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Fourier Analysis of XHS (SPDR® S&P Health Care Services ETF)


XHS (SPDR® S&P Health Care Services ETF) appears to have interesting cyclic behaviour every 32 weeks (1.4877*sine), 29 weeks (1.2738*sine), and 26 weeks (.5076*cosine).

XHS (SPDR® S&P Health Care Services ETF) has an average price of 47.12 (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 10/9/2017 for XHS (SPDR® S&P Health Care Services ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
047.11951   0 
1-5.82961 -13.0406 (1*2π)/316316 weeks
21.09342 -3.7749 (2*2π)/316158 weeks
31.26617 -5.44897 (3*2π)/316105 weeks
4-.6267 -2.33241 (4*2π)/31679 weeks
5.69261 -2.42413 (5*2π)/31663 weeks
6-.92356 -3.17222 (6*2π)/31653 weeks
7-1.25497 -1.28711 (7*2π)/31645 weeks
8-.25625 -.94168 (8*2π)/31640 weeks
9-.15874 -1.10134 (9*2π)/31635 weeks
10-.28286 -1.48766 (10*2π)/31632 weeks
11-.24091 -1.27379 (11*2π)/31629 weeks
12-.50759 -1.03908 (12*2π)/31626 weeks
13.14797 -.73844 (13*2π)/31624 weeks
14-.15575 -.61628 (14*2π)/31623 weeks
15-.27313 -.19152 (15*2π)/31621 weeks
16.21613 -.30937 (16*2π)/31620 weeks
17.12715 -.96575 (17*2π)/31619 weeks
18-.29342 -.36651 (18*2π)/31618 weeks
19.19498 -.41849 (19*2π)/31617 weeks
20-.06515 -.78046 (20*2π)/31616 weeks
21-.21215 -.63921 (21*2π)/31615 weeks
22-.19115 -.61689 (22*2π)/31614 weeks
23.13923 -.37355 (23*2π)/31614 weeks
24-.0812 -.78815 (24*2π)/31613 weeks
25-.22572 -.39298 (25*2π)/31613 weeks
26-.262 -.47855 (26*2π)/31612 weeks
27-.24305 -.32283 (27*2π)/31612 weeks
28-.27814 -.34296 (28*2π)/31611 weeks
29-.03653 -.61991 (29*2π)/31611 weeks
30-.1692 -.55658 (30*2π)/31611 weeks
31-.23546 -.58562 (31*2π)/31610 weeks
32-.33123 -.33431 (32*2π)/31610 weeks
33-.15285 -.17703 (33*2π)/31610 weeks
34-.15362 -.19181 (34*2π)/3169 weeks
35-.25414 -.36511 (35*2π)/3169 weeks
36-.2528 -.35717 (36*2π)/3169 weeks
37-.12795 -.22157 (37*2π)/3169 weeks
38-.29922 -.19376 (38*2π)/3168 weeks
39-.14444 -.301 (39*2π)/3168 weeks
40-.01507 -.11642 (40*2π)/3168 weeks
41.02098 -.39443 (41*2π)/3168 weeks
42-.24442 -.35795 (42*2π)/3168 weeks
43-.17357 -.16919 (43*2π)/3167 weeks
44-.14789 -.31621 (44*2π)/3167 weeks
45-.03409 -.31786 (45*2π)/3167 weeks
46-.22597 -.17983 (46*2π)/3167 weeks
47-.06907 -.20149 (47*2π)/3167 weeks
48.0036 -.18388 (48*2π)/3167 weeks
49-.04684 -.35876 (49*2π)/3166 weeks
50-.11801 -.41123 (50*2π)/3166 weeks
51-.29166 -.16813 (51*2π)/3166 weeks
52-.11956 -.106 (52*2π)/3166 weeks
53.04442 -.2941 (53*2π)/3166 weeks
54-.15156 -.20852 (54*2π)/3166 weeks
55-.0747 -.24203 (55*2π)/3166 weeks
56-.08564 -.24733 (56*2π)/3166 weeks
57-.11436 -.1879 (57*2π)/3166 weeks
58-.14774 -.31132 (58*2π)/3165 weeks
59-.16466 -.22997 (59*2π)/3165 weeks
60-.13222 -.18416 (60*2π)/3165 weeks
61-.06494 -.2862 (61*2π)/3165 weeks
62-.30065 -.1632 (62*2π)/3165 weeks
63-.0669 -.07511 (63*2π)/3165 weeks
64-.1677 -.20644 (64*2π)/3165 weeks
65-.11906 -.08168 (65*2π)/3165 weeks
66-.04558 -.11257 (66*2π)/3165 weeks
67-.05539 -.2348 (67*2π)/3165 weeks
68-.14118 -.22998 (68*2π)/3165 weeks
69-.2073 -.02488 (69*2π)/3165 weeks
70-.07835 -.1671 (70*2π)/3165 weeks
71-.06584 -.16914 (71*2π)/3164 weeks
72-.21088 -.06975 (72*2π)/3164 weeks
73-.01825 -.07548 (73*2π)/3164 weeks
74-.16312 -.17953 (74*2π)/3164 weeks
75-.03196 -.1395 (75*2π)/3164 weeks
76-.25998 -.08046 (76*2π)/3164 weeks
77-.04474 .04648 (77*2π)/3164 weeks
78-.03478 -.17873 (78*2π)/3164 weeks
79-.17112 -.05623 (79*2π)/3164 weeks
80-.03325 -.07407 (80*2π)/3164 weeks
81-.11165 -.21093 (81*2π)/3164 weeks
82-.26142 -.17643 (82*2π)/3164 weeks
83-.13153 .01613 (83*2π)/3164 weeks
84-.0568 -.05918 (84*2π)/3164 weeks
85-.17983 -.03796 (85*2π)/3164 weeks
86-.14016 -.07472 (86*2π)/3164 weeks
87-.12169 -.11662 (87*2π)/3164 weeks
88-.16368 -.17513 (88*2π)/3164 weeks
89-.20895 -.02524 (89*2π)/3164 weeks
90-.06637 -.03627 (90*2π)/3164 weeks
91-.17063 -.09391 (91*2π)/3163 weeks
92-.09223 -.03171 (92*2π)/3163 weeks
93-.04628 -.02974 (93*2π)/3163 weeks
94-.06333 -.14834 (94*2π)/3163 weeks
95-.12783 -.02715 (95*2π)/3163 weeks
96-.03083 -.04542 (96*2π)/3163 weeks
97-.09285 -.11541 (97*2π)/3163 weeks
98-.06615 -.06957 (98*2π)/3163 weeks
99-.05649 -.14473 (99*2π)/3163 weeks
100-.19468 -.09016 (100*2π)/3163 weeks
101-.07965 .01345 (101*2π)/3163 weeks
102-.04077 -.07763 (102*2π)/3163 weeks
103-.11805 -.12318 (103*2π)/3163 weeks
104-.10596 -.05332 (104*2π)/3163 weeks
105-.03788 -.07895 (105*2π)/3163 weeks
106-.11706 -.07394 (106*2π)/3163 weeks
107-.17397 .02548 (107*2π)/3163 weeks
108-.06647 -.05268 (108*2π)/3163 weeks
109-.10446 .02183 (109*2π)/3163 weeks
110-.06846 -.03221 (110*2π)/3163 weeks
111-.11875 .0102 (111*2π)/3163 weeks
112-.082 -.01199 (112*2π)/3163 weeks
113-.18557 -.03789 (113*2π)/3163 weeks
114-.09061 -.04795 (114*2π)/3163 weeks
115-.14411 -.04584 (115*2π)/3163 weeks
116-.18372 .00622 (116*2π)/3163 weeks
117-.09288 -.03976 (117*2π)/3163 weeks
118-.1169 -.08552 (118*2π)/3163 weeks
119-.14922 -.01307 (119*2π)/3163 weeks
120-.08662 -.04134 (120*2π)/3163 weeks
121-.09705 .00352 (121*2π)/3163 weeks
122-.0893 -.08152 (122*2π)/3163 weeks
123-.18021 .00619 (123*2π)/3163 weeks
124-.07358 -.05156 (124*2π)/3163 weeks
125-.16837 -.05025 (125*2π)/3163 weeks
126-.13072 -.01818 (126*2π)/3163 weeks
127-.10426 -.12061 (127*2π)/3162 weeks
128-.10716 .00306 (128*2π)/3162 weeks
129-.06794 -.10659 (129*2π)/3162 weeks
130-.08369 -.03586 (130*2π)/3162 weeks
131-.11507 -.05285 (131*2π)/3162 weeks
132-.1249 .03613 (132*2π)/3162 weeks
133-.02424 -.03754 (133*2π)/3162 weeks
134-.11921 -.11028 (134*2π)/3162 weeks
135-.11623 -.05488 (135*2π)/3162 weeks
136-.11742 -.05642 (136*2π)/3162 weeks
137-.1156 -.12334 (137*2π)/3162 weeks
138-.08986 .01118 (138*2π)/3162 weeks
139-.04745 -.01966 (139*2π)/3162 weeks
140-.10513 .00242 (140*2π)/3162 weeks
141-.07876 -.03878 (141*2π)/3162 weeks
142-.08056 -.1158 (142*2π)/3162 weeks
143-.11658 .04142 (143*2π)/3162 weeks
144-.12954 -.04815 (144*2π)/3162 weeks
145-.08341 -.01056 (145*2π)/3162 weeks
146-.11289 -.06935 (146*2π)/3162 weeks
147-.0774 -.03213 (147*2π)/3162 weeks
148-.13761 -.01542 (148*2π)/3162 weeks
149-.10001 -.02732 (149*2π)/3162 weeks
150-.08897 .05281 (150*2π)/3162 weeks
151-.09946 -.01731 (151*2π)/3162 weeks
152-.13382 -.0165 (152*2π)/3162 weeks
153-.0489 -.06956 (153*2π)/3162 weeks
154-.12658 .03087 (154*2π)/3162 weeks
155-.08603 -.01804 (155*2π)/3162 weeks
156-.10138 -.07889 (156*2π)/3162 weeks
157-.13421 -.00354 (157*2π)/3162 weeks
158-.11877   (158*2π)/3162 weeks
159-.13421 .00354 (159*2π)/3162 weeks
160-.10138 .07889 (160*2π)/3162 weeks
161-.08603 .01804 (161*2π)/3162 weeks
162-.12658 -.03087 (162*2π)/3162 weeks
163-.0489 .06956 (163*2π)/3162 weeks
164-.13382 .0165 (164*2π)/3162 weeks
165-.09946 .01731 (165*2π)/3162 weeks
166-.08897 -.05281 (166*2π)/3162 weeks
167-.10001 .02732 (167*2π)/3162 weeks
168-.13761 .01542 (168*2π)/3162 weeks
169-.0774 .03213 (169*2π)/3162 weeks
170-.11289 .06935 (170*2π)/3162 weeks
171-.08341 .01056 (171*2π)/3162 weeks
172-.12954 .04815 (172*2π)/3162 weeks
173-.11658 -.04142 (173*2π)/3162 weeks
174-.08056 .1158 (174*2π)/3162 weeks
175-.07876 .03878 (175*2π)/3162 weeks
176-.10513 -.00242 (176*2π)/3162 weeks
177-.04745 .01966 (177*2π)/3162 weeks
178-.08986 -.01118 (178*2π)/3162 weeks
179-.1156 .12334 (179*2π)/3162 weeks
180-.11742 .05642 (180*2π)/3162 weeks
181-.11623 .05488 (181*2π)/3162 weeks
182-.11921 .11028 (182*2π)/3162 weeks
183-.02424 .03754 (183*2π)/3162 weeks
184-.1249 -.03613 (184*2π)/3162 weeks
185-.11507 .05285 (185*2π)/3162 weeks
186-.08369 .03586 (186*2π)/3162 weeks
187-.06794 .10659 (187*2π)/3162 weeks
188-.10716 -.00306 (188*2π)/3162 weeks
189-.10426 .12061 (189*2π)/3162 weeks
190-.13072 .01818 (190*2π)/3162 weeks
191-.16837 .05025 (191*2π)/3162 weeks
192-.07358 .05156 (192*2π)/3162 weeks
193-.18021 -.00619 (193*2π)/3162 weeks
194-.0893 .08152 (194*2π)/3162 weeks
195-.09705 -.00352 (195*2π)/3162 weeks
196-.08662 .04134 (196*2π)/3162 weeks
197-.14922 .01307 (197*2π)/3162 weeks
198-.1169 .08552 (198*2π)/3162 weeks
199-.09288 .03976 (199*2π)/3162 weeks
200-.18372 -.00622 (200*2π)/3162 weeks
201-.14411 .04584 (201*2π)/3162 weeks
202-.09061 .04795 (202*2π)/3162 weeks
203-.18557 .03789 (203*2π)/3162 weeks
204-.082 .01199 (204*2π)/3162 weeks
205-.11875 -.0102 (205*2π)/3162 weeks
206-.06846 .03221 (206*2π)/3162 weeks
207-.10446 -.02183 (207*2π)/3162 weeks
208-.06647 .05268 (208*2π)/3162 weeks
209-.17397 -.02548 (209*2π)/3162 weeks
210-.11706 .07394 (210*2π)/3162 weeks
211-.03788 .07895 (211*2π)/3161 weeks
212-.10596 .05332 (212*2π)/3161 weeks
213-.11805 .12318 (213*2π)/3161 weeks
214-.04077 .07763 (214*2π)/3161 weeks
215-.07965 -.01345 (215*2π)/3161 weeks
216-.19468 .09016 (216*2π)/3161 weeks
217-.05649 .14473 (217*2π)/3161 weeks
218-.06615 .06957 (218*2π)/3161 weeks
219-.09285 .11541 (219*2π)/3161 weeks
220-.03083 .04542 (220*2π)/3161 weeks
221-.12783 .02715 (221*2π)/3161 weeks
222-.06333 .14834 (222*2π)/3161 weeks
223-.04628 .02974 (223*2π)/3161 weeks
224-.09223 .03171 (224*2π)/3161 weeks
225-.17063 .09391 (225*2π)/3161 weeks
226-.06637 .03627 (226*2π)/3161 weeks
227-.20895 .02524 (227*2π)/3161 weeks
228-.16368 .17513 (228*2π)/3161 weeks
229-.12169 .11662 (229*2π)/3161 weeks
230-.14016 .07472 (230*2π)/3161 weeks
231-.17983 .03796 (231*2π)/3161 weeks
232-.0568 .05918 (232*2π)/3161 weeks
233-.13153 -.01613 (233*2π)/3161 weeks
234-.26142 .17643 (234*2π)/3161 weeks
235-.11165 .21093 (235*2π)/3161 weeks
236-.03325 .07407 (236*2π)/3161 weeks
237-.17112 .05623 (237*2π)/3161 weeks
238-.03478 .17873 (238*2π)/3161 weeks
239-.04474 -.04648 (239*2π)/3161 weeks
240-.25998 .08046 (240*2π)/3161 weeks
241-.03196 .1395 (241*2π)/3161 weeks
242-.16312 .17953 (242*2π)/3161 weeks
243-.01825 .07548 (243*2π)/3161 weeks
244-.21088 .06975 (244*2π)/3161 weeks
245-.06584 .16914 (245*2π)/3161 weeks
246-.07835 .1671 (246*2π)/3161 weeks
247-.2073 .02488 (247*2π)/3161 weeks
248-.14118 .22998 (248*2π)/3161 weeks
249-.05539 .2348 (249*2π)/3161 weeks
250-.04558 .11257 (250*2π)/3161 weeks
251-.11906 .08168 (251*2π)/3161 weeks
252-.1677 .20644 (252*2π)/3161 weeks
253-.0669 .07511 (253*2π)/3161 weeks
254-.30065 .1632 (254*2π)/3161 weeks
255-.06494 .2862 (255*2π)/3161 weeks
256-.13222 .18416 (256*2π)/3161 weeks
257-.16466 .22997 (257*2π)/3161 weeks
258-.14774 .31132 (258*2π)/3161 weeks
259-.11436 .1879 (259*2π)/3161 weeks
260-.08564 .24733 (260*2π)/3161 weeks
261-.0747 .24203 (261*2π)/3161 weeks
262-.15156 .20852 (262*2π)/3161 weeks
263.04442 .2941 (263*2π)/3161 weeks
264-.11956 .106 (264*2π)/3161 weeks
265-.29166 .16813 (265*2π)/3161 weeks
266-.11801 .41123 (266*2π)/3161 weeks
267-.04684 .35876 (267*2π)/3161 weeks
268.0036 .18388 (268*2π)/3161 weeks
269-.06907 .20149 (269*2π)/3161 weeks
270-.22597 .17983 (270*2π)/3161 weeks
271-.03409 .31786 (271*2π)/3161 weeks
272-.14789 .31621 (272*2π)/3161 weeks
273-.17357 .16919 (273*2π)/3161 weeks
274-.24442 .35795 (274*2π)/3161 weeks
275.02098 .39443 (275*2π)/3161 weeks
276-.01507 .11642 (276*2π)/3161 weeks
277-.14444 .301 (277*2π)/3161 weeks
278-.29922 .19376 (278*2π)/3161 weeks
279-.12795 .22157 (279*2π)/3161 weeks
280-.2528 .35717 (280*2π)/3161 weeks
281-.25414 .36511 (281*2π)/3161 weeks
282-.15362 .19181 (282*2π)/3161 weeks
283-.15285 .17703 (283*2π)/3161 weeks
284-.33123 .33431 (284*2π)/3161 weeks
285-.23546 .58562 (285*2π)/3161 weeks
286-.1692 .55658 (286*2π)/3161 weeks
287-.03653 .61991 (287*2π)/3161 weeks
288-.27814 .34296 (288*2π)/3161 weeks
289-.24305 .32283 (289*2π)/3161 weeks
290-.262 .47855 (290*2π)/3161 weeks
291-.22572 .39298 (291*2π)/3161 weeks
292-.0812 .78815 (292*2π)/3161 weeks
293.13923 .37355 (293*2π)/3161 weeks
294-.19115 .61689 (294*2π)/3161 weeks
295-.21215 .63921 (295*2π)/3161 weeks
296-.06515 .78046 (296*2π)/3161 weeks
297.19498 .41849 (297*2π)/3161 weeks
298-.29342 .36651 (298*2π)/3161 weeks
299.12715 .96575 (299*2π)/3161 weeks
300.21613 .30937 (300*2π)/3161 weeks
301-.27313 .19152 (301*2π)/3161 weeks
302-.15575 .61628 (302*2π)/3161 weeks
303.14797 .73844 (303*2π)/3161 weeks
304-.50759 1.03908 (304*2π)/3161 weeks
305-.24091 1.27379 (305*2π)/3161 weeks
306-.28286 1.48766 (306*2π)/3161 weeks
307-.15874 1.10134 (307*2π)/3161 weeks
308-.25625 .94168 (308*2π)/3161 weeks
309-1.25497 1.28711 (309*2π)/3161 weeks
310-.92356 3.17222 (310*2π)/3161 weeks
311.69261 2.42413 (311*2π)/3161 weeks
312-.6267 2.33241 (312*2π)/3161 weeks
3131.26617 5.44897 (313*2π)/3161 weeks
3141.09342 3.7749 (314*2π)/3161 weeks



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