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Fourier Analysis of Y (Alleghany Corporation)


Y (Alleghany Corporation) appears to have interesting cyclic behaviour every 213 weeks (23.8993*sine), 164 weeks (23.8552*sine), and 194 weeks (17.6473*sine).

Y (Alleghany Corporation) has an average price of 201.41 (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 2/22/2021 for Y (Alleghany Corporation), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
0201.4119   0 
178.34801 -192.5611 (1*2π)/21332,133 weeks
233.96236 -97.42062 (2*2π)/21331,067 weeks
316.40524 -83.31088 (3*2π)/2133711 weeks
4-9.17862 -70.07692 (4*2π)/2133533 weeks
5-4.7174 -31.58607 (5*2π)/2133427 weeks
64.20917 -42.46336 (6*2π)/2133356 weeks
7-7.0827 -32.1011 (7*2π)/2133305 weeks
8-6.21699 -22.9168 (8*2π)/2133267 weeks
9.96478 -23.82731 (9*2π)/2133237 weeks
10-4.83658 -23.89928 (10*2π)/2133213 weeks
11-8.36972 -17.64733 (11*2π)/2133194 weeks
12.79701 -12.28814 (12*2π)/2133178 weeks
13-4.74802 -23.85521 (13*2π)/2133164 weeks
14-12.4232 -7.15778 (14*2π)/2133152 weeks
15-2.0278 -9.31244 (15*2π)/2133142 weeks
16-4.64008 -11.08882 (16*2π)/2133133 weeks
17-7.53094 -6.42311 (17*2π)/2133125 weeks
18-1.49623 -3.23311 (18*2π)/2133119 weeks
19-2.05394 -2.81761 (19*2π)/2133112 weeks
20.44018 -3.70217 (20*2π)/2133107 weeks
213.20844 -4.13085 (21*2π)/2133102 weeks
22.42023 -7.87554 (22*2π)/213397 weeks
23-.25293 -3.93343 (23*2π)/213393 weeks
24.90177 -3.69468 (24*2π)/213389 weeks
251.27153 -4.26548 (25*2π)/213385 weeks
261.18325 -1.06071 (26*2π)/213382 weeks
275.22662 -4.02861 (27*2π)/213379 weeks
282.98187 -2.70935 (28*2π)/213376 weeks
296.66299 -4.99509 (29*2π)/213374 weeks
304.56056 -6.06669 (30*2π)/213371 weeks
314.19894 -6.10085 (31*2π)/213369 weeks
325.30808 -5.97443 (32*2π)/213367 weeks
334.15646 -9.41796 (33*2π)/213365 weeks
342.9953 -8.61822 (34*2π)/213363 weeks
351.7839 -8.65419 (35*2π)/213361 weeks
36.86163 -7.56263 (36*2π)/213359 weeks
372.18484 -6.68797 (37*2π)/213358 weeks
381.44402 -8.96688 (38*2π)/213356 weeks
39-.37022 -7.83231 (39*2π)/213355 weeks
40-.57087 -7.52364 (40*2π)/213353 weeks
41.56113 -5.34563 (41*2π)/213352 weeks
421.50578 -7.38938 (42*2π)/213351 weeks
43-.69945 -8.73671 (43*2π)/213350 weeks
44-2.3048 -7.51083 (44*2π)/213348 weeks
45-2.30555 -5.79762 (45*2π)/213347 weeks
46-1.72436 -5.59918 (46*2π)/213346 weeks
47-2.7273 -6.21605 (47*2π)/213345 weeks
48-2.62958 -2.83127 (48*2π)/213344 weeks
49-.789 -3.86461 (49*2π)/213344 weeks
50-1.61016 -3.52442 (50*2π)/213343 weeks
51-1.34884 -3.83751 (51*2π)/213342 weeks
52.07663 -3.75173 (52*2π)/213341 weeks
53-1.91613 -4.74585 (53*2π)/213340 weeks
54-1.09784 -3.34039 (54*2π)/213340 weeks
55-1.09072 -3.90085 (55*2π)/213339 weeks
56-2.24764 -4.3634 (56*2π)/213338 weeks
57-3.13821 -1.79188 (57*2π)/213337 weeks
58-.65614 -2.00822 (58*2π)/213337 weeks
59-1.91273 -2.39296 (59*2π)/213336 weeks
60-.29982 -.39529 (60*2π)/213336 weeks
611.13061 -2.33086 (61*2π)/213335 weeks
62-.74115 -2.61757 (62*2π)/213334 weeks
63-.39812 -2.5239 (63*2π)/213334 weeks
64-.75524 -2.19142 (64*2π)/213333 weeks
65-.49491 -1.68868 (65*2π)/213333 weeks
66.3571 -.54894 (66*2π)/213332 weeks
671.46083 -1.56262 (67*2π)/213332 weeks
681.26314 -2.26323 (68*2π)/213331 weeks
691.04867 -2.97997 (69*2π)/213331 weeks
70.96783 -3.07175 (70*2π)/213330 weeks
711.03017 -3.10209 (71*2π)/213330 weeks
72.72058 -3.81643 (72*2π)/213330 weeks
73-.37615 -3.29085 (73*2π)/213329 weeks
74-.79941 -2.86237 (74*2π)/213329 weeks
75-.62339 -2.2826 (75*2π)/213328 weeks
76-.06715 -2.16869 (76*2π)/213328 weeks
77.76028 -1.14374 (77*2π)/213328 weeks
782.1104 -2.2806 (78*2π)/213327 weeks
791.28773 -3.84762 (79*2π)/213327 weeks
80-.11141 -3.43811 (80*2π)/213327 weeks
81.4383 -3.65121 (81*2π)/213326 weeks
82-.01187 -4.00422 (82*2π)/213326 weeks
83-.1176 -3.50264 (83*2π)/213326 weeks
84-.63421 -3.49302 (84*2π)/213325 weeks
85-.98891 -3.19285 (85*2π)/213325 weeks
86-1.29716 -3.13736 (86*2π)/213325 weeks
87-.98057 -2.81652 (87*2π)/213325 weeks
88-.72967 -3.27817 (88*2π)/213324 weeks
89-1.78583 -2.78736 (89*2π)/213324 weeks
90-1.22959 -1.4605 (90*2π)/213324 weeks
91-1.25567 -2.12534 (91*2π)/213323 weeks
92-.55892 -1.9231 (92*2π)/213323 weeks
93-1.12379 -2.78743 (93*2π)/213323 weeks
94-1.32333 -2.21809 (94*2π)/213323 weeks
95-1.46366 -1.1087 (95*2π)/213322 weeks
96-.42371 -1.61767 (96*2π)/213322 weeks
97-1.26031 -1.10912 (97*2π)/213322 weeks
98-.57314 -1.34808 (98*2π)/213322 weeks
99-.49109 -1.5709 (99*2π)/213322 weeks
100-.87281 -1.52101 (100*2π)/213321 weeks
101.13358 -.54077 (101*2π)/213321 weeks
102.29009 -1.89159 (102*2π)/213321 weeks
103-1.2008 -2.46054 (103*2π)/213321 weeks
104-1.78534 -.43615 (104*2π)/213321 weeks
105.49938 -1.08418 (105*2π)/213320 weeks
106-.60773 -1.6904 (106*2π)/213320 weeks
107-.79336 -.48374 (107*2π)/213320 weeks
108.4981 .0433 (108*2π)/213320 weeks
109.39484 -1.57358 (109*2π)/213320 weeks
110.34383 -.78503 (110*2π)/213319 weeks
111.6731 -1.21579 (111*2π)/213319 weeks
1121.06607 -1.87041 (112*2π)/213319 weeks
113-.05728 -1.45243 (113*2π)/213319 weeks
114.90058 -1.08656 (114*2π)/213319 weeks
1151.35371 -2.31307 (115*2π)/213319 weeks
116-.31419 -2.88253 (116*2π)/213318 weeks
117.6805 -1.38794 (117*2π)/213318 weeks
118.62123 -3.4039 (118*2π)/213318 weeks
119-.76045 -2.91489 (119*2π)/213318 weeks
120-1.31372 -1.92899 (120*2π)/213318 weeks
121-.75624 -1.73745 (121*2π)/213318 weeks
122-.90546 -1.27966 (122*2π)/213317 weeks
123.48268 -1.41292 (123*2π)/213317 weeks
124-.05465 -2.04025 (124*2π)/213317 weeks
125-.26662 -2.45103 (125*2π)/213317 weeks
126-1.31977 -1.96711 (126*2π)/213317 weeks
127-1.03085 -1.4244 (127*2π)/213317 weeks
128-.52211 -1.89956 (128*2π)/213317 weeks
129-1.88799 -1.93633 (129*2π)/213317 weeks
130-1.45667 -.0843 (130*2π)/213316 weeks
131.08803 -.41841 (131*2π)/213316 weeks
132-.19391 -1.62695 (132*2π)/213316 weeks
133-1.54371 -.94091 (133*2π)/213316 weeks
134-.28744 -.05865 (134*2π)/213316 weeks
135.25654 -.97974 (135*2π)/213316 weeks
136-.3284 -1.03086 (136*2π)/213316 weeks
137-.1991 -.43622 (137*2π)/213316 weeks
138.55761 -.95319 (138*2π)/213315 weeks
139-.59063 -1.6837 (139*2π)/213315 weeks
140-.53054 -.20919 (140*2π)/213315 weeks
141.51002 -1.08826 (141*2π)/213315 weeks
142-.27123 -1.0759 (142*2π)/213315 weeks
143-.26065 -.50231 (143*2π)/213315 weeks
144.68543 -.29529 (144*2π)/213315 weeks
145.65811 -1.42682 (145*2π)/213315 weeks
146.22586 -1.1568 (146*2π)/213315 weeks
147.46961 -1.53074 (147*2π)/213315 weeks
148.3072 -1.41383 (148*2π)/213314 weeks
149-.1725 -1.61406 (149*2π)/213314 weeks
150-.01956 -.77862 (150*2π)/213314 weeks
151.06727 -1.29359 (151*2π)/213314 weeks
152.18974 -1.0466 (152*2π)/213314 weeks
153.27152 -1.22314 (153*2π)/213314 weeks
154.67155 -1.01685 (154*2π)/213314 weeks
155.30521 -1.90254 (155*2π)/213314 weeks
156-.4513 -1.12362 (156*2π)/213314 weeks
157.86423 -1.02879 (157*2π)/213314 weeks
158.49018 -2.25182 (158*2π)/213314 weeks
159-.54346 -1.63346 (159*2π)/213313 weeks
160.34874 -.82093 (160*2π)/213313 weeks
161.68699 -1.75685 (161*2π)/213313 weeks
162-.21196 -2.11229 (162*2π)/213313 weeks
163-.26614 -1.49857 (163*2π)/213313 weeks
164.49231 -1.72256 (164*2π)/213313 weeks
165-.26672 -2.53699 (165*2π)/213313 weeks
166-.73821 -1.46182 (166*2π)/213313 weeks
167.02298 -1.96776 (167*2π)/213313 weeks
168-1.16806 -2.20221 (168*2π)/213313 weeks
169-1.17685 -1.28522 (169*2π)/213313 weeks
170-.24324 -1.00237 (170*2π)/213313 weeks
171-.43858 -1.92975 (171*2π)/213312 weeks
172-.99765 -1.4929 (172*2π)/213312 weeks
173-1.22083 -.9999 (173*2π)/213312 weeks
174-.58105 -.89918 (174*2π)/213312 weeks
175-1.12422 -1.04399 (175*2π)/213312 weeks
176-.26329 -.49907 (176*2π)/213312 weeks
177-.24483 -1.12508 (177*2π)/213312 weeks
178-.74637 -1.0644 (178*2π)/213312 weeks
179-.79702 -.61919 (179*2π)/213312 weeks
180-.36684 -.84007 (180*2π)/213312 weeks
181-.60528 -.65314 (181*2π)/213312 weeks
182-.15535 -.52122 (182*2π)/213312 weeks
183.19286 -.63182 (183*2π)/213312 weeks
184.19975 -1.35328 (184*2π)/213312 weeks
185-.6594 -1.48504 (185*2π)/213312 weeks
186-.74811 -.64259 (186*2π)/213311 weeks
187-.37376 -.86106 (187*2π)/213311 weeks
188-.36235 -.57378 (188*2π)/213311 weeks
189-.30372 -.91487 (189*2π)/213311 weeks
190-.57313 -.5497 (190*2π)/213311 weeks
191-.30953 -.44923 (191*2π)/213311 weeks
192.05831 -.58068 (192*2π)/213311 weeks
193-.19261 -.45968 (193*2π)/213311 weeks
194.71021 -.56232 (194*2π)/213311 weeks
195.31841 -1.18475 (195*2π)/213311 weeks
196-.08073 -1.25318 (196*2π)/213311 weeks
197-.09787 -.90371 (197*2π)/213311 weeks
198.12693 -1.08554 (198*2π)/213311 weeks
199-.08447 -1.36139 (199*2π)/213311 weeks
200-.28291 -.88835 (200*2π)/213311 weeks
201.03533 -1.25853 (201*2π)/213311 weeks
202-.66062 -1.0159 (202*2π)/213311 weeks
203.03802 -.63037 (203*2π)/213311 weeks
204.19131 -1.36155 (204*2π)/213310 weeks
205-.19193 -1.49921 (205*2π)/213310 weeks
206-.51494 -1.40377 (206*2π)/213310 weeks
207-.67063 -1.30872 (207*2π)/213310 weeks
208-.77505 -1.13713 (208*2π)/213310 weeks
209-.86243 -.86788 (209*2π)/213310 weeks
210-.64302 -.69908 (210*2π)/213310 weeks
211-.64758 -.82142 (211*2π)/213310 weeks
212-.81644 -.41872 (212*2π)/213310 weeks
213-.16963 -.34339 (213*2π)/213310 weeks
214-.65818 -.66973 (214*2π)/213310 weeks
215-.22785 -.38678 (215*2π)/213310 weeks
216-.39577 -.5412 (216*2π)/213310 weeks
217-.26672 -.53504 (217*2π)/213310 weeks
218-.40505 -.31743 (218*2π)/213310 weeks
219-.05831 -.12714 (219*2π)/213310 weeks
220.21311 -.38553 (220*2π)/213310 weeks
221.07607 -.65235 (221*2π)/213310 weeks
222.17238 -.66369 (222*2π)/213310 weeks
223.17055 -.66352 (223*2π)/213310 weeks
224.05817 -.91715 (224*2π)/213310 weeks
225-.34817 -.67863 (225*2π)/21339 weeks
226-.10591 -.56696 (226*2π)/21339 weeks
227.14646 -.57234 (227*2π)/21339 weeks
228-.00478 -.82916 (228*2π)/21339 weeks
229-.0436 -.556 (229*2π)/21339 weeks
230.19409 -.41189 (230*2π)/21339 weeks
231.16134 -.6086 (231*2π)/21339 weeks
232.63098 -.30252 (232*2π)/21339 weeks
233.7464 -1.47374 (233*2π)/21339 weeks
234-.01033 -1.13668 (234*2π)/21339 weeks
235.17262 -.88162 (235*2π)/21339 weeks
236.41604 -.86669 (236*2π)/21339 weeks
237.23665 -1.32013 (237*2π)/21339 weeks
238.07775 -1.39941 (238*2π)/21339 weeks
239-.22907 -1.20008 (239*2π)/21339 weeks
240.18578 -1.21928 (240*2π)/21339 weeks
241-.0495 -1.52258 (241*2π)/21339 weeks
242-.30306 -1.38531 (242*2π)/21339 weeks
243-.63901 -1.39114 (243*2π)/21339 weeks
244-.66419 -.93262 (244*2π)/21339 weeks
245-.24814 -1.06359 (245*2π)/21339 weeks
246-.44432 -.86375 (246*2π)/21339 weeks
247-.08053 -1.07616 (247*2π)/21339 weeks
248-.61192 -1.04098 (248*2π)/21339 weeks
249-.56424 -.83257 (249*2π)/21339 weeks
250-.33975 -.92572 (250*2π)/21339 weeks
251-.50831 -1.11582 (251*2π)/21338 weeks
252-.57747 -.75477 (252*2π)/21338 weeks
253-.34405 -.80036 (253*2π)/21338 weeks
254-.40207 -1.04897 (254*2π)/21338 weeks
255-1.07808 -.86326 (255*2π)/21338 weeks
256-.45434 -.2401 (256*2π)/21338 weeks
257-.26903 -.95602 (257*2π)/21338 weeks
258-.80694 -.66319 (258*2π)/21338 weeks
259-.47065 -.25431 (259*2π)/21338 weeks
260-.43066 -.67085 (260*2π)/21338 weeks
261-1.11055 -.22491 (261*2π)/21338 weeks
262-.17942 .33425 (262*2π)/21338 weeks
263.30637 -.28479 (263*2π)/21338 weeks
264.16513 -.64267 (264*2π)/21338 weeks
265-.23642 -.4456 (265*2π)/21338 weeks
266-.00572 -.52573 (266*2π)/21338 weeks
267-.18702 -.45863 (267*2π)/21338 weeks
268.02909 -.41245 (268*2π)/21338 weeks
269.10307 -.54887 (269*2π)/21338 weeks
270.16885 -.49807 (270*2π)/21338 weeks
271.12829 -.50714 (271*2π)/21338 weeks
272.2703 -.63076 (272*2π)/21338 weeks
273.1924 -.93477 (273*2π)/21338 weeks
274-.08309 -.93254 (274*2π)/21338 weeks
275.02936 -.79558 (275*2π)/21338 weeks
276.12535 -.91182 (276*2π)/21338 weeks
277-.10646 -.86419 (277*2π)/21338 weeks
278-.19948 -1.02013 (278*2π)/21338 weeks
279-.26778 -.77899 (279*2π)/21338 weeks
280-.15758 -.70598 (280*2π)/21338 weeks
281.00494 -.68709 (281*2π)/21338 weeks
282.04874 -.79832 (282*2π)/21338 weeks
283-.01489 -.70182 (283*2π)/21338 weeks
284.14206 -.64042 (284*2π)/21338 weeks
285.32191 -1.01038 (285*2π)/21337 weeks
286.11955 -1.48445 (286*2π)/21337 weeks
287-.41281 -1.22832 (287*2π)/21337 weeks
288-.09105 -.9039 (288*2π)/21337 weeks
289-.10933 -1.46496 (289*2π)/21337 weeks
290-.61367 -1.2329 (290*2π)/21337 weeks
291-.62944 -1.1501 (291*2π)/21337 weeks
292-.73175 -1.0444 (292*2π)/21337 weeks
293-.59498 -.79949 (293*2π)/21337 weeks
294-.64118 -.71974 (294*2π)/21337 weeks
295-.49136 -.68829 (295*2π)/21337 weeks
296-.7445 -.62372 (296*2π)/21337 weeks
297-.34164 -.57476 (297*2π)/21337 weeks
298-.39966 -.91153 (298*2π)/21337 weeks
299-.75342 -.95861 (299*2π)/21337 weeks
300-.96374 -.39426 (300*2π)/21337 weeks
301-.55711 -.09717 (301*2π)/21337 weeks
302-.2188 -.33341 (302*2π)/21337 weeks
303-.58853 -.55406 (303*2π)/21337 weeks
304-.34549 -.06699 (304*2π)/21337 weeks
305.13525 -.52806 (305*2π)/21337 weeks
306-.37324 -.80024 (306*2π)/21337 weeks
307-.62121 -.33489 (307*2π)/21337 weeks
308-.21303 -.29482 (308*2π)/21337 weeks
309-.39 -.65121 (309*2π)/21337 weeks
310-.56104 -.35574 (310*2π)/21337 weeks
311-.15748 -.16102 (311*2π)/21337 weeks
312-.20768 -.3835 (312*2π)/21337 weeks
313-.59536 -.23149 (313*2π)/21337 weeks
314-.15162 .44036 (314*2π)/21337 weeks
315.56773 -.19652 (315*2π)/21337 weeks
316.12578 -.50732 (316*2π)/21337 weeks
317.37896 -.18077 (317*2π)/21337 weeks
318.75137 -.52449 (318*2π)/21337 weeks
319.37883 -1.11557 (319*2π)/21337 weeks
320-.09446 -.92274 (320*2π)/21337 weeks
321.03573 -.8408 (321*2π)/21337 weeks
322.02749 -.87749 (322*2π)/21337 weeks
323-.20545 -.90322 (323*2π)/21337 weeks
324-.11528 -.40738 (324*2π)/21337 weeks
325.19199 -.83514 (325*2π)/21337 weeks
326-.10262 -.90808 (326*2π)/21337 weeks
327-.31577 -.8768 (327*2π)/21337 weeks
328.2776 -.48161 (328*2π)/21337 weeks
329.1024 -1.33362 (329*2π)/21336 weeks
330-.38747 -.7069 (330*2π)/21336 weeks
331.05427 -.73223 (331*2π)/21336 weeks
332-.02542 -1.15164 (332*2π)/21336 weeks
333-.40756 -1.09399 (333*2π)/21336 weeks
334-.23817 -.77753 (334*2π)/21336 weeks
335-.19123 -.96492 (335*2π)/21336 weeks
336-.49193 -.90463 (336*2π)/21336 weeks
337-.35593 -.52577 (337*2π)/21336 weeks
338-.07733 -.91504 (338*2π)/21336 weeks
339-.38187 -1.20129 (339*2π)/21336 weeks
340-.67603 -.5626 (340*2π)/21336 weeks
341-.02677 -.52109 (341*2π)/21336 weeks
342-.10505 -.89933 (342*2π)/21336 weeks
343-.37525 -.93262 (343*2π)/21336 weeks
344-.13797 -.87194 (344*2π)/21336 weeks
345-.35821 -1.23063 (345*2π)/21336 weeks
346-.53424 -.95133 (346*2π)/21336 weeks
347-.56787 -1.00345 (347*2π)/21336 weeks
348-.76734 -.97502 (348*2π)/21336 weeks
349-1.10477 -.66241 (349*2π)/21336 weeks
350-.50532 -.16176 (350*2π)/21336 weeks
351-.2677 -.56809 (351*2π)/21336 weeks
352-.32771 -.74999 (352*2π)/21336 weeks
353-.71962 -.72024 (353*2π)/21336 weeks
354-.52065 -.30674 (354*2π)/21336 weeks
355-.26278 -.63523 (355*2π)/21336 weeks
356-.60709 -.7299 (356*2π)/21336 weeks
357-.52939 -.42292 (357*2π)/21336 weeks
358-.22528 -.59028 (358*2π)/21336 weeks
359-.7133 -.81513 (359*2π)/21336 weeks
360-.57238 -.21162 (360*2π)/21336 weeks
361-.25125 -.62602 (361*2π)/21336 weeks
362-.54224 -.62673 (362*2π)/21336 weeks
363-.57829 -.50588 (363*2π)/21336 weeks
364-.47358 -.3681 (364*2π)/21336 weeks
365-.63183 -.58651 (365*2π)/21336 weeks
366-.69368 -.18142 (366*2π)/21336 weeks
367-.20776 -.04968 (367*2π)/21336 weeks
368-.12843 -.50557 (368*2π)/21336 weeks
369-.40326 -.37873 (369*2π)/21336 weeks
370-.19399 -.22287 (370*2π)/21336 weeks
371-.00124 -.52415 (371*2π)/21336 weeks
372-.25885 -.84913 (372*2π)/21336 weeks
373-.66034 -.50968 (373*2π)/21336 weeks
374-.26405 -.48237 (374*2π)/21336 weeks
375-.56849 -.70178 (375*2π)/21336 weeks
376-.67692 -.22129 (376*2π)/21336 weeks
377-.12162 -.13687 (377*2π)/21336 weeks
378-.32882 -.66936 (378*2π)/21336 weeks
379-.49257 -.3029 (379*2π)/21336 weeks
380-.19342 -.19807