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Fourier Analysis of AMTG (Apollo Residential Mortgage, In)


AMTG (Apollo Residential Mortgage, In) appears to have interesting cyclic behaviour every 27 weeks (.2466*sine), 22 weeks (.1951*cosine), and 14 weeks (.1493*cosine).

AMTG (Apollo Residential Mortgage, In) has an average price of 13.54 (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 7/22/2011 to 8/29/2016 for AMTG (Apollo Residential Mortgage, In), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
013.54278   0 
1-1.29801 -.22735 (1*2π)/268268 weeks
2-1.36649 -.25515 (2*2π)/268134 weeks
3.6836 -.91792 (3*2π)/26889 weeks
4.53372 .05052 (4*2π)/26867 weeks
5-.10936 -.76805 (5*2π)/26854 weeks
6.23384 -.39631 (6*2π)/26845 weeks
7-.11666 -.05169 (7*2π)/26838 weeks
8.00529 -.25152 (8*2π)/26834 weeks
9.16233 -.00052 (9*2π)/26830 weeks
10-.05879 .24663 (10*2π)/26827 weeks
11-.04899 .01735 (11*2π)/26824 weeks
12.19505 .01053 (12*2π)/26822 weeks
13-.01717 -.08797 (13*2π)/26821 weeks
14.13786 -.09813 (14*2π)/26819 weeks
15-.08627 -.13984 (15*2π)/26818 weeks
16-.06836 -.1725 (16*2π)/26817 weeks
17-.01221 -.06926 (17*2π)/26816 weeks
18-.0581 .13279 (18*2π)/26815 weeks
19-.14926 -.03254 (19*2π)/26814 weeks
20.07628 -.01207 (20*2π)/26813 weeks
21.07185 .01096 (21*2π)/26813 weeks
22.08673 -.06118 (22*2π)/26812 weeks
23.02833 -.07134 (23*2π)/26812 weeks
24-.10391 -.06164 (24*2π)/26811 weeks
25-.00837 -.07865 (25*2π)/26811 weeks
26-.06065 -.03261 (26*2π)/26810 weeks
27-.07907 .02964 (27*2π)/26810 weeks
28-.02392 .00878 (28*2π)/26810 weeks
29-.01527 -.02623 (29*2π)/2689 weeks
30.03524 -.05648 (30*2π)/2689 weeks
31.07766 -.04962 (31*2π)/2689 weeks
32-.03349 -.01683 (32*2π)/2688 weeks
33.01007 -.09691 (33*2π)/2688 weeks
34-.02041 -.0372 (34*2π)/2688 weeks
35-.05548 -.0101 (35*2π)/2688 weeks
36.00351 -.01928 (36*2π)/2687 weeks
37.00851 -.01122 (37*2π)/2687 weeks
38.01979 .02503 (38*2π)/2687 weeks
39.02238 .00119 (39*2π)/2687 weeks
40.05789 .01243 (40*2π)/2687 weeks
41.04092 .02927 (41*2π)/2687 weeks
42-.03815 -.0217 (42*2π)/2686 weeks
43.01798 -.03215 (43*2π)/2686 weeks
44-.04205 -.0202 (44*2π)/2686 weeks
45-.01372 -.00832 (45*2π)/2686 weeks
46-.03307 .03431 (46*2π)/2686 weeks
47-.08647 -.06979 (47*2π)/2686 weeks
48.01633 -.03322 (48*2π)/2686 weeks
49.00423 .01983 (49*2π)/2685 weeks
50-.02919 -.01015 (50*2π)/2685 weeks
51.01444 -.04838 (51*2π)/2685 weeks
52.04393 -.02866 (52*2π)/2685 weeks
53-.00104 -.05103 (53*2π)/2685 weeks
54-.06051 -.03419 (54*2π)/2685 weeks
55-.05532 -.00589 (55*2π)/2685 weeks
56-.01755 -.00219 (56*2π)/2685 weeks
57.05462 .06187 (57*2π)/2685 weeks
58.00938 .03636 (58*2π)/2685 weeks
59.03431 -.06143 (59*2π)/2685 weeks
60-.01009 -.02097 (60*2π)/2684 weeks
61-.03244 -.0581 (61*2π)/2684 weeks
62-.02911 -.00269 (62*2π)/2684 weeks
63-.00674 -.01751 (63*2π)/2684 weeks
64.01718 -.0156 (64*2π)/2684 weeks
65-.027 .04047 (65*2π)/2684 weeks
66-.00467 .02441 (66*2π)/2684 weeks
67.01602 .00357 (67*2π)/2684 weeks
68-.00376 -.00288 (68*2π)/2684 weeks
69-.01558 -.01477 (69*2π)/2684 weeks
70-.00398 -.04295 (70*2π)/2684 weeks
71-.00714 -.01385 (71*2π)/2684 weeks
72-.0206 -.02436 (72*2π)/2684 weeks
73-.02198 -.00515 (73*2π)/2684 weeks
74-.0266 -.00438 (74*2π)/2684 weeks
75.00266 -.00064 (75*2π)/2684 weeks
76.00417 .00658 (76*2π)/2684 weeks
77.03108 -.00495 (77*2π)/2683 weeks
78.01603 .00857 (78*2π)/2683 weeks
79.03373 -.04811 (79*2π)/2683 weeks
80.02128 -.04114 (80*2π)/2683 weeks
81-.02451 -.01539 (81*2π)/2683 weeks
82-.08502 -.00793 (82*2π)/2683 weeks
83-.02094 .03499 (83*2π)/2683 weeks
84-.00911 .01048 (84*2π)/2683 weeks
85.00655 .00632 (85*2π)/2683 weeks
86-.00894 -.0079 (86*2π)/2683 weeks
87.0031 -.0299 (87*2π)/2683 weeks
88-.0162 -.00565 (88*2π)/2683 weeks
89-.02522 -.00825 (89*2π)/2683 weeks
90-.0085 -.0277 (90*2π)/2683 weeks
91-.00365 .02449 (91*2π)/2683 weeks
92-.02834 -.0177 (92*2π)/2683 weeks
93.0047 -.00655 (93*2π)/2683 weeks
94-.00298 -.00181 (94*2π)/2683 weeks
95-.00803 -.0186 (95*2π)/2683 weeks
96-.01292 .00755 (96*2π)/2683 weeks
97-.01818 -.03785 (97*2π)/2683 weeks
98.03885 -.00857 (98*2π)/2683 weeks
99-.01889 .03357 (99*2π)/2683 weeks
100-.00128 -.01082 (100*2π)/2683 weeks
101.00276 -.00625 (101*2π)/2683 weeks
102-.01215 -.02822 (102*2π)/2683 weeks
103-.02884 .00329 (103*2π)/2683 weeks
104-.00606 .01558 (104*2π)/2683 weeks
105.00165 .00222 (105*2π)/2683 weeks
106.01497 .00304 (106*2π)/2683 weeks
107.01462 -.00751 (107*2π)/2683 weeks
108.0036 -.02394 (108*2π)/2682 weeks
109-.02962 .00119 (109*2π)/2682 weeks
110-.0237 -.0175 (110*2π)/2682 weeks
111-.00296 .00798 (111*2π)/2682 weeks
112-.01251 .0196 (112*2π)/2682 weeks
113.00135 -.00679 (113*2π)/2682 weeks
114.02856 .01547 (114*2π)/2682 weeks
115.00198 .01281 (115*2π)/2682 weeks
116.02213 .01045 (116*2π)/2682 weeks
117-.02831 .01692 (117*2π)/2682 weeks
118-.05464 -.01641 (118*2π)/2682 weeks
119-.01425 -.03012 (119*2π)/2682 weeks
120.00775 .02622 (120*2π)/2682 weeks
121-.04694 .01668 (121*2π)/2682 weeks
122.01204 -.00628 (122*2π)/2682 weeks
123-.01118 .01458 (123*2π)/2682 weeks
124.00834 -.00325 (124*2π)/2682 weeks
125-.01148 -.00395 (125*2π)/2682 weeks
126-.0434 -.0374 (126*2π)/2682 weeks
127-.00139 -.0352 (127*2π)/2682 weeks
128.01978 -.00365 (128*2π)/2682 weeks
129-.03043 -.00593 (129*2π)/2682 weeks
130-.00643 -.02129 (130*2π)/2682 weeks
131-.01083 -.0031 (131*2π)/2682 weeks
132-.01509 .01605 (132*2π)/2682 weeks
133.01525 -.01459 (133*2π)/2682 weeks
134.04042   (134*2π)/2682 weeks
135.01525 .01459 (135*2π)/2682 weeks
136-.01509 -.01605 (136*2π)/2682 weeks
137-.01083 .0031 (137*2π)/2682 weeks
138-.00643 .02129 (138*2π)/2682 weeks
139-.03043 .00593 (139*2π)/2682 weeks
140.01978 .00365 (140*2π)/2682 weeks
141-.00139 .0352 (141*2π)/2682 weeks
142-.0434 .0374 (142*2π)/2682 weeks
143-.01148 .00395 (143*2π)/2682 weeks
144.00834 .00325 (144*2π)/2682 weeks
145-.01118 -.01458 (145*2π)/2682 weeks
146.01204 .00628 (146*2π)/2682 weeks
147-.04694 -.01668 (147*2π)/2682 weeks
148.00775 -.02622 (148*2π)/2682 weeks
149-.01425 .03012 (149*2π)/2682 weeks
150-.05464 .01641 (150*2π)/2682 weeks
151-.02831 -.01692 (151*2π)/2682 weeks
152.02213 -.01045 (152*2π)/2682 weeks
153.00198 -.01281 (153*2π)/2682 weeks
154.02856 -.01547 (154*2π)/2682 weeks
155.00135 .00679 (155*2π)/2682 weeks
156-.01251 -.0196 (156*2π)/2682 weeks
157-.00296 -.00798 (157*2π)/2682 weeks
158-.0237 .0175 (158*2π)/2682 weeks
159-.02962 -.00119 (159*2π)/2682 weeks
160.0036 .02394 (160*2π)/2682 weeks
161.01462 .00751 (161*2π)/2682 weeks
162.01497 -.00304 (162*2π)/2682 weeks
163.00165 -.00222 (163*2π)/2682 weeks
164-.00606 -.01558 (164*2π)/2682 weeks
165-.02884 -.00329 (165*2π)/2682 weeks
166-.01215 .02822 (166*2π)/2682 weeks
167.00276 .00625 (167*2π)/2682 weeks
168-.00128 .01082 (168*2π)/2682 weeks
169-.01889 -.03357 (169*2π)/2682 weeks
170.03885 .00857 (170*2π)/2682 weeks
171-.01818 .03785 (171*2π)/2682 weeks
172-.01292 -.00755 (172*2π)/2682 weeks
173-.00803 .0186 (173*2π)/2682 weeks
174-.00298 .00181 (174*2π)/2682 weeks
175.0047 .00655 (175*2π)/2682 weeks
176-.02834 .0177 (176*2π)/2682 weeks
177-.00365 -.02449 (177*2π)/2682 weeks
178-.0085 .0277 (178*2π)/2682 weeks
179-.02522 .00825 (179*2π)/2681 weeks
180-.0162 .00565 (180*2π)/2681 weeks
181.0031 .0299 (181*2π)/2681 weeks
182-.00894 .0079 (182*2π)/2681 weeks
183.00655 -.00632 (183*2π)/2681 weeks
184-.00911 -.01048 (184*2π)/2681 weeks
185-.02094 -.03499 (185*2π)/2681 weeks
186-.08502 .00793 (186*2π)/2681 weeks
187-.02451 .01539 (187*2π)/2681 weeks
188.02128 .04114 (188*2π)/2681 weeks
189.03373 .04811 (189*2π)/2681 weeks
190.01603 -.00857 (190*2π)/2681 weeks
191.03108 .00495 (191*2π)/2681 weeks
192.00417 -.00658 (192*2π)/2681 weeks
193.00266 .00064 (193*2π)/2681 weeks
194-.0266 .00438 (194*2π)/2681 weeks
195-.02198 .00515 (195*2π)/2681 weeks
196-.0206 .02436 (196*2π)/2681 weeks
197-.00714 .01385 (197*2π)/2681 weeks
198-.00398 .04295 (198*2π)/2681 weeks
199-.01558 .01477 (199*2π)/2681 weeks
200-.00376 .00288 (200*2π)/2681 weeks
201.01602 -.00357 (201*2π)/2681 weeks
202-.00467 -.02441 (202*2π)/2681 weeks
203-.027 -.04047 (203*2π)/2681 weeks
204.01718 .0156 (204*2π)/2681 weeks
205-.00674 .01751 (205*2π)/2681 weeks
206-.02911 .00269 (206*2π)/2681 weeks
207-.03244 .0581 (207*2π)/2681 weeks
208-.01009 .02097 (208*2π)/2681 weeks
209.03431 .06143 (209*2π)/2681 weeks
210.00938 -.03636 (210*2π)/2681 weeks
211.05462 -.06187 (211*2π)/2681 weeks
212-.01755 .00219 (212*2π)/2681 weeks
213-.05532 .00589 (213*2π)/2681 weeks
214-.06051 .03419 (214*2π)/2681 weeks
215-.00104 .05103 (215*2π)/2681 weeks
216.04393 .02866 (216*2π)/2681 weeks
217.01444 .04838 (217*2π)/2681 weeks
218-.02919 .01015 (218*2π)/2681 weeks
219.00423 -.01983 (219*2π)/2681 weeks
220.01633 .03322 (220*2π)/2681 weeks
221-.08647 .06979 (221*2π)/2681 weeks
222-.03307 -.03431 (222*2π)/2681 weeks
223-.01372 .00832 (223*2π)/2681 weeks
224-.04205 .0202 (224*2π)/2681 weeks
225.01798 .03215 (225*2π)/2681 weeks
226-.03815 .0217 (226*2π)/2681 weeks
227.04092 -.02927 (227*2π)/2681 weeks
228.05789 -.01243 (228*2π)/2681 weeks
229.02238 -.00119 (229*2π)/2681 weeks
230.01979 -.02503 (230*2π)/2681 weeks
231.00851 .01122 (231*2π)/2681 weeks
232.00351 .01928 (232*2π)/2681 weeks
233-.05548 .0101 (233*2π)/2681 weeks
234-.02041 .0372 (234*2π)/2681 weeks
235.01007 .09691 (235*2π)/2681 weeks
236-.03349 .01683 (236*2π)/2681 weeks
237.07766 .04962 (237*2π)/2681 weeks
238.03524 .05648 (238*2π)/2681 weeks
239-.01527 .02623 (239*2π)/2681 weeks
240-.02392 -.00878 (240*2π)/2681 weeks
241-.07907 -.02964 (241*2π)/2681 weeks
242-.06065 .03261 (242*2π)/2681 weeks
243-.00837 .07865 (243*2π)/2681 weeks
244-.10391 .06164 (244*2π)/2681 weeks
245.02833 .07134 (245*2π)/2681 weeks
246.08673 .06118 (246*2π)/2681 weeks
247.07185 -.01096 (247*2π)/2681 weeks
248.07628 .01207 (248*2π)/2681 weeks
249-.14926 .03254 (249*2π)/2681 weeks
250-.0581 -.13279 (250*2π)/2681 weeks
251-.01221 .06926 (251*2π)/2681 weeks
252-.06836 .1725 (252*2π)/2681 weeks
253-.08627 .13984 (253*2π)/2681 weeks
254.13786 .09813 (254*2π)/2681 weeks
255-.01717 .08797 (255*2π)/2681 weeks
256.19505 -.01053 (256*2π)/2681 weeks
257-.04899 -.01735 (257*2π)/2681 weeks
258-.05879 -.24663 (258*2π)/2681 weeks
259.16233 .00052 (259*2π)/2681 weeks
260.00529 .25152 (260*2π)/2681 weeks
261-.11666 .05169 (261*2π)/2681 weeks
262.23384 .39631 (262*2π)/2681 weeks
263-.10936 .76805 (263*2π)/2681 weeks
264.53372 -.05052 (264*2π)/2681 weeks
265.6836 .91792 (265*2π)/2681 weeks
266-1.36649 .25515 (266*2π)/2681 weeks

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