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Fourier Analysis of KAR (KAR Auction Services, Inc Commo)


KAR (KAR Auction Services, Inc Commo) appears to have interesting cyclic behaviour every 29 weeks (1.1699*sine), 35 weeks (1.0994*sine), and 32 weeks (.9709*sine).

KAR (KAR Auction Services, Inc Commo) has an average price of 24.01 (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 12/11/2009 to 3/20/2017 for KAR (KAR Auction Services, Inc Commo), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
024.00992   0 
12.33883 -12.68985 (1*2π)/381381 weeks
2.68314 -4.11222 (2*2π)/381191 weeks
3-.01784 -3.51692 (3*2π)/381127 weeks
4.96188 -3.00846 (4*2π)/38195 weeks
5.29755 -3.01082 (5*2π)/38176 weeks
6-.23077 -.99701 (6*2π)/38164 weeks
7-.31412 -.76731 (7*2π)/38154 weeks
8-.28703 -1.22457 (8*2π)/38148 weeks
9-.004 -1.40568 (9*2π)/38142 weeks
10.61198 -.8582 (10*2π)/38138 weeks
11-.15024 -1.09943 (11*2π)/38135 weeks
12-.41456 -.97089 (12*2π)/38132 weeks
13-.11098 -1.16993 (13*2π)/38129 weeks
14-.19088 -.84042 (14*2π)/38127 weeks
15-.04377 -.71165 (15*2π)/38125 weeks
16.15333 -.64701 (16*2π)/38124 weeks
17-.2438 -.91273 (17*2π)/38122 weeks
18-.26209 -.80876 (18*2π)/38121 weeks
19.0141 -.6435 (19*2π)/38120 weeks
20-.39128 -.4897 (20*2π)/38119 weeks
21.00915 -.18899 (21*2π)/38118 weeks
22-.09746 -.41992 (22*2π)/38117 weeks
23-.18351 -.67919 (23*2π)/38117 weeks
24-.3114 -.26605 (24*2π)/38116 weeks
25-.25453 -.44685 (25*2π)/38115 weeks
26-.0481 -.21636 (26*2π)/38115 weeks
27-.1597 -.24466 (27*2π)/38114 weeks
28.10038 -.10982 (28*2π)/38114 weeks
29-.08791 -.31062 (29*2π)/38113 weeks
30-.18667 -.46082 (30*2π)/38113 weeks
31-.01155 -.28978 (31*2π)/38112 weeks
32-.04455 -.45577 (32*2π)/38112 weeks
33-.30624 -.21378 (33*2π)/38112 weeks
34.10943 -.33007 (34*2π)/38111 weeks
35-.20569 -.41818 (35*2π)/38111 weeks
36-.06443 -.4667 (36*2π)/38111 weeks
37-.09447 -.2792 (37*2π)/38110 weeks
38-.24016 -.21088 (38*2π)/38110 weeks
39-.30598 -.15119 (39*2π)/38110 weeks
40.04824 -.15834 (40*2π)/38110 weeks
41-.11485 -.26062 (41*2π)/3819 weeks
42-.15195 -.19464 (42*2π)/3819 weeks
43.05467 -.19888 (43*2π)/3819 weeks
44-.24404 -.18172 (44*2π)/3819 weeks
45.03918 -.23937 (45*2π)/3818 weeks
46-.05155 -.33695 (46*2π)/3818 weeks
47-.13381 -.19325 (47*2π)/3818 weeks
48-.14458 -.17571 (48*2π)/3818 weeks
49-.00105 -.22456 (49*2π)/3818 weeks
50-.00624 -.27213 (50*2π)/3818 weeks
51-.04371 -.13118 (51*2π)/3817 weeks
52-.06493 -.19328 (52*2π)/3817 weeks
53-.16623 -.29595 (53*2π)/3817 weeks
54-.16106 -.24978 (54*2π)/3817 weeks
55-.07207 -.22817 (55*2π)/3817 weeks
56-.2322 -.14125 (56*2π)/3817 weeks
57-.189 -.22456 (57*2π)/3817 weeks
58-.12817 -.1195 (58*2π)/3817 weeks
59-.1214 -.07688 (59*2π)/3816 weeks
60-.08289 -.06019 (60*2π)/3816 weeks
61-.05204 -.05549 (61*2π)/3816 weeks
62-.02158 -.16343 (62*2π)/3816 weeks
63-.1112 -.18289 (63*2π)/3816 weeks
64-.13713 -.13405 (64*2π)/3816 weeks
65-.1112 -.14723 (65*2π)/3816 weeks
66-.09596 -.14181 (66*2π)/3816 weeks
67-.04598 -.16796 (67*2π)/3816 weeks
68-.08292 -.15151 (68*2π)/3816 weeks
69-.10213 -.14155 (69*2π)/3816 weeks
70-.01552 -.21082 (70*2π)/3815 weeks
71-.04208 -.12561 (71*2π)/3815 weeks
72-.12277 -.12306 (72*2π)/3815 weeks
73-.13709 -.18078 (73*2π)/3815 weeks
74-.06555 -.11999 (74*2π)/3815 weeks
75-.09613 -.14555 (75*2π)/3815 weeks
76-.05799 -.14636 (76*2π)/3815 weeks
77-.11228 -.17424 (77*2π)/3815 weeks
78-.13823 -.15274 (78*2π)/3815 weeks
79-.14198 -.14899 (79*2π)/3815 weeks
80-.07477 -.08607 (80*2π)/3815 weeks
81-.06781 -.10658 (81*2π)/3815 weeks
82-.10492 -.04219 (82*2π)/3815 weeks
83-.10153 -.1527 (83*2π)/3815 weeks
84-.08191 -.11293 (84*2π)/3815 weeks
85-.10674 -.08369 (85*2π)/3814 weeks
86-.09444 -.03369 (86*2π)/3814 weeks
87-.08045 -.08177 (87*2π)/3814 weeks
88-.05309 -.13433 (88*2π)/3814 weeks
89-.07667 -.15064 (89*2π)/3814 weeks
90-.13488 -.11779 (90*2π)/3814 weeks
91-.15968 -.11889 (91*2π)/3814 weeks
92-.16984 -.00653 (92*2π)/3814 weeks
93-.10226 -.06375 (93*2π)/3814 weeks
94-.10898 -.0807 (94*2π)/3814 weeks
95-.08654 -.02383 (95*2π)/3814 weeks
96-.14825 -.01039 (96*2π)/3814 weeks
97-.11507 .01294 (97*2π)/3814 weeks
98.00044 -.07252 (98*2π)/3814 weeks
99-.0298 -.0537 (99*2π)/3814 weeks
100-.04771 -.09707 (100*2π)/3814 weeks
101-.08732 -.07976 (101*2π)/3814 weeks
102-.11091 -.05333 (102*2π)/3814 weeks
103-.10723 -.04602 (103*2π)/3814 weeks
104-.06113 -.05663 (104*2π)/3814 weeks
105-.1046 -.07445 (105*2π)/3814 weeks
106-.10412 -.05946 (106*2π)/3814 weeks
107-.0948 -.10439 (107*2π)/3814 weeks
108-.12107 -.05686 (108*2π)/3814 weeks
109-.11522 -.03815 (109*2π)/3813 weeks
110-.14002 -.09832 (110*2π)/3813 weeks
111-.05079 -.11515 (111*2π)/3813 weeks
112-.11374 -.0327 (112*2π)/3813 weeks
113-.11814 -.02736 (113*2π)/3813 weeks
114-.08021 -.05107 (114*2π)/3813 weeks
115-.11809 -.05484 (115*2π)/3813 weeks
116-.04113 -.03607 (116*2π)/3813 weeks
117-.05109 -.0145 (117*2π)/3813 weeks
118-.09872 -.07977 (118*2π)/3813 weeks
119-.08975 -.02776 (119*2π)/3813 weeks
120-.06576 -.10472 (120*2π)/3813 weeks
121-.09329 -.04088 (121*2π)/3813 weeks
122-.09425 -.07029 (122*2π)/3813 weeks
123-.07632 -.01546 (123*2π)/3813 weeks
124-.10332 -.0509 (124*2π)/3813 weeks
125-.02868 -.0717 (125*2π)/3813 weeks
126-.07885 -.05099 (126*2π)/3813 weeks
127-.14084 .00335 (127*2π)/3813 weeks
128-.03111 -.05611 (128*2π)/3813 weeks
129-.01795 -.05934 (129*2π)/3813 weeks
130-.14534 -.07837 (130*2π)/3813 weeks
131-.10604 -.075 (131*2π)/3813 weeks
132-.081 -.0183 (132*2π)/3813 weeks
133-.0846 -.04399 (133*2π)/3813 weeks
134-.09464 -.01984 (134*2π)/3813 weeks
135-.12145 -.04896 (135*2π)/3813 weeks
136-.07266 -.05487 (136*2π)/3813 weeks
137-.0982 .03034 (137*2π)/3813 weeks
138-.09313 -.03167 (138*2π)/3813 weeks
139-.07617 -.03013 (139*2π)/3813 weeks
140-.03841 -.06927 (140*2π)/3813 weeks
141-.06706 -.08663 (141*2π)/3813 weeks
142-.11774 -.04481 (142*2π)/3813 weeks
143-.14605 .01215 (143*2π)/3813 weeks
144-.08331 -.01768 (144*2π)/3813 weeks
145-.12902 -.05887 (145*2π)/3813 weeks
146-.11273 -.02457 (146*2π)/3813 weeks
147-.10785 -.05335 (147*2π)/3813 weeks
148-.12974 -.05809 (148*2π)/3813 weeks
149-.11042 -.03059 (149*2π)/3813 weeks
150-.13415 -.01321 (150*2π)/3813 weeks
151-.09925 .00773 (151*2π)/3813 weeks
152-.07869 -.01839 (152*2π)/3813 weeks
153-.06481 -.00196 (153*2π)/3812 weeks
154-.06866 -.03954 (154*2π)/3812 weeks
155-.06313 -.01982 (155*2π)/3812 weeks
156-.09948 -.04504 (156*2π)/3812 weeks
157-.11848 -.00389 (157*2π)/3812 weeks
158-.07641 -.0351 (158*2π)/3812 weeks
159-.11391 -.02577 (159*2π)/3812 weeks
160-.09181 .01253 (160*2π)/3812 weeks
161-.11108 .01597 (161*2π)/3812 weeks
162-.09919 .02332 (162*2π)/3812 weeks
163-.07797 -.00117 (163*2π)/3812 weeks
164-.07025 .01021 (164*2π)/3812 weeks
165-.11153 .00463 (165*2π)/3812 weeks
166-.06078 -.02486 (166*2π)/3812 weeks
167-.113 .01248 (167*2π)/3812 weeks
168-.09652 .00837 (168*2π)/3812 weeks
169-.06567 .01212 (169*2π)/3812 weeks
170-.03128 -.00672 (170*2π)/3812 weeks
171-.04328 -.00786 (171*2π)/3812 weeks
172-.13419 -.03636 (172*2π)/3812 weeks
173-.0595 .01973 (173*2π)/3812 weeks
174-.07031 -.05195 (174*2π)/3812 weeks
175-.10803 .00612 (175*2π)/3812 weeks
176-.06601 -.02524 (176*2π)/3812 weeks
177-.09926 -.02782 (177*2π)/3812 weeks
178-.09219 -.01084 (178*2π)/3812 weeks
179-.08334 .01371 (179*2π)/3812 weeks
180-.08133 -.00113 (180*2π)/3812 weeks
181-.06311 -.02112 (181*2π)/3812 weeks
182-.1086 .04764 (182*2π)/3812 weeks
183-.11262 .00408 (183*2π)/3812 weeks
184-.03148 .02624 (184*2π)/3812 weeks
185-.12826 -.03703 (185*2π)/3812 weeks
186-.0592 .02831 (186*2π)/3812 weeks
187-.04728 .0495 (187*2π)/3812 weeks
188-.05616 .01164 (188*2π)/3812 weeks
189-.08577 -.05042 (189*2π)/3812 weeks
190-.04695 -.01141 (190*2π)/3812 weeks
191-.04695 .01141 (191*2π)/3812 weeks
192-.08577 .05042 (192*2π)/3812 weeks
193-.05616 -.01164 (193*2π)/3812 weeks
194-.04728 -.0495 (194*2π)/3812 weeks
195-.0592 -.02831 (195*2π)/3812 weeks
196-.12826 .03703 (196*2π)/3812 weeks
197-.03148 -.02624 (197*2π)/3812 weeks
198-.11262 -.00408 (198*2π)/3812 weeks
199-.1086 -.04764 (199*2π)/3812 weeks
200-.06311 .02112 (200*2π)/3812 weeks
201-.08133 .00113 (201*2π)/3812 weeks
202-.08334 -.01371 (202*2π)/3812 weeks
203-.09219 .01084 (203*2π)/3812 weeks
204-.09926 .02782 (204*2π)/3812 weeks
205-.06601 .02524 (205*2π)/3812 weeks
206-.10803 -.00612 (206*2π)/3812 weeks
207-.07031 .05195 (207*2π)/3812 weeks
208-.0595 -.01973 (208*2π)/3812 weeks
209-.13419 .03636 (209*2π)/3812 weeks
210-.04328 .00786 (210*2π)/3812 weeks
211-.03128 .00672 (211*2π)/3812 weeks
212-.06567 -.01212 (212*2π)/3812 weeks
213-.09652 -.00837 (213*2π)/3812 weeks
214-.113 -.01248 (214*2π)/3812 weeks
215-.06078 .02486 (215*2π)/3812 weeks
216-.11153 -.00463 (216*2π)/3812 weeks
217-.07025 -.01021 (217*2π)/3812 weeks
218-.07797 .00117 (218*2π)/3812 weeks
219-.09919 -.02332 (219*2π)/3812 weeks
220-.11108 -.01597 (220*2π)/3812 weeks
221-.09181 -.01253 (221*2π)/3812 weeks
222-.11391 .02577 (222*2π)/3812 weeks
223-.07641 .0351 (223*2π)/3812 weeks
224-.11848 .00389 (224*2π)/3812 weeks
225-.09948 .04504 (225*2π)/3812 weeks
226-.06313 .01982 (226*2π)/3812 weeks
227-.06866 .03954 (227*2π)/3812 weeks
228-.06481 .00196 (228*2π)/3812 weeks
229-.07869 .01839 (229*2π)/3812 weeks
230-.09925 -.00773 (230*2π)/3812 weeks
231-.13415 .01321 (231*2π)/3812 weeks
232-.11042 .03059 (232*2π)/3812 weeks
233-.12974 .05809 (233*2π)/3812 weeks
234-.10785 .05335 (234*2π)/3812 weeks
235-.11273 .02457 (235*2π)/3812 weeks
236-.12902 .05887 (236*2π)/3812 weeks
237-.08331 .01768 (237*2π)/3812 weeks
238-.14605 -.01215 (238*2π)/3812 weeks
239-.11774 .04481 (239*2π)/3812 weeks
240-.06706 .08663 (240*2π)/3812 weeks
241-.03841 .06927 (241*2π)/3812 weeks
242-.07617 .03013 (242*2π)/3812 weeks
243-.09313 .03167 (243*2π)/3812 weeks
244-.0982 -.03034 (244*2π)/3812 weeks
245-.07266 .05487 (245*2π)/3812 weeks
246-.12145 .04896 (246*2π)/3812 weeks
247-.09464 .01984 (247*2π)/3812 weeks
248-.0846 .04399 (248*2π)/3812 weeks
249-.081 .0183 (249*2π)/3812 weeks
250-.10604 .075 (250*2π)/3812 weeks
251-.14534 .07837 (251*2π)/3812 weeks
252-.01795 .05934 (252*2π)/3812 weeks
253-.03111 .05611 (253*2π)/3812 weeks
254-.14084 -.00335 (254*2π)/3812 weeks
255-.07885 .05099 (255*2π)/3811 weeks
256-.02868 .0717 (256*2π)/3811 weeks
257-.10332 .0509 (257*2π)/3811 weeks
258-.07632 .01546 (258*2π)/3811 weeks
259-.09425 .07029 (259*2π)/3811 weeks
260-.09329 .04088 (260*2π)/3811 weeks
261-.06576 .10472 (261*2π)/3811 weeks
262-.08975 .02776 (262*2π)/3811 weeks
263-.09872 .07977 (263*2π)/3811 weeks
264-.05109 .0145 (264*2π)/3811 weeks
265-.04113 .03607 (265*2π)/3811 weeks
266-.11809 .05484 (266*2π)/3811 weeks
267-.08021 .05107 (267*2π)/3811 weeks
268-.11814 .02736 (268*2π)/3811 weeks
269-.11374 .0327 (269*2π)/3811 weeks
270-.05079 .11515 (270*2π)/3811 weeks
271-.14002 .09832 (271*2π)/3811 weeks
272-.11522 .03815 (272*2π)/3811 weeks
273-.12107 .05686 (273*2π)/3811 weeks
274-.0948 .10439 (274*2π)/3811 weeks
275-.10412 .05946 (275*2π)/3811 weeks
276-.1046 .07445 (276*2π)/3811 weeks
277-.06113 .05663 (277*2π)/3811 weeks
278-.10723 .04602 (278*2π)/3811 weeks
279-.11091 .05333 (279*2π)/3811 weeks
280-.08732 .07976 (280*2π)/3811 weeks
281-.04771 .09707 (281*2π)/3811 weeks
282-.0298 .0537 (282*2π)/3811 weeks
283.00044 .07252 (283*2π)/3811 weeks
284-.11507 -.01294 (284*2π)/3811 weeks
285-.14825 .01039 (285*2π)/3811 weeks
286-.08654 .02383 (286*2π)/3811 weeks
287-.10898 .0807 (287*2π)/3811 weeks
288-.10226 .06375 (288*2π)/3811 weeks
289-.16984 .00653 (289*2π)/3811 weeks
290-.15968 .11889 (290*2π)/3811 weeks
291-.13488 .11779 (291*2π)/3811 weeks
292-.07667 .15064 (292*2π)/3811 weeks
293-.05309 .13433 (293*2π)/3811 weeks
294-.08045 .08177 (294*2π)/3811 weeks
295-.09444 .03369 (295*2π)/3811 weeks
296-.10674 .08369 (296*2π)/3811 weeks
297-.08191 .11293 (297*2π)/3811 weeks
298-.10153 .1527 (298*2π)/3811 weeks
299-.10492 .04219 (299*2π)/3811 weeks
300-.06781 .10658 (300*2π)/3811 weeks
301-.07477 .08607 (301*2π)/3811 weeks
302-.14198 .14899 (302*2π)/3811 weeks
303-.13823 .15274 (303*2π)/3811 weeks
304-.11228 .17424 (304*2π)/3811 weeks
305-.05799 .14636 (305*2π)/3811 weeks
306-.09613 .14555 (306*2π)/3811 weeks
307-.06555 .11999 (307*2π)/3811 weeks
308-.13709 .18078 (308*2π)/3811 weeks
309-.12277 .12306 (309*2π)/3811 weeks
310-.04208 .12561 (310*2π)/3811 weeks
311-.01552 .21082 (311*2π)/3811 weeks
312-.10213 .14155 (312*2π)/3811 weeks
313-.08292 .15151 (313*2π)/3811 weeks
314-.04598 .16796 (314*2π)/3811 weeks
315-.09596 .14181 (315*2π)/3811 weeks
316-.1112 .14723 (316*2π)/3811 weeks
317-.13713 .13405 (317*2π)/3811 weeks
318-.1112 .18289 (318*2π)/3811 weeks
319-.02158 .16343 (319*2π)/3811 weeks
320-.05204 .05549 (320*2π)/3811 weeks
321-.08289 .06019 (321*2π)/3811 weeks
322-.1214 .07688 (322*2π)/3811 weeks
323-.12817 .1195 (323*2π)/3811 weeks
324-.189 .22456 (324*2π)/3811 weeks
325-.2322 .14125 (325*2π)/3811 weeks
326-.07207 .22817 (326*2π)/3811 weeks
327-.16106 .24978 (327*2π)/3811 weeks
328-.16623 .29595 (328*2π)/3811 weeks
329-.06493 .19328 (329*2π)/3811 weeks
330-.04371 .13118 (330*2π)/3811 weeks
331-.00624 .27213 (331*2π)/3811 weeks
332-.00105 .22456 (332*2π)/3811 weeks
333-.14458 .17571 (333*2π)/3811 weeks
334-.13381 .19325 (334*2π)/3811 weeks
335-.05155 .33695 (335*2π)/3811 weeks
336.03918 .23937 (336*2π)/3811 weeks
337-.24404 .18172 (337*2π)/3811 weeks
338.05467 .19888 (338*2π)/3811 weeks
339-.15195 .19464 (339*2π)/3811 weeks
340-.11485 .26062 (340*2π)/3811 weeks
341.04824 .15834 (341*2π)/3811 weeks
342-.30598 .15119 (342*2π)/3811 weeks
343-.24016 .21088 (343*2π)/3811 weeks
344-.09447 .2792 (344*2π)/3811 weeks
345-.06443 .4667 (345*2π)/3811 weeks
346-.20569 .41818 (346*2π)/3811 weeks
347.10943 .33007 (347*2π)/3811 weeks
348-.30624 .21378 (348*2π)/3811 weeks
349-.04455 .45577 (349*2π)/3811 weeks
350-.01155 .28978 (350*2π)/3811 weeks
351-.18667 .46082 (351*2π)/3811 weeks
352-.08791 .31062 (352*2π)/3811 weeks
353.10038 .10982 (353*2π)/3811 weeks
354-.1597 .24466 (354*2π)/3811 weeks
355-.0481 .21636 (355*2π)/3811 weeks
356-.25453 .44685 (356*2π)/3811 weeks
357-.3114 .26605 (357*2π)/3811 weeks
358-.18351 .67919 (358*2π)/3811 weeks
359-.09746 .41992 (359*2π)/3811 weeks
360.00915 .18899 (360*2π)/3811 weeks
361-.39128 .4897 (361*2π)/3811 weeks
362.0141 .6435 (362*2π)/3811 weeks
363-.26209 .80876 (363*2π)/3811 weeks
364-.2438 .91273 (364*2π)/3811 weeks
365.15333 .64701 (365*2π)/3811 weeks
366-.04377 .71165 (366*2π)/3811 weeks
367-.19088 .84042 (367*2π)/3811 weeks
368-.11098 1.16993 (368*2π)/3811 weeks
369-.41456 .97089 (369*2π)/3811 weeks
370-.15024 1.09943 (370*2π)/3811 weeks
371.61198 .8582 (371*2π)/3811 weeks
372-.004 1.40568 (372*2π)/3811 weeks
373-.28703 1.22457 (373*2π)/3811 weeks
374-.31412 .76731 (374*2π)/3811 weeks
375-.23077 .99701 (375*2π)/3811 weeks
376.29755 3.01082 (376*2π)/3811 weeks
377.96188 3.00846 (377*2π)/3811 weeks
378-.01784 3.51692 (378*2π)/3811 weeks
379.68314 4.11222 (379*2π)/3811 weeks

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