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Fourier Analysis of XAR (SPDR S&P Aerospace & Defense ET)


XAR (SPDR S&P Aerospace & Defense ET) appears to have interesting cyclic behaviour every 28 weeks (1.7596*sine), 25 weeks (1.6701*sine), and 17 weeks (.5799*cosine).

XAR (SPDR S&P Aerospace & Defense ET) has an average price of 43.86 (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 9/29/2011 to 1/17/2017 for XAR (SPDR S&P Aerospace & Defense ET), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
043.85701   0 
1-3.76846 -12.91092 (1*2π)/278278 weeks
22.15133 -4.98317 (2*2π)/278139 weeks
31.67132 -3.11001 (3*2π)/27893 weeks
4-.41413 -4.52784 (4*2π)/27870 weeks
5-.60457 -1.67255 (5*2π)/27856 weeks
6-.09297 -2.1758 (6*2π)/27846 weeks
7-.16036 -1.77425 (7*2π)/27840 weeks
8-.13002 -1.49337 (8*2π)/27835 weeks
9.43125 -1.78439 (9*2π)/27831 weeks
10.04648 -1.75964 (10*2π)/27828 weeks
11-.24246 -1.67006 (11*2π)/27825 weeks
12-.07735 -.99311 (12*2π)/27823 weeks
13-.02591 -.82431 (13*2π)/27821 weeks
14.10299 -1.1767 (14*2π)/27820 weeks
15-.27598 -1.27415 (15*2π)/27819 weeks
16-.57988 -.91943 (16*2π)/27817 weeks
17-.32889 -.66573 (17*2π)/27816 weeks
18-.23697 -.58568 (18*2π)/27815 weeks
19-.45976 -.66901 (19*2π)/27815 weeks
20-.10831 -.60441 (20*2π)/27814 weeks
21-.50378 -.49456 (21*2π)/27813 weeks
22-.13702 -.23615 (22*2π)/27813 weeks
23-.30258 -.49674 (23*2π)/27812 weeks
24-.13917 -.26085 (24*2π)/27812 weeks
25-.09669 -.6417 (25*2π)/27811 weeks
26-.09849 -.41472 (26*2π)/27811 weeks
27-.18858 -.47334 (27*2π)/27810 weeks
28-.31262 -.41197 (28*2π)/27810 weeks
29.04545 -.30479 (29*2π)/27810 weeks
30-.0675 -.33094 (30*2π)/2789 weeks
31-.07859 -.39173 (31*2π)/2789 weeks
32-.2159 -.55226 (32*2π)/2789 weeks
33-.04547 -.25313 (33*2π)/2788 weeks
34-.24072 -.52165 (34*2π)/2788 weeks
35-.03078 -.45608 (35*2π)/2788 weeks
36-.07034 -.40109 (36*2π)/2788 weeks
37-.20811 -.47994 (37*2π)/2788 weeks
38-.15935 -.27025 (38*2π)/2787 weeks
39-.24735 -.51177 (39*2π)/2787 weeks
40-.23673 -.25578 (40*2π)/2787 weeks
41-.11404 -.38843 (41*2π)/2787 weeks
42-.23094 -.41212 (42*2π)/2787 weeks
43-.19635 -.38634 (43*2π)/2786 weeks
44-.13847 -.33287 (44*2π)/2786 weeks
45-.28898 -.29927 (45*2π)/2786 weeks
46-.15689 -.17235 (46*2π)/2786 weeks
47-.12263 -.20181 (47*2π)/2786 weeks
48-.17649 -.22004 (48*2π)/2786 weeks
49-.07037 -.17387 (49*2π)/2786 weeks
50-.07867 -.2198 (50*2π)/2786 weeks
51-.14037 -.35205 (51*2π)/2785 weeks
52-.1832 -.22667 (52*2π)/2785 weeks
53-.2158 -.30161 (53*2π)/2785 weeks
54-.02546 -.16222 (54*2π)/2785 weeks
55-.08681 -.29939 (55*2π)/2785 weeks
56-.21954 -.1804 (56*2π)/2785 weeks
57-.17464 -.21093 (57*2π)/2785 weeks
58-.19316 -.08992 (58*2π)/2785 weeks
59-.02148 -.21708 (59*2π)/2785 weeks
60-.15867 -.22652 (60*2π)/2785 weeks
61-.2393 -.18927 (61*2π)/2785 weeks
62-.14715 -.16695 (62*2π)/2784 weeks
63-.13263 -.06491 (63*2π)/2784 weeks
64-.09989 -.21473 (64*2π)/2784 weeks
65-.13881 -.14224 (65*2π)/2784 weeks
66-.07512 -.20308 (66*2π)/2784 weeks
67-.22678 -.22448 (67*2π)/2784 weeks
68-.23278 .01578 (68*2π)/2784 weeks
69.0272 -.16896 (69*2π)/2784 weeks
70-.16278 -.26344 (70*2π)/2784 weeks
71-.28871 -.173 (71*2π)/2784 weeks
72-.21504 -.08795 (72*2π)/2784 weeks
73-.14603 -.00465 (73*2π)/2784 weeks
74-.0643 -.07203 (74*2π)/2784 weeks
75-.26932 -.10865 (75*2π)/2784 weeks
76-.16464 -.05172 (76*2π)/2784 weeks
77-.08128 -.1279 (77*2π)/2784 weeks
78-.14653 -.10492 (78*2π)/2784 weeks
79-.09106 -.0783 (79*2π)/2784 weeks
80-.19427 -.12509 (80*2π)/2783 weeks
81-.08734 -.14071 (81*2π)/2783 weeks
82-.13084 -.12364 (82*2π)/2783 weeks
83-.12129 -.21977 (83*2π)/2783 weeks
84-.13815 -.08528 (84*2π)/2783 weeks
85-.18497 -.10273 (85*2π)/2783 weeks
86-.10035 -.12254 (86*2π)/2783 weeks
87-.14686 -.19891 (87*2π)/2783 weeks
88-.20214 -.09829 (88*2π)/2783 weeks
89-.18287 -.07709 (89*2π)/2783 weeks
90-.15218 -.09461 (90*2π)/2783 weeks
91-.14388 -.09033 (91*2π)/2783 weeks
92-.1409 -.06834 (92*2π)/2783 weeks
93-.16504 .01208 (93*2π)/2783 weeks
94-.08106 .00713 (94*2π)/2783 weeks
95-.1598 -.14411 (95*2π)/2783 weeks
96-.18761 .0062 (96*2π)/2783 weeks
97-.1586 -.00828 (97*2π)/2783 weeks
98-.10403 -.02887 (98*2π)/2783 weeks
99-.19672 -.01376 (99*2π)/2783 weeks
100-.1496 -.07786 (100*2π)/2783 weeks
101-.13635 -.00008 (101*2π)/2783 weeks
102-.17857 -.02389 (102*2π)/2783 weeks
103-.15339 -.05979 (103*2π)/2783 weeks
104-.12915 -.15019 (104*2π)/2783 weeks
105-.12753 -.03922 (105*2π)/2783 weeks
106-.11409 -.0424 (106*2π)/2783 weeks
107-.13222 -.06725 (107*2π)/2783 weeks
108-.19832 -.03578 (108*2π)/2783 weeks
109-.12207 -.07638 (109*2π)/2783 weeks
110-.16509 -.105 (110*2π)/2783 weeks
111-.18131 -.07623 (111*2π)/2783 weeks
112-.12833 -.13139 (112*2π)/2782 weeks
113-.19166 -.03291 (113*2π)/2782 weeks
114-.1617 -.09572 (114*2π)/2782 weeks
115-.21189 -.08437 (115*2π)/2782 weeks
116-.20458 .00126 (116*2π)/2782 weeks
117-.12726 -.02573 (117*2π)/2782 weeks
118-.14303 -.02016 (118*2π)/2782 weeks
119-.15647 -.00633 (119*2π)/2782 weeks
120-.24452 -.05641 (120*2π)/2782 weeks
121-.01612 -.0187 (121*2π)/2782 weeks
122-.07823 -.03436 (122*2π)/2782 weeks
123-.14693 .00438 (123*2π)/2782 weeks
124-.11714 .01682 (124*2π)/2782 weeks
125-.06376 -.12066 (125*2π)/2782 weeks
126-.16519 .03591 (126*2π)/2782 weeks
127-.09022 -.07484 (127*2π)/2782 weeks
128-.19362 -.01104 (128*2π)/2782 weeks
129-.08024 -.04252 (129*2π)/2782 weeks
130-.12675 -.02041 (130*2π)/2782 weeks
131-.07424 -.1056 (131*2π)/2782 weeks
132-.13479 -.02015 (132*2π)/2782 weeks
133-.25267 -.09642 (133*2π)/2782 weeks
134-.2076 .03177 (134*2π)/2782 weeks
135-.09139 -.04653 (135*2π)/2782 weeks
136-.16134 -.10931 (136*2π)/2782 weeks
137-.28221 -.03586 (137*2π)/2782 weeks
138-.18872 .02157 (138*2π)/2782 weeks
139-.18862   (139*2π)/2782 weeks
140-.18872 -.02157 (140*2π)/2782 weeks
141-.28221 .03586 (141*2π)/2782 weeks
142-.16134 .10931 (142*2π)/2782 weeks
143-.09139 .04653 (143*2π)/2782 weeks
144-.2076 -.03177 (144*2π)/2782 weeks
145-.25267 .09642 (145*2π)/2782 weeks
146-.13479 .02015 (146*2π)/2782 weeks
147-.07424 .1056 (147*2π)/2782 weeks
148-.12675 .02041 (148*2π)/2782 weeks
149-.08024 .04252 (149*2π)/2782 weeks
150-.19362 .01104 (150*2π)/2782 weeks
151-.09022 .07484 (151*2π)/2782 weeks
152-.16519 -.03591 (152*2π)/2782 weeks
153-.06376 .12066 (153*2π)/2782 weeks
154-.11714 -.01682 (154*2π)/2782 weeks
155-.14693 -.00438 (155*2π)/2782 weeks
156-.07823 .03436 (156*2π)/2782 weeks
157-.01612 .0187 (157*2π)/2782 weeks
158-.24452 .05641 (158*2π)/2782 weeks
159-.15647 .00633 (159*2π)/2782 weeks
160-.14303 .02016 (160*2π)/2782 weeks
161-.12726 .02573 (161*2π)/2782 weeks
162-.20458 -.00126 (162*2π)/2782 weeks
163-.21189 .08437 (163*2π)/2782 weeks
164-.1617 .09572 (164*2π)/2782 weeks
165-.19166 .03291 (165*2π)/2782 weeks
166-.12833 .13139 (166*2π)/2782 weeks
167-.18131 .07623 (167*2π)/2782 weeks
168-.16509 .105 (168*2π)/2782 weeks
169-.12207 .07638 (169*2π)/2782 weeks
170-.19832 .03578 (170*2π)/2782 weeks
171-.13222 .06725 (171*2π)/2782 weeks
172-.11409 .0424 (172*2π)/2782 weeks
173-.12753 .03922 (173*2π)/2782 weeks
174-.12915 .15019 (174*2π)/2782 weeks
175-.15339 .05979 (175*2π)/2782 weeks
176-.17857 .02389 (176*2π)/2782 weeks
177-.13635 .00008 (177*2π)/2782 weeks
178-.1496 .07786 (178*2π)/2782 weeks
179-.19672 .01376 (179*2π)/2782 weeks
180-.10403 .02887 (180*2π)/2782 weeks
181-.1586 .00828 (181*2π)/2782 weeks
182-.18761 -.0062 (182*2π)/2782 weeks
183-.1598 .14411 (183*2π)/2782 weeks
184-.08106 -.00713 (184*2π)/2782 weeks
185-.16504 -.01208 (185*2π)/2782 weeks
186-.1409 .06834 (186*2π)/2781 weeks
187-.14388 .09033 (187*2π)/2781 weeks
188-.15218 .09461 (188*2π)/2781 weeks
189-.18287 .07709 (189*2π)/2781 weeks
190-.20214 .09829 (190*2π)/2781 weeks
191-.14686 .19891 (191*2π)/2781 weeks
192-.10035 .12254 (192*2π)/2781 weeks
193-.18497 .10273 (193*2π)/2781 weeks
194-.13815 .08528 (194*2π)/2781 weeks
195-.12129 .21977 (195*2π)/2781 weeks
196-.13084 .12364 (196*2π)/2781 weeks
197-.08734 .14071 (197*2π)/2781 weeks
198-.19427 .12509 (198*2π)/2781 weeks
199-.09106 .0783 (199*2π)/2781 weeks
200-.14653 .10492 (200*2π)/2781 weeks
201-.08128 .1279 (201*2π)/2781 weeks
202-.16464 .05172 (202*2π)/2781 weeks
203-.26932 .10865 (203*2π)/2781 weeks
204-.0643 .07203 (204*2π)/2781 weeks
205-.14603 .00465 (205*2π)/2781 weeks
206-.21504 .08795 (206*2π)/2781 weeks
207-.28871 .173 (207*2π)/2781 weeks
208-.16278 .26344 (208*2π)/2781 weeks
209.0272 .16896 (209*2π)/2781 weeks
210-.23278 -.01578 (210*2π)/2781 weeks
211-.22678 .22448 (211*2π)/2781 weeks
212-.07512 .20308 (212*2π)/2781 weeks
213-.13881 .14224 (213*2π)/2781 weeks
214-.09989 .21473 (214*2π)/2781 weeks
215-.13263 .06491 (215*2π)/2781 weeks
216-.14715 .16695 (216*2π)/2781 weeks
217-.2393 .18927 (217*2π)/2781 weeks
218-.15867 .22652 (218*2π)/2781 weeks
219-.02148 .21708 (219*2π)/2781 weeks
220-.19316 .08992 (220*2π)/2781 weeks
221-.17464 .21093 (221*2π)/2781 weeks
222-.21954 .1804 (222*2π)/2781 weeks
223-.08681 .29939 (223*2π)/2781 weeks
224-.02546 .16222 (224*2π)/2781 weeks
225-.2158 .30161 (225*2π)/2781 weeks
226-.1832 .22667 (226*2π)/2781 weeks
227-.14037 .35205 (227*2π)/2781 weeks
228-.07867 .2198 (228*2π)/2781 weeks
229-.07037 .17387 (229*2π)/2781 weeks
230-.17649 .22004 (230*2π)/2781 weeks
231-.12263 .20181 (231*2π)/2781 weeks
232-.15689 .17235 (232*2π)/2781 weeks
233-.28898 .29927 (233*2π)/2781 weeks
234-.13847 .33287 (234*2π)/2781 weeks
235-.19635 .38634 (235*2π)/2781 weeks
236-.23094 .41212 (236*2π)/2781 weeks
237-.11404 .38843 (237*2π)/2781 weeks
238-.23673 .25578 (238*2π)/2781 weeks
239-.24735 .51177 (239*2π)/2781 weeks
240-.15935 .27025 (240*2π)/2781 weeks
241-.20811 .47994 (241*2π)/2781 weeks
242-.07034 .40109 (242*2π)/2781 weeks
243-.03078 .45608 (243*2π)/2781 weeks
244-.24072 .52165 (244*2π)/2781 weeks
245-.04547 .25313 (245*2π)/2781 weeks
246-.2159 .55226 (246*2π)/2781 weeks
247-.07859 .39173 (247*2π)/2781 weeks
248-.0675 .33094 (248*2π)/2781 weeks
249.04545 .30479 (249*2π)/2781 weeks
250-.31262 .41197 (250*2π)/2781 weeks
251-.18858 .47334 (251*2π)/2781 weeks
252-.09849 .41472 (252*2π)/2781 weeks
253-.09669 .6417 (253*2π)/2781 weeks
254-.13917 .26085 (254*2π)/2781 weeks
255-.30258 .49674 (255*2π)/2781 weeks
256-.13702 .23615 (256*2π)/2781 weeks
257-.50378 .49456 (257*2π)/2781 weeks
258-.10831 .60441 (258*2π)/2781 weeks
259-.45976 .66901 (259*2π)/2781 weeks
260-.23697 .58568 (260*2π)/2781 weeks
261-.32889 .66573 (261*2π)/2781 weeks
262-.57988 .91943 (262*2π)/2781 weeks
263-.27598 1.27415 (263*2π)/2781 weeks
264.10299 1.1767 (264*2π)/2781 weeks
265-.02591 .82431 (265*2π)/2781 weeks
266-.07735 .99311 (266*2π)/2781 weeks
267-.24246 1.67006 (267*2π)/2781 weeks
268.04648 1.75964 (268*2π)/2781 weeks
269.43125 1.78439 (269*2π)/2781 weeks
270-.13002 1.49337 (270*2π)/2781 weeks
271-.16036 1.77425 (271*2π)/2781 weeks
272-.09297 2.1758 (272*2π)/2781 weeks
273-.60457 1.67255 (273*2π)/2781 weeks
274-.41413 4.52784 (274*2π)/2781 weeks
2751.67132 3.11001 (275*2π)/2781 weeks
2762.15133 4.98317 (276*2π)/2781 weeks

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