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Fourier Analysis of Y (Alleghany Corporation)


Y (Alleghany Corporation) appears to have interesting cyclic behaviour every 216 weeks (21.085*sine), 166 weeks (19.4809*sine), and 196 weeks (13.6742*sine).

Y (Alleghany Corporation) has an average price of 206.25 (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 3/17/1980 to 7/26/2021 for Y (Alleghany Corporation), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0206.2461   0 
180.75814 -197.4112 (1*2π)/21552,155 weeks
234.66105 -101.3767 (2*2π)/21551,078 weeks
314.17255 -85.99663 (3*2π)/2155718 weeks
4-11.89706 -68.25449 (4*2π)/2155539 weeks
5-2.56667 -30.65747 (5*2π)/2155431 weeks
62.6217 -43.09169 (6*2π)/2155359 weeks
7-7.39271 -29.42402 (7*2π)/2155308 weeks
8-4.28084 -20.90918 (8*2π)/2155269 weeks
91.31945 -23.76989 (9*2π)/2155239 weeks
10-5.14628 -21.08501 (10*2π)/2155216 weeks
11-5.6911 -13.67416 (11*2π)/2155196 weeks
123.87275 -12.74921 (12*2π)/2155180 weeks
13-6.56586 -19.48092 (13*2π)/2155166 weeks
14-4.68609 -1.01443 (14*2π)/2155154 weeks
153.61938 -9.46471 (15*2π)/2155144 weeks
16-.16286 -9.03385 (16*2π)/2155135 weeks
17.8433 -3.99619 (17*2π)/2155127 weeks
187.4293 -5.93478 (18*2π)/2155120 weeks
195.99324 -6.45914 (19*2π)/2155113 weeks
206.71371 -9.48004 (20*2π)/2155108 weeks
216.98051 -11.35404 (21*2π)/2155103 weeks
222.01631 -11.49925 (22*2π)/215598 weeks
234.56536 -8.1769 (23*2π)/215594 weeks
244.87667 -9.7073 (24*2π)/215590 weeks
254.23279 -10.48709 (25*2π)/215586 weeks
265.5906 -9.29125 (26*2π)/215583 weeks
274.33053 -14.25116 (27*2π)/215580 weeks
282.66401 -11.24208 (28*2π)/215577 weeks
291.70713 -14.91733 (29*2π)/215574 weeks
30-1.16042 -12.14871 (30*2π)/215572 weeks
31-1.46825 -11.36768 (31*2π)/215570 weeks
32-1.74771 -11.41376 (32*2π)/215567 weeks
33-5.16397 -10.49739 (33*2π)/215565 weeks
34-3.84153 -7.88079 (34*2π)/215563 weeks
35-3.7369 -6.53054 (35*2π)/215562 weeks
36-2.61397 -5.57059 (36*2π)/215560 weeks
37-1.91718 -6.37014 (37*2π)/215558 weeks
38-4.00916 -5.44125 (38*2π)/215557 weeks
39-2.27934 -3.38171 (39*2π)/215555 weeks
40-1.49584 -3.94394 (40*2π)/215554 weeks
41.05396 -4.57242 (41*2π)/215553 weeks
42-2.36926 -4.72703 (42*2π)/215551 weeks
43-2.36755 -2.08421 (43*2π)/215550 weeks
44.14161 -1.53559 (44*2π)/215549 weeks
451.6023 -2.70629 (45*2π)/215548 weeks
461.20394 -3.6386 (46*2π)/215547 weeks
471.06885 -3.21753 (47*2π)/215546 weeks
483.40041 -4.31886 (48*2π)/215545 weeks
49.73179 -5.76034 (49*2π)/215544 weeks
50.87355 -4.41117 (50*2π)/215543 weeks
51.2724 -4.9734 (51*2π)/215542 weeks
52.24118 -5.40598 (52*2π)/215541 weeks
53.05488 -3.37839 (53*2π)/215541 weeks
541.23298 -5.08094 (54*2π)/215540 weeks
55.31906 -4.51902 (55*2π)/215539 weeks
56.77974 -4.09057 (56*2π)/215538 weeks
572.1113 -5.35868 (57*2π)/215538 weeks
58-.45862 -6.9484 (58*2π)/215537 weeks
59-.42444 -5.08176 (59*2π)/215537 weeks
60-.43164 -6.68993 (60*2π)/215536 weeks
61-2.68024 -4.98917 (61*2π)/215535 weeks
62-1.01983 -3.24136 (62*2π)/215535 weeks
63-1.15508 -4.45679 (63*2π)/215534 weeks
64-.95826 -4.33078 (64*2π)/215534 weeks
65-1.32574 -4.69433 (65*2π)/215533 weeks
66-1.7875 -4.65753 (66*2π)/215533 weeks
67-3.00316 -3.25461 (67*2π)/215532 weeks
68-2.10753 -2.11197 (68*2π)/215532 weeks
69-1.56878 -1.93314 (69*2π)/215531 weeks
70-.88063 -2.21055 (70*2π)/215531 weeks
71-.53922 -2.22387 (71*2π)/215530 weeks
72-.19759 -1.96272 (72*2π)/215530 weeks
73.65085 -2.53938 (73*2π)/215530 weeks
74-.06646 -3.15192 (74*2π)/215529 weeks
75-.73823 -3.47175 (75*2π)/215529 weeks
76-1.27471 -3.15923 (76*2π)/215528 weeks
77-1.1706 -2.83415 (77*2π)/215528 weeks
78-1.42817 -1.23614 (78*2π)/215528 weeks
79.42099 -.65413 (79*2π)/215527 weeks
801.25898 -2.16221 (80*2π)/215527 weeks
81.09232 -2.78812 (81*2π)/215527 weeks
82.67958 -2.8268 (82*2π)/215526 weeks
83.62598 -3.52502 (83*2π)/215526 weeks
84.40618 -3.29458 (84*2π)/215526 weeks
85-.04244 -3.58955 (85*2π)/215525 weeks
86-.55745 -3.54154 (86*2π)/215525 weeks
87-1.00948 -3.66628 (87*2π)/215525 weeks
88-.94262 -3.26814 (88*2π)/215524 weeks
89-.55266 -3.6517 (89*2π)/215524 weeks
90-1.76324 -3.55043 (90*2π)/215524 weeks
91-1.67692 -2.03424 (91*2π)/215524 weeks
92-1.62202 -2.54067 (92*2π)/215523 weeks
93-.96504 -2.14856 (93*2π)/215523 weeks
94-1.38041 -3.05328 (94*2π)/215523 weeks
95-1.6727 -2.50365 (95*2π)/215523 weeks
96-1.91049 -1.32246 (96*2π)/215522 weeks
97-.81813 -1.70208 (97*2π)/215522 weeks
98-1.61036 -1.15866 (98*2π)/215522 weeks
99-.87971 -1.368 (99*2π)/215522 weeks
100-.77237 -1.56667 (100*2π)/215522 weeks
101-1.08776 -1.44644 (101*2π)/215521 weeks
102.0602 -.63044 (102*2π)/215521 weeks
103-.0454 -2.01677 (103*2π)/215521 weeks
104-1.58059 -2.15607 (104*2π)/215521 weeks
105-1.48255 -.06922 (105*2π)/215521 weeks
106.60439 -1.37261 (106*2π)/215520 weeks
107-.66567 -1.5679 (107*2π)/215520 weeks
108-.2831 -.41267 (108*2π)/215520 weeks
1091.07038 -.64737 (109*2π)/215520 weeks
110.26155 -2.1682 (110*2π)/215520 weeks
111.50821 -1.42427 (111*2π)/215519 weeks
112.51915 -2.08956 (112*2π)/215519 weeks
113.39496 -2.71506 (113*2π)/215519 weeks
114-.37635 -1.77261 (114*2π)/215519 weeks
115.53591 -2.16017 (115*2π)/215519 weeks
116-.13618 -3.26376 (116*2π)/215519 weeks
117-1.66341 -2.43915 (117*2π)/215518 weeks
118.01479 -1.89144 (118*2π)/215518 weeks
119-1.52678 -3.10876 (119*2π)/215518 weeks
120-1.8868 -1.35012 (120*2π)/215518 weeks
121-1.21085 -.49216 (121*2π)/215518 weeks
122-.54077 -1.02721 (122*2π)/215518 weeks
123-.33077 -.86847 (123*2π)/215518 weeks
124.17492 -1.98788 (124*2π)/215517 weeks
125-.90848 -1.62663 (125*2π)/215517 weeks
126-1.11168 -1.37105 (126*2π)/215517 weeks
127-.94859 -.28656 (127*2π)/215517 weeks
128-.17789 -.62622 (128*2π)/215517 weeks
129-.33393 -1.19811 (129*2π)/215517 weeks
130-.53319 -.12938 (130*2π)/215517 weeks
1311.32612 -.44896 (131*2π)/215516 weeks
132.85739 -2.13418 (132*2π)/215516 weeks
133-.43931 -1.75375 (133*2π)/215516 weeks
134.14654 -.5696 (134*2π)/215516 weeks
1351.03878 -1.985 (135*2π)/215516 weeks
136-.14042 -2.38566 (136*2π)/215516 weeks
137-.18979 -1.58974 (137*2π)/215516 weeks
138.22783 -1.77496 (138*2π)/215516 weeks
139-.42511 -2.27969 (139*2π)/215516 weeks
140-.87951 -1.1709 (140*2π)/215515 weeks
141.50881 -1.55173 (141*2π)/215515 weeks
142-.65498 -2.46129 (142*2π)/215515 weeks
143-.4805 -1.39796 (143*2π)/215515 weeks
144-.11141 -1.77873 (144*2π)/215515 weeks
145-.52195 -2.39681 (145*2π)/215515 weeks
146-1.53794 -1.71403 (146*2π)/215515 weeks
147-.84312 -1.19849 (147*2π)/215515 weeks
148-1.05103 -1.38852 (148*2π)/215515 weeks
149-.66886 -1.04482 (149*2π)/215514 weeks
150-.62141 -.82057 (150*2π)/215514 weeks
151-.10267 -1.29435 (151*2π)/215514 weeks
152-.88133 -1.21147 (152*2π)/215514 weeks
153-.57213 -1.26048 (153*2π)/215514 weeks
154-.79813 -1.12549 (154*2π)/215514 weeks
155-.6936 -1.11725 (155*2π)/215514 weeks
156-.96369 -.37867 (156*2π)/215514 weeks
157.01677 -.5801 (157*2π)/215514 weeks
158-.80164 -1.41154 (158*2π)/215514 weeks
159-.88981 -.08392 (159*2π)/215514 weeks
160.41647 -.32198 (160*2π)/215513 weeks
161-.08107 -1.35005 (161*2π)/215513 weeks
162-.75558 -.3779 (162*2π)/215513 weeks
163.13605 .0174 (163*2π)/215513 weeks
164.39859 -.86576 (164*2π)/215513 weeks
165-.14995 -.88591 (165*2π)/215513 weeks
166.4007 -.1545 (166*2π)/215513 weeks
1671.08033 -1.17326 (167*2π)/215513 weeks
168.01716 -1.19391 (168*2π)/215513 weeks
169.88809 -.82559 (169*2π)/215513 weeks
170.59311 -2.06356 (170*2π)/215513 weeks
171-.25583 -1.93107 (171*2π)/215513 weeks
172-.06513 -.96976 (172*2π)/215513 weeks
173.5884 -1.64063 (173*2π)/215512 weeks
174.05953 -1.89902 (174*2π)/215512 weeks
175-.62013 -1.83859 (175*2π)/215512 weeks
176-.32565 -1.34223 (176*2π)/215512 weeks
177-.78366 -1.82132 (177*2π)/215512 weeks
178-.51574 -.84539 (178*2π)/215512 weeks
179-.07713 -1.19776 (179*2π)/215512 weeks
180-.47096 -1.46488 (180*2π)/215512 weeks
181-.848 -1.12328 (181*2π)/215512 weeks
182-.41889 -1.08422 (182*2π)/215512 weeks
183-.7336 -1.00156 (183*2π)/215512 weeks
184-.42305 -.64206 (184*2π)/215512 weeks
185-.00084 -.49783 (185*2π)/215512 weeks
186.3868 -1.15083 (186*2π)/215512 weeks
187-.33586 -1.65931 (187*2π)/215512 weeks
188-.72942 -.91571 (188*2π)/215511 weeks
189-.3509 -1.00238 (189*2π)/215511 weeks
190-.38333 -.69613 (190*2π)/215511 weeks
191-.24983 -1.01065 (191*2π)/215511 weeks
192-.56464 -.68929 (192*2π)/215511 weeks
193-.31137 -.53787 (193*2π)/215511 weeks
194.09587 -.6382 (194*2π)/215511 weeks
195-.13008 -.53992 (195*2π)/215511 weeks
196.79369 -.66062 (196*2π)/215511 weeks
197.3892 -1.31524 (197*2π)/215511 weeks
198-.02643 -1.37727 (198*2π)/215511 weeks
199-.01724 -1.04477 (199*2π)/215511 weeks
200.1649 -1.27645 (200*2π)/215511 weeks
201-.11448 -1.50481 (201*2π)/215511 weeks
202-.22563 -1.01112 (202*2π)/215511 weeks
203-.02282 -1.43998 (203*2π)/215511 weeks
204-.61289 -1.0201 (204*2π)/215511 weeks
205.17031 -.91797 (205*2π)/215511 weeks
206-.0216 -1.66555 (206*2π)/215510 weeks
207-.48674 -1.55471 (207*2π)/215510 weeks
208-.72503 -1.26469 (208*2π)/215510 weeks
209-.76401 -1.06159 (209*2π)/215510 weeks
210-.70423 -.82843 (210*2π)/215510 weeks
211-.5667 -.5762 (211*2π)/215510 weeks
212-.25322 -.5991 (212*2π)/215510 weeks
213-.29306 -.7085 (213*2π)/215510 weeks
214-.13514 -.36732 (214*2π)/215510 weeks
215.35706 -.78492 (215*2π)/215510 weeks
216-.24456 -.7828 (216*2π)/215510 weeks
217.29353 -.87059 (217*2π)/215510 weeks
218.00897 -.92338 (218*2π)/215510 weeks
219.13648 -1.01837 (219*2π)/215510 weeks
220.18892 -.86099 (220*2π)/215510 weeks
221.4486 -1.14362 (221*2π)/215510 weeks
222.21793 -1.52099 (222*2π)/215510 weeks
223-.14437 -1.49406 (223*2π)/215510 weeks
224-.10493 -1.49378 (224*2π)/215510 weeks
225-.19431 -1.41317 (225*2π)/215510 weeks
226-.45042 -1.35756 (226*2π)/215510 weeks
227-.35607 -.96275 (227*2π)/21559 weeks
228-.14732 -1.28804 (228*2π)/21559 weeks
229-.18831 -1.46608 (229*2π)/21559 weeks
230-.49256 -1.35786 (230*2π)/21559 weeks
231-.23612 -1.25121 (231*2π)/21559 weeks
232-.22419 -1.45785 (232*2π)/21559 weeks
233-.56285 -1.47794 (233*2π)/21559 weeks
234-.42976 -1.67288 (234*2π)/21559 weeks
235-1.46801 -1.63311 (235*2π)/21559 weeks
236-.91472 -.66083 (236*2π)/21559 weeks
237-.64695 -.98997 (237*2π)/21559 weeks
238-.79569 -1.06119 (238*2π)/21559 weeks
239-1.1863 -.75665 (239*2π)/21559 weeks
240-.95466 -.54798 (240*2π)/21559 weeks
241-.67168 -.3849 (241*2π)/21559 weeks
242-.67429 -.75308 (242*2π)/21559 weeks
243-.78347 -.32864 (243*2π)/21559 weeks
244-.39565 -.18454 (244*2π)/21559 weeks
245-.26392 -.18707 (245*2π)/21559 weeks
246.07187 -.54032 (246*2π)/21559 weeks
247-.24759 -.88846 (247*2π)/21559 weeks
248-.09932 -.61381 (248*2π)/21559 weeks
249-.34562 -.811 (249*2π)/21559 weeks
250-.09946 -.35125 (250*2π)/21559 weeks
251-.05082 -.74952 (251*2π)/21559 weeks
252-.26266 -.86451 (252*2π)/21559 weeks
253-.21086 -.66956 (253*2π)/21559 weeks
254.07559 -.86539 (254*2π)/21558 weeks
255-.2216 -.96407 (255*2π)/21558 weeks
256-.21696 -.74455 (256*2π)/21558 weeks
257.15432 -.71372 (257*2π)/21558 weeks
258-.09624 -1.53661 (258*2π)/21558 weeks
259-.67247 -.93608 (259*2π)/21558 weeks
260.02125 -.89391 (260*2π)/21558 weeks
261-.2871 -1.35867 (261*2π)/21558 weeks
262-.62636 -.95631 (262*2π)/21558 weeks
263-.20526 -1.04708 (263*2π)/21558 weeks
264-.99233 -1.66567 (264*2π)/21558 weeks
265-1.36903 -.69756 (265*2π)/21558 weeks
266-.76672 -.32923 (266*2π)/21558 weeks
267-.36956 -.45614 (267*2π)/21558 weeks
268-.70139 -.6217 (268*2π)/21558 weeks
269-.50228 -.50807 (269*2π)/21558 weeks
270-.67363 -.58529 (270*2π)/21558 weeks
271-.60192 -.38171 (271*2π)/21558 weeks
272-.43803 -.3818 (272*2π)/21558 weeks
273-.36858 -.25494 (273*2π)/21558 weeks
274-.37933 -.21841 (274*2π)/21558 weeks
275-.16039 -.15364 (275*2π)/21558 weeks
276.05406 -.42007 (276*2π)/21558 weeks
277-.11637 -.63791 (277*2π)/21558 weeks
278-.09007 -.50707 (278*2π)/21558 weeks
279.10373 -.56332 (279*2π)/21558 weeks
280-.07897 -.63886 (280*2π)/21558 weeks
281-.09857 -.87572 (281*2π)/21558 weeks
282-.27769 -.73701 (282*2π)/21558 weeks
283-.23701 -.63399 (283*2π)/21558 weeks
284-.09081 -.55116 (284*2π)/21558 weeks
285.00763 -.64722 (285*2π)/21558 weeks
286-.07072 -.5829 (286*2π)/21558 weeks
287.06944 -.4707 (287*2π)/21558 weeks
288.35227 -.79505 (288*2π)/21557 weeks
289.26197 -1.35782 (289*2π)/21557 weeks
290-.33186 -1.23866 (290*2π)/21557 weeks
291-.08529 -.88821 (291*2π)/21557 weeks
292-.07873 -1.45987 (292*2π)/21557 weeks
293-.62813 -1.26154 (293*2π)/21557 weeks
294-.68031 -1.1637 (294*2π)/21557 weeks
295-.80132 -1.03128 (295*2π)/21557 weeks
296-.66224 -.7704 (296*2π)/21557 weeks
297-.70211 -.67054 (297*2π)/21557 weeks
298-.55266 -.64254 (298*2π)/21557 weeks
299-.77739 -.53204 (299*2π)/21557 weeks
300-.36945 -.56161 (300*2π)/21557 weeks
301-.52945 -.85119 (301*2π)/21557 weeks
302-.86297 -.72989 (302*2π)/21557 weeks
303-.81764 -.11171 (303*2π)/21557 weeks
304-.2853 -.0367 (304*2π)/21557 weeks
305-.09253 -.42358 (305*2π)/21557 weeks
306-.49748 -.4717 (306*2π)/21557 weeks
307-.04254 -.18936 (307*2π)/21557 weeks
308.08532 -.83787 (308*2π)/21557 weeks
309-.51601 -.7297 (309*2π)/21557 weeks
310-.3959 -.22357 (310*2π)/21557 weeks
311-.03869 -.49435 (311*2π)/21557 weeks
312-.38772 -.66239 (312*2π)/21557 weeks
313-.25144 -.33682 (313*2π)/21557 weeks
314.15861 -.51345 (314*2π)/21557 weeks
315-.09181 -.6523 (315*2π)/21557 weeks
316-.17004 -.357 (316*2π)/21557 weeks
317.54708 -.45718 (317*2π)/21557 weeks
318.29699 -1.45255 (318*2π)/21557 weeks
319-.30867 -1.1732 (319*2π)/21557 weeks
320.03615 -1.15951 (320*2π)/21557 weeks
321-.27612 -1.54008 (321*2π)/21557 weeks
322-.98595 -1.29559 (322*2π)/21557 weeks
323-.89159 -.71458 (323*2π)/21557 weeks
324-.66889 -.82451 (324*2π)/21557 weeks
325-.70455 -.77079 (325*2π)/21557 weeks
326-.73976 -.57635 (326*2π)/21557 weeks
327-.33858 -.55219 (327*2π)/21557 weeks
328-.73571 -.94971 (328*2π)/21557 weeks
329-.83923 -.55152 (329*2π)/21557 weeks
330-.73108 -.46452 (330*2π)/21557 weeks
331-.34289 -.82761 (331*2π)/21557 weeks
332-1.16831 -.63339 (332*2π)/21556 weeks
333-.4961 -.04937 (333*2π)/21556 weeks
334-.58485 -.5914 (334*2π)/21556 weeks
335-.92618 -.37447 (335*2π)/21556 weeks
336-.65608 -.03395 (336*2π)/21556 weeks
337-.32068 -.27268 (337*2π)/21556 weeks
338-.53925 -.26905 (338*2π)/21556 weeks
339-.38824 -.05167 (339*2π)/21556 weeks
340-.16837 -.31875 (340*2π)/21556 weeks
341-.62344 -.44867 (341*2π)/21556 weeks
342-.52541 -.06758 (342*2π)/21556 weeks
343.09513 -.12139 (343*2π)/21556 weeks
344-.2787 -.70024 (344*2π)/21556 weeks
345-.58433 -.2328 (345*2π)/21556 weeks
346-.35585 -.05244 (346*2π)/21556 weeks
347-.26965 -.28647 (347*2π)/21556 weeks
348-.33005 .01783 (348*2π)/21556 weeks
349.13654 -.08835 (349*2π)/21556 weeks
350.05348 -.20917 (350*2π)/21556 weeks
351.19926 -.25714 (351*2π)/21556 weeks
352.36105 -.48382 (352*2π)/21556 weeks
353.0949 -1.11516 (353*2π)/21556 weeks
354-.45159 -.66895 (354*2π)/21556 weeks
355-.23243 -.43178 (355*2π)/21556 weeks
356.01986 -.3839 (356*2π)/21556 weeks
357-.02594 -.82168 (357*2π)/21556 weeks
358-.4356 -.60077 (358*2π)/21556 weeks
359-.11558 -.40215 (359*2π)/21556 weeks
360-.09235 -.76121 (360*2π)/21556 weeks
361-.37475 -.64944 (361*2π)/21556 weeks
362-.09686 -.36909 (362*2π)/21556 weeks
363-.06932 -.95386 (363*2π)/21556 weeks
364-.57366 -.60235 (364*2π)/21556 weeks
365-.12202 -.51233 (365*2π)/21556 weeks
366-.20693 -.7307 (366*2π)/21556 weeks
367-.32893 -.75676 (367*2π)/21556 weeks
368-.3916 -.56939 (368*2π)/21556 weeks
369-.35499 -.87461