2π)/3492 weeks
187-.00209 .00508 (187*2π)/3492 weeks
188-.01212 .00088 (188*2π)/3492 weeks
189-.00417 -.00406 (189*2π)/3492 weeks
190.00207 .00206 (190*2π)/3492 weeks
191-.00518 -.00685 (191*2π)/3492 weeks
192-.00352 -.00344 (192*2π)/3492 weeks
193-.01659 .00366 (193*2π)/3492 weeks
194-.00748 .00415 (194*2π)/3492 weeks
195-.00508 -.00051 (195*2π)/3492 weeks
196-.00059 .00697 (196*2π)/3492 weeks
197-.00965 -.00382 (197*2π)/3492 weeks
198-.00026 -.00008 (198*2π)/3492 weeks
199-.00299 .00382 (199*2π)/3492 weeks
200.00005 -.00544 (200*2π)/3492 weeks
201-.00938 -.00424 (201*2π)/3492 weeks
202-.00347 .00507 (202*2π)/3492 weeks
203-.01644 .00068 (203*2π)/3492 weeks
204.00031 .00109 (204*2π)/3492 weeks
205-.00237 .00535 (205*2π)/3492 weeks
206-.00597 .00038 (206*2π)/3492 weeks
207-.00229 .00302 (207*2π)/3492 weeks
208-.01009 .00088 (208*2π)/3492 weeks
209.00024 -.00266 (209*2π)/3492 weeks
210-.00631 .00354 (210*2π)/3492 weeks
211-.00999 .00221 (211*2π)/3492 weeks
212-.00806 -.00537 (212*2π)/3492 weeks
213-.00073 -.00133 (213*2π)/3492 weeks
214-.00619 .00772 (214*2π)/3492 weeks
215-.00886 .00171 (215*2π)/3492 weeks
216-.01211 .00144 (216*2π)/3492 weeks
217-.00547 .00576 (217*2π)/3492 weeks
218-.00412 .00558 (218*2π)/3492 weeks
219-.00844 -.00089 (219*2π)/3492 weeks
220-.0034 .00419 (220*2π)/3492 weeks
221-.00732 -.00317 (221*2π)/3492 weeks
222-.00924 .00004 (222*2π)/3492 weeks
223-.01102 .00251 (223*2π)/3492 weeks
224-.00949 .00531 (224*2π)/3492 weeks
225.0059 -.00221 (225*2π)/3492 weeks
226-.01501 .00724 (226*2π)/3492 weeks
227-.0107 .00842 (227*2π)/3492 weeks
228-.00124 -.00453 (228*2π)/3492 weeks
229-.00402 -.00017 (229*2π)/3492 weeks
230-.01097 .00794 (230*2π)/3492 weeks
231.001 .0046 (231*2π)/3492 weeks
232.00445 -.00069 (232*2π)/3492 weeks
233-.00999 .00519 (233*2π)/3491 weeks
234-.00273 .0106 (234*2π)/3491 weeks
235.002 -.0084 (235*2π)/3491 weeks
236-.01628 .00419 (236*2π)/3491 weeks
237-.00525 .0099 (237*2π)/3491 weeks
238.00845 .00554 (238*2π)/3491 weeks
239-.01507 .00147 (239*2π)/3491 weeks
240-.00296 .00388 (240*2π)/3491 weeks
241-.00213 -.00277 (241*2π)/3491 weeks
242-.00868 .00677 (242*2π)/3491 weeks
243-.00433 .01496 (243*2π)/3491 weeks
244.00117 .003 (244*2π)/3491 weeks
245-.00235 .001 (245*2π)/3491 weeks
246-.01181 -.00047 (246*2π)/3491 weeks
247-.00267 .01177 (247*2π)/3491 weeks
248-.00577 -.00912 (248*2π)/3491 weeks
249-.0122 .00394 (249*2π)/3491 weeks
250-.00095 .00636 (250*2π)/3491 weeks
251.00092 .01547 (251*2π)/3491 weeks
252.00459 .00461 (252*2π)/3491 weeks
253.00125 .00424 (253*2π)/3491 weeks
254.00283 -.00604 (254*2π)/3491 weeks
255-.01068 -.00329 (255*2π)/3491 weeks
256-.00417 .01484 (256*2π)/3491 weeks
257-.00472 -.00031 (257*2π)/3491 weeks
258-.00372 -.00795 (258*2π)/3491 weeks
259-.01606 .00928 (259*2π)/3491 weeks
260-.00519 .006 (260*2π)/3491 weeks
261.00089 .00638 (261*2π)/3491 weeks
262-.01301 .00564 (262*2π)/3491 weeks
263-.00321 -.00439 (263*2π)/3491 weeks
264-.00234 .0064 (264*2π)/3491 weeks
265-.00369 .00963 (265*2π)/3491 weeks
266-.01793 .00393 (266*2π)/3491 weeks
267-.00767 .00198 (267*2π)/3491 weeks
268-.00874 .00049 (268*2π)/3491 weeks
269-.00226 .01673 (269*2π)/3491 weeks
270-.00905 .01086 (270*2π)/3491 weeks
271-.01509 -.00697 (271*2π)/3491 weeks
272-.01545 .01183 (272*2π)/3491 weeks
273-.01368 .00477 (273*2π)/3491 weeks
274-.01013 .01418 (274*2π)/3491 weeks
275-.02216 .01442 (275*2π)/3491 weeks
276-.01633 .00288 (276*2π)/3491 weeks
277-.01256 .00863 (277*2π)/3491 weeks
278-.02559 .01281 (278*2π)/3491 weeks
279.015 .00088 (279*2π)/3491 weeks
280-.01113 .00981 (280*2π)/3491 weeks
281-.02442 .01255 (281*2π)/3491 weeks
282-.01103 .00725 (282*2π)/3491 weeks
283.00235 .02199 (283*2π)/3491 weeks
284-.02255 -.00655 (284*2π)/3491 weeks
285.01493 .01023 (285*2π)/3491 weeks
286-.03006 .00662 (286*2π)/3491 weeks
287-.00317 .0027 (287*2π)/3491 weeks
288.00088 .01815 (288*2π)/3491 weeks
289-.00912 .01776 (289*2π)/3491 weeks
290-.00418 .021 (290*2π)/3491 weeks
291-.0219 .01306 (291*2π)/3491 weeks
292.0063 .02213 (292*2π)/3491 weeks
293.00574 .01893 (293*2π)/3491 weeks
294-.01992 .01677 (294*2π)/3491 weeks
295-.00675 .01833 (295*2π)/3491 weeks
296-.00103 -.01386 (296*2π)/3491 weeks
297-.01028 .00994 (297*2π)/3491 weeks
298-.0038 .02773 (298*2π)/3491 weeks
299-.0043 .02083 (299*2π)/3491 weeks
300-.02351 .01888 (300*2π)/3491 weeks
301-.0249 .03201 (301*2π)/3491 weeks
302-.00735 .02665 (302*2π)/3491 weeks
303-.00035 .01625 (303*2π)/3491 weeks
304-.01527 .00441 (304*2π)/3491 weeks
305-.00785 .0294 (305*2π)/3491 weeks
306-.00382 .02196 (306*2π)/3491 weeks
307-.01041 .03278 (307*2π)/3491 weeks
308.01792 .00897 (308*2π)/3491 weeks
309-.00952 .01195 (309*2π)/3491 weeks
310-.01844 .02199 (310*2π)/3491 weeks
311.01013 .03232 (311*2π)/3491 weeks
312.00267 .00373 (312*2π)/3491 weeks
313-.0273 .00477 (313*2π)/3491 weeks
314-.03027 .00194 (314*2π)/3491 weeks
315-.02191 .02198 (315*2π)/3491 weeks
316-.01868 .02457 (316*2π)/3491 weeks
317-.00186 .05271 (317*2π)/3491 weeks
318-.0103 .01111 (318*2π)/3491 weeks
319-.00247 -.02258 (319*2π)/3491 weeks
320.02358 .00282 (320*2π)/3491 weeks
321-.01504 .01419 (321*2π)/3491 weeks
322-.04516 -.01799 (322*2π)/3491 weeks
323-.02745 .02323 (323*2π)/3491 weeks
324-.02414 .01998 (324*2π)/3491 weeks
325.00039 .04534 (325*2π)/3491 weeks
326-.03587 .03669 (326*2π)/3491 weeks
327.03789 .04412 (327*2π)/3491 weeks
328-.01662 .03225 (328*2π)/3491 weeks
329.00889 .03052 (329*2π)/3491 weeks
330.02583 .03335 (330*2π)/3491 weeks
331-.02677 -.00118 (331*2π)/3491 weeks
332.03215 .0463 (332*2π)/3491 weeks
333-.06151 .10313 (333*2π)/3491 weeks
334-.0367 .01111 (334*2π)/3491 weeks
335.01164 .17203 (335*2π)/3491 weeks
336-.0037 .05636 (336*2π)/3491 weeks
337-.01385 .05525 (337*2π)/3491 weeks
338.02424 .0907 (338*2π)/3491 weeks
339-.05572 .16864 (339*2π)/3491 weeks
340-.04138 .07767 (340*2π)/3491 weeks
341.00481 .11417 (341*2π)/3491 weeks
342.1437 -.00483 (342*2π)/3491 weeks
343.06518 .13886 (343*2π)/3491 weeks
344-.12291 -.01316 (344*2π)/3491 weeks
345.08796 .38313 (345*2π)/3491 weeks
346.10935 .433 (346*2π)/3491 weeks
347-.12903 -.1916 (347*2π)/3491 weeks