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# Fourier Analysis of MTGE (American Capital Mortgage Investment Crp)

MTGE (American Capital Mortgage Investment Crp) appears to have interesting cyclic behaviour every 31 weeks (.4443*sine), 23 weeks (.3542*sine), and 29 weeks (.3255*sine).

MTGE (American Capital Mortgage Investment Crp) has an average price of 13.29 (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 8/4/2011 to 3/12/2018 for MTGE (American Capital Mortgage Investment Crp), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
013.28575   0
1.53157 -1.07303 (1*2π)/346346 weeks
2.06169 -1.74773 (2*2π)/346173 weeks
3-1.12203 -1.48504 (3*2π)/346115 weeks
4.17909 -1.22801 (4*2π)/34687 weeks
5-.0321 -.89859 (5*2π)/34669 weeks
6-.49526 -.57212 (6*2π)/34658 weeks
7-.1823 -.39662 (7*2π)/34649 weeks
8.18983 -.39223 (8*2π)/34643 weeks
9.16288 -.28304 (9*2π)/34638 weeks
10-.09816 -.25247 (10*2π)/34635 weeks
11-.0622 -.44434 (11*2π)/34631 weeks
12.15377 -.32551 (12*2π)/34629 weeks
13-.01506 -.0073 (13*2π)/34627 weeks
14-.09897 -.20082 (14*2π)/34625 weeks
15-.00027 -.35418 (15*2π)/34623 weeks
16.0754 -.04191 (16*2π)/34622 weeks
17-.06273 -.13852 (17*2π)/34620 weeks
18-.0143 -.2898 (18*2π)/34619 weeks
19-.02614 -.13756 (19*2π)/34618 weeks
20-.0427 -.07968 (20*2π)/34617 weeks
21-.05363 -.17364 (21*2π)/34616 weeks
22-.01798 -.11177 (22*2π)/34616 weeks
23.04546 -.11242 (23*2π)/34615 weeks
24.01205 .00165 (24*2π)/34614 weeks
25-.08643 -.08946 (25*2π)/34614 weeks
26.03287 -.11087 (26*2π)/34613 weeks
27.03553 -.02918 (27*2π)/34613 weeks
28-.01096 -.08236 (28*2π)/34612 weeks
29.06238 -.09247 (29*2π)/34612 weeks
30.03096 -.15139 (30*2π)/34612 weeks
31-.0566 -.07907 (31*2π)/34611 weeks
32-.03591 -.10814 (32*2π)/34611 weeks
33.02311 -.11312 (33*2π)/34610 weeks
34-.00004 -.13582 (34*2π)/34610 weeks
35.00687 -.09034 (35*2π)/34610 weeks
36-.0008 -.07268 (36*2π)/34610 weeks
37-.04566 -.0429 (37*2π)/3469 weeks
38-.09907 -.06207 (38*2π)/3469 weeks
39-.07391 -.0957 (39*2π)/3469 weeks
40-.0508 -.06782 (40*2π)/3469 weeks
41-.03556 -.06325 (41*2π)/3468 weeks
42-.04696 -.04666 (42*2π)/3468 weeks
43-.01067 -.06139 (43*2π)/3468 weeks
44-.00527 -.03785 (44*2π)/3468 weeks
45.01818 -.10131 (45*2π)/3468 weeks
46-.01156 -.13045 (46*2π)/3468 weeks
47-.05272 -.07104 (47*2π)/3467 weeks
48-.04117 -.08186 (48*2π)/3467 weeks
49-.02748 -.08589 (49*2π)/3467 weeks
50-.01472 -.06693 (50*2π)/3467 weeks
51-.01806 -.0539 (51*2π)/3467 weeks
52-.03799 -.06661 (52*2π)/3467 weeks
53-.02727 -.05892 (53*2π)/3467 weeks
54-.00187 -.02421 (54*2π)/3466 weeks
55-.06761 -.02208 (55*2π)/3466 weeks
56-.03118 -.00804 (56*2π)/3466 weeks
57-.01606 -.02836 (57*2π)/3466 weeks
58-.03752 -.02755 (58*2π)/3466 weeks
59-.03749 -.02606 (59*2π)/3466 weeks
60-.00022 -.01502 (60*2π)/3466 weeks
61-.02397 .01038 (61*2π)/3466 weeks
62-.02306 -.03136 (62*2π)/3466 weeks
63-.02711 -.07124 (63*2π)/3465 weeks
64-.03597 -.01363 (64*2π)/3465 weeks
65-.02456 .01406 (65*2π)/3465 weeks
66.00836 -.02131 (66*2π)/3465 weeks
67-.02169 -.02976 (67*2π)/3465 weeks
68-.00897 -.0543 (68*2π)/3465 weeks
69-.02948 -.04614 (69*2π)/3465 weeks
70-.04639 -.0303 (70*2π)/3465 weeks
71-.02959 -.01681 (71*2π)/3465 weeks
72-.02918 -.03769 (72*2π)/3465 weeks
73-.05682 -.02233 (73*2π)/3465 weeks
74-.01276 -.03239 (74*2π)/3465 weeks
75-.02509 -.03964 (75*2π)/3465 weeks
76-.03488 -.00019 (76*2π)/3465 weeks
77-.02493 -.02092 (77*2π)/3464 weeks
78-.00623 -.05094 (78*2π)/3464 weeks
79-.01584 -.02858 (79*2π)/3464 weeks
80-.00318 -.01704 (80*2π)/3464 weeks
81-.00779 -.01402 (81*2π)/3464 weeks
82-.02677 -.06138 (82*2π)/3464 weeks
83-.04309 -.04511 (83*2π)/3464 weeks
84-.00755 -.05113 (84*2π)/3464 weeks
85-.03905 -.05747 (85*2π)/3464 weeks
86-.02569 -.03652 (86*2π)/3464 weeks
87-.01413 -.0384 (87*2π)/3464 weeks
88-.02822 -.02985 (88*2π)/3464 weeks
89-.00185 -.04126 (89*2π)/3464 weeks
90-.03343 -.03239 (90*2π)/3464 weeks
91-.0506 -.03383 (91*2π)/3464 weeks
92-.04052 -.01338 (92*2π)/3464 weeks
93-.01888 -.0025 (93*2π)/3464 weeks
94-.03177 -.03652 (94*2π)/3464 weeks
95-.03127 -.06096 (95*2π)/3464 weeks
96-.01521 -.03956 (96*2π)/3464 weeks
97-.03733 -.03366 (97*2π)/3464 weeks
98-.04485 -.04292 (98*2π)/3464 weeks
99-.02633 -.04863 (99*2π)/3463 weeks
100-.0387 -.05596 (100*2π)/3463 weeks
101-.04367 -.04584 (101*2π)/3463 weeks
102-.04097 .01517 (102*2π)/3463 weeks
103-.03145 -.01964 (103*2π)/3463 weeks
104-.04605 -.02457 (104*2π)/3463 weeks
105-.05386 -.01295 (105*2π)/3463 weeks
106-.01806 -.03448 (106*2π)/3463 weeks
107-.02957 -.03419 (107*2π)/3463 weeks
108-.0227 -.02717 (108*2π)/3463 weeks
109-.04605 -.02651 (109*2π)/3463 weeks
110-.03424 -.01368 (110*2π)/3463 weeks
111-.02171 -.03635 (111*2π)/3463 weeks
112-.01102 -.00677 (112*2π)/3463 weeks
113-.04359 -.00306 (113*2π)/3463 weeks
114-.03882 .0003 (114*2π)/3463 weeks
115-.02022 -.00332 (115*2π)/3463 weeks
116-.01184 -.01354 (116*2π)/3463 weeks
117-.04595 .02173 (117*2π)/3463 weeks
118-.0417 -.02461 (118*2π)/3463 weeks
119-.02094 -.02404 (119*2π)/3463 weeks
120-.01492 .00599 (120*2π)/3463 weeks
121-.0401 -.03361 (121*2π)/3463 weeks
122-.03582 -.01777 (122*2π)/3463 weeks
123-.00748 .01791 (123*2π)/3463 weeks
124-.02771 .00391 (124*2π)/3463 weeks
125-.02138 -.02813 (125*2π)/3463 weeks
126-.01498 .01029 (126*2π)/3463 weeks
127-.04238 .01344 (127*2π)/3463 weeks
128-.05119 -.02087 (128*2π)/3463 weeks
129-.03054 -.00348 (129*2π)/3463 weeks
130-.02636 .00947 (130*2π)/3463 weeks
131-.03258 -.01837 (131*2π)/3463 weeks
132-.02694 -.01022 (132*2π)/3463 weeks
133-.04446 -.00248 (133*2π)/3463 weeks
134-.02659 .01185 (134*2π)/3463 weeks
135-.02333 -.01663 (135*2π)/3463 weeks
136-.02201 -.00627 (136*2π)/3463 weeks
137-.02259 .00537 (137*2π)/3463 weeks
138-.02195 .01869 (138*2π)/3463 weeks
139-.02557 -.01899 (139*2π)/3462 weeks
140-.03274 -.00395 (140*2π)/3462 weeks
141-.04723 -.01099 (141*2π)/3462 weeks
142-.02385 -.00564 (142*2π)/3462 weeks
143-.01693 -.00121 (143*2π)/3462 weeks
144-.01513 -.0033 (144*2π)/3462 weeks
145-.02726 -.00895 (145*2π)/3462 weeks
146-.02429 -.02589 (146*2π)/3462 weeks
147-.03005 .00099 (147*2π)/3462 weeks
148-.03876 .01288 (148*2π)/3462 weeks
149-.01726 -.00362 (149*2π)/3462 weeks
150-.02199 .00248 (150*2π)/3462 weeks
151-.03828 -.02225 (151*2π)/3462 weeks
152-.06325 -.02147 (152*2π)/3462 weeks
153-.04406 -.00306 (153*2π)/3462 weeks
154-.02795 -.00162 (154*2π)/3462 weeks
155-.02059 .01109 (155*2π)/3462 weeks
156-.02989 -.00608 (156*2π)/3462 weeks
157-.04215 -.01558 (157*2π)/3462 weeks
158-.03037 -.01658 (158*2π)/3462 weeks
159-.02655 -.01579 (159*2π)/3462 weeks
160-.02473 -.01261 (160*2π)/3462 weeks
161-.05038 .01306 (161*2π)/3462 weeks
162-.0612 -.01075 (162*2π)/3462 weeks
163-.0364 -.03402 (163*2π)/3462 weeks
164-.02192 -.00736 (164*2π)/3462 weeks
165.00599 .01609 (165*2π)/3462 weeks
166-.03079 -.00052 (166*2π)/3462 weeks
167-.04381 -.01458 (167*2π)/3462 weeks
168-.01296 -.00094 (168*2π)/3462 weeks
169-.02719 .00953 (169*2π)/3462 weeks
170-.02832 .02286 (170*2π)/3462 weeks
171-.00334 -.01131 (171*2π)/3462 weeks
172-.03019 -.02875 (172*2π)/3462 weeks
173-.03875   (173*2π)/3462 weeks
174-.03019 .02875 (174*2π)/3462 weeks
175-.00334 .01131 (175*2π)/3462 weeks
176-.02832 -.02286 (176*2π)/3462 weeks
177-.02719 -.00953 (177*2π)/3462 weeks
178-.01296 .00094 (178*2π)/3462 weeks
179-.04381 .01458 (179*2π)/3462 weeks
180-.03079 .00052 (180*2π)/3462 weeks
181.00599 -.01609 (181*2π)/3462 weeks
182-.02192 .00736 (182*2π)/3462 weeks
183-.0364 .03402 (183*2π)/3462 weeks
184-.0612 .01075 (184*2π)/3462 weeks
185-.05038 -.01306 (185*2π)/3462 weeks
186-.02473 .01261 (186*2π)/3462 weeks
187-.02655 .01579 (187*2π)/3462 weeks
188-.03037 .01658 (188*2π)/3462 weeks
189-.04215 .01558 (189*2π)/3462 weeks
190-.02989 .00608 (190*2π)/3462 weeks
191-.02059 -.01109 (191*2π)/3462 weeks
192-.02795 .00162 (192*2π)/3462 weeks
193-.04406 .00306 (193*2π)/3462 weeks
194-.06325 .02147 (194*2π)/3462 weeks
195-.03828 .02225 (195*2π)/3462 weeks
196-.02199 -.00248 (196*2π)/3462 weeks
197-.01726 .00362 (197*2π)/3462 weeks
198-.03876 -.01288 (198*2π)/3462 weeks
199-.03005 -.00099 (199*2π)/3462 weeks
200-.02429 .02589 (200*2π)/3462 weeks
201-.02726 .00895 (201*2π)/3462 weeks
202-.01513 .0033 (202*2π)/3462 weeks
203-.01693 .00121 (203*2π)/3462 weeks
204-.02385 .00564 (204*2π)/3462 weeks
205-.04723 .01099 (205*2π)/3462 weeks
206-.03274 .00395 (206*2π)/3462 weeks
207-.02557 .01899 (207*2π)/3462 weeks
208-.02195 -.01869 (208*2π)/3462 weeks
209-.02259 -.00537 (209*2π)/3462 weeks
210-.02201 .00627 (210*2π)/3462 weeks
211-.02333 .01663 (211*2π)/3462 weeks
212-.02659 -.01185 (212*2π)/3462 weeks
213-.04446 .00248 (213*2π)/3462 weeks
214-.02694 .01022 (214*2π)/3462 weeks
215-.03258 .01837 (215*2π)/3462 weeks
216-.02636 -.00947 (216*2π)/3462 weeks
217-.03054 .00348 (217*2π)/3462 weeks
218-.05119 .02087 (218*2π)/3462 weeks
219-.04238 -.01344 (219*2π)/3462 weeks
220-.01498 -.01029 (220*2π)/3462 weeks
221-.02138 .02813 (221*2π)/3462 weeks
222-.02771 -.00391 (222*2π)/3462 weeks
223-.00748 -.01791 (223*2π)/3462 weeks
224-.03582 .01777 (224*2π)/3462 weeks
225-.0401 .03361 (225*2π)/3462 weeks
226-.01492 -.00599 (226*2π)/3462 weeks
227-.02094 .02404 (227*2π)/3462 weeks
228-.0417 .02461 (228*2π)/3462 weeks
229-.04595 -.02173 (229*2π)/3462 weeks
230-.01184 .01354 (230*2π)/3462 weeks
231-.02022 .00332 (231*2π)/3461 weeks
232-.03882 -.0003 (232*2π)/3461 weeks
233-.04359 .00306 (233*2π)/3461 weeks
234-.01102 .00677 (234*2π)/3461 weeks
235-.02171 .03635 (235*2π)/3461 weeks
236-.03424 .01368 (236*2π)/3461 weeks
237-.04605 .02651 (237*2π)/3461 weeks
238-.0227 .02717 (238*2π)/3461 weeks
239-.02957 .03419 (239*2π)/3461 weeks
240-.01806 .03448 (240*2π)/3461 weeks
241-.05386 .01295 (241*2π)/3461 weeks
242-.04605 .02457 (242*2π)/3461 weeks
243-.03145 .01964 (243*2π)/3461 weeks
244-.04097 -.01517 (244*2π)/3461 weeks
245-.04367 .04584 (245*2π)/3461 weeks
246-.0387 .05596 (246*2π)/3461 weeks
247-.02633 .04863 (247*2π)/3461 weeks
248-.04485 .04292 (248*2π)/3461 weeks
249-.03733 .03366 (249*2π)/3461 weeks
250-.01521 .03956 (250*2π)/3461 weeks
251-.03127 .06096 (251*2π)/3461 weeks
252-.03177 .03652 (252*2π)/3461 weeks
253-.01888 .0025 (253*2π)/3461 weeks
254-.04052 .01338 (254*2π)/3461 weeks
255-.0506 .03383 (255*2π)/3461 weeks
256-.03343 .03239 (256*2π)/3461 weeks
257-.00185 .04126 (257*2π)/3461 weeks
258-.02822 .02985 (258*2π)/3461 weeks
259-.01413 .0384 (259*2π)/3461 weeks
260-.02569 .03652 (260*2π)/3461 weeks
261-.03905 .05747 (261*2π)/3461 weeks
262-.00755 .05113 (262*2π)/3461 weeks
263-.04309 .04511 (263*2π)/3461 weeks
264-.02677 .06138 (264*2π)/3461 weeks
265-.00779 .01402 (265*2π)/3461 weeks
266-.00318 .01704 (266*2π)/3461 weeks
267-.01584 .02858 (267*2π)/3461 weeks
268-.00623 .05094 (268*2π)/3461 weeks
269-.02493 .02092 (269*2π)/3461 weeks
270-.03488 .00019 (270*2π)/3461 weeks
271-.02509 .03964 (271*2π)/3461 weeks
272-.01276 .03239 (272*2π)/3461 weeks
273-.05682 .02233 (273*2π)/3461 weeks
274-.02918 .03769 (274*2π)/3461 weeks
275-.02959 .01681 (275*2π)/3461 weeks
276-.04639 .0303 (276*2π)/3461 weeks
277-.02948 .04614 (277*2π)/3461 weeks
278-.00897 .0543 (278*2π)/3461 weeks
279-.02169 .02976 (279*2π)/3461 weeks
280.00836 .02131 (280*2π)/3461 weeks
281-.02456 -.01406 (281*2π)/3461 weeks
282-.03597 .01363 (282*2π)/3461 weeks
283-.02711 .07124 (283*2π)/3461 weeks
284-.02306 .03136 (284*2π)/3461 weeks
285-.02397 -.01038 (285*2π)/3461 weeks
286-.00022 .01502 (286*2π)/3461 weeks
287-.03749 .02606 (287*2π)/3461 weeks
288-.03752 .02755 (288*2π)/3461 weeks
289-.01606 .02836 (289*2π)/3461 weeks
290-.03118 .00804 (290*2π)/3461 weeks
291-.06761 .02208 (291*2π)/3461 weeks
292-.00187 .02421 (292*2π)/3461 weeks
293-.02727 .05892 (293*2π)/3461 weeks
294-.03799 .06661 (294*2π)/3461 weeks
295-.01806 .0539 (295*2π)/3461 weeks
296-.01472 .06693 (296*2π)/3461 weeks
297-.02748 .08589 (297*2π)/3461 weeks
298-.04117 .08186 (298*2π)/3461 weeks
299-.05272 .07104 (299*2π)/3461 weeks
300-.01156 .13045 (300*2π)/3461 weeks
301.01818 .10131 (301*2π)/3461 weeks
302-.00527 .03785 (302*2π)/3461 weeks
303-.01067 .06139 (303*2π)/3461 weeks
304-.04696 .04666 (304*2π)/3461 weeks
305-.03556 .06325 (305*2π)/3461 weeks
306-.0508 .06782 (306*2π)/3461 weeks
307-.07391 .0957 (307*2π)/3461 weeks
308-.09907 .06207 (308*2π)/3461 weeks
309-.04566 .0429 (309*2π)/3461 weeks
310-.0008 .07268 (310*2π)/3461 weeks
311.00687 .09034 (311*2π)/3461 weeks
312-.00004 .13582 (312*2π)/3461 weeks
313.02311 .11312 (313*2π)/3461 weeks
314-.03591 .10814 (314*2π)/3461 weeks
315-.0566 .07907 (315*2π)/3461 weeks
316.03096 .15139 (316*2π)/3461 weeks
317.06238 .09247 (317*2π)/3461 weeks
318-.01096 .08236 (318*2π)/3461 weeks
319.03553 .02918 (319*2π)/3461 weeks
320.03287 .11087 (320*2π)/3461 weeks
321-.08643 .08946 (321*2π)/3461 weeks
322.01205 -.00165 (322*2π)/3461 weeks
323.04546 .11242 (323*2π)/3461 weeks
324-.01798 .11177 (324*2π)/3461 weeks
325-.05363 .17364 (325*2π)/3461 weeks
326-.0427 .07968 (326*2π)/3461 weeks
327-.02614 .13756 (327*2π)/3461 weeks
328-.0143 .2898 (328*2π)/3461 weeks
329-.06273 .13852 (329*2π)/3461 weeks
330.0754 .04191 (330*2π)/3461 weeks
331-.00027 .35418 (331*2π)/3461 weeks
332-.09897 .20082 (332*2π)/3461 weeks
333-.01506 .0073 (333*2π)/3461 weeks
334.15377 .32551 (334*2π)/3461 weeks
335-.0622 .44434 (335*2π)/3461 weeks
336-.09816 .25247 (336*2π)/3461 weeks
337.16288 .28304 (337*2π)/3461 weeks
338.18983 .39223 (338*2π)/3461 weeks
339-.1823 .39662 (339*2π)/3461 weeks
340-.49526 .57212 (340*2π)/3461 weeks
341-.0321 .89859 (341*2π)/3461 weeks
342.17909 1.22801 (342*2π)/3461 weeks
343-1.12203 1.48504 (343*2π)/3461 weeks
344.06169 1.74773 (344*2π)/3461 weeks