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# Fourier Analysis of Z (Zillow Group)

Z (Zillow Group) appears to have interesting cyclic behaviour every 27 weeks (5.6825*sine), 30 weeks (5.2593*sine), and 27 weeks (3.5274*cosine).

Z (Zillow Group) has an average price of 49.51 (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 8/3/2015 to 4/12/2021 for Z (Zillow Group), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
049.50597   0
112.93984 -10.38425 (1*2π)/298298 weeks
215.05064 -18.38748 (2*2π)/298149 weeks
34.96549 -15.59678 (3*2π)/29899 weeks
45.34533 -14.8685 (4*2π)/29875 weeks
5-1.4905 -10.69855 (5*2π)/29860 weeks
62.90368 -8.08833 (6*2π)/29850 weeks
7-2.93322 -5.80764 (7*2π)/29843 weeks
8-.80762 -3.91759 (8*2π)/29837 weeks
9-.04916 -4.88996 (9*2π)/29833 weeks
10-1.20431 -5.25926 (10*2π)/29830 weeks
11-3.52737 -5.68252 (11*2π)/29827 weeks
12-1.45454 -2.22602 (12*2π)/29825 weeks
13-.59741 -2.45265 (13*2π)/29823 weeks
14-2.2813 -2.91667 (14*2π)/29821 weeks
15-2.24006 -2.45791 (15*2π)/29820 weeks
16-1.12114 -1.29241 (16*2π)/29819 weeks
17-2.35114 -1.88325 (17*2π)/29818 weeks
18-.13567 .10185 (18*2π)/29817 weeks
19.10701 -1.22275 (19*2π)/29816 weeks
20.03505 -1.68945 (20*2π)/29815 weeks
21-1.29019 -1.97008 (21*2π)/29814 weeks
22-1.07116 -.76594 (22*2π)/29814 weeks
23-1.03784 -.76385 (23*2π)/29813 weeks
24.32222 -.58134 (24*2π)/29812 weeks
25-.36028 -1.31677 (25*2π)/29812 weeks
26-.05464 -1.18088 (26*2π)/29811 weeks
27-.46322 -.72005 (27*2π)/29811 weeks
28-.17139 -.53704 (28*2π)/29811 weeks
29.95727 -.28023 (29*2π)/29810 weeks
30.8105 -1.0238 (30*2π)/29810 weeks
31.55828 -.7375 (31*2π)/29810 weeks
32.34892 -1.10726 (32*2π)/2989 weeks
33.60794 -.69844 (33*2π)/2989 weeks
34.30706 -1.4114 (34*2π)/2989 weeks
35.4891 -1.55895 (35*2π)/2989 weeks
36.02788 -1.64011 (36*2π)/2988 weeks
37-.10879 -1.34378 (37*2π)/2988 weeks
38-.42349 -.97989 (38*2π)/2988 weeks
39.65658 -1.36989 (39*2π)/2988 weeks
40.15452 -1.82238 (40*2π)/2987 weeks
41-.72203 -1.71256 (41*2π)/2987 weeks
42-.72324 -1.47584 (42*2π)/2987 weeks
43-.82937 -1.30236 (43*2π)/2987 weeks
44-1.05015 -1.41279 (44*2π)/2987 weeks
45-1.13737 -1.24674 (45*2π)/2987 weeks
46-1.10661 -1.27883 (46*2π)/2986 weeks
47-1.78612 -.08065 (47*2π)/2986 weeks
48-.62768 -.16239 (48*2π)/2986 weeks
49-.71723 -.13819 (49*2π)/2986 weeks
50-.02957 -.22825 (50*2π)/2986 weeks
51-.57316 -.79045 (51*2π)/2986 weeks
52-.37941 -.34083 (52*2π)/2986 weeks
53-.22397 -.40308 (53*2π)/2986 weeks
54-.3389 -.7035 (54*2π)/2986 weeks
55-.30579 -.34748 (55*2π)/2985 weeks
56-.67385 -.7009 (56*2π)/2985 weeks
57-.81693 -.20847 (57*2π)/2985 weeks
58-.19825 -.02733 (58*2π)/2985 weeks
59-.10476 .10864 (59*2π)/2985 weeks
60.52637 -.27389 (60*2π)/2985 weeks
61-.20654 -.38382 (61*2π)/2985 weeks
62.20439 -.23229 (62*2π)/2985 weeks
63.22174 -.46754 (63*2π)/2985 weeks
64.37019 -.46724 (64*2π)/2985 weeks
65.14075 -1.05405 (65*2π)/2985 weeks
66-.10451 -1.09485 (66*2π)/2985 weeks
67-.28319 -.91993 (67*2π)/2984 weeks
68-.53497 -1.14124 (68*2π)/2984 weeks
69-.38654 -.89713 (69*2π)/2984 weeks
70-.64697 -1.29658 (70*2π)/2984 weeks
71-.8238 -.75358 (71*2π)/2984 weeks
72-.71558 -.91548 (72*2π)/2984 weeks
73-.91884 -.38471 (73*2π)/2984 weeks
74-.95869 -.91021 (74*2π)/2984 weeks
75-.98689 -.30478 (75*2π)/2984 weeks
76-.84603 -.21094 (76*2π)/2984 weeks
77-.99845 -.27697 (77*2π)/2984 weeks
78-1.0794 -.08324 (78*2π)/2984 weeks
79-.58841 -.06395 (79*2π)/2984 weeks
80-.77733 -.1209 (80*2π)/2984 weeks
81-.73422 -.04879 (81*2π)/2984 weeks
82-.5562 .17802 (82*2π)/2984 weeks
83-.65326 .01506 (83*2π)/2984 weeks
84-.60423 -.04477 (84*2π)/2984 weeks
85-.46483 .07306 (85*2π)/2984 weeks
86-.27822 .21858 (86*2π)/2983 weeks
87-.33216 -.08572 (87*2π)/2983 weeks
88.00609 -.03879 (88*2π)/2983 weeks
89-.1438 -.21732 (89*2π)/2983 weeks
90-.21543 -.25973 (90*2π)/2983 weeks
91-.561 -.43887 (91*2π)/2983 weeks
92-.26936 -.03276 (92*2π)/2983 weeks
93-.58747 -.18595 (93*2π)/2983 weeks
94-.28011 -.00013 (94*2π)/2983 weeks
95-.01562 .02225 (95*2π)/2983 weeks
96-.07135 -.25448 (96*2π)/2983 weeks
97-.09631 -.30436 (97*2π)/2983 weeks
98-.25066 -.06125 (98*2π)/2983 weeks
99-.2653 -.23293 (99*2π)/2983 weeks
100-.15505 -.08487 (100*2π)/2983 weeks
101-.24778 -.26338 (101*2π)/2983 weeks
102-.45011 -.15773 (102*2π)/2983 weeks
103-.32196 -.43799 (103*2π)/2983 weeks
104-.55205 -.28254 (104*2π)/2983 weeks
105-.61648 -.04906 (105*2π)/2983 weeks
106-.22464 .00172 (106*2π)/2983 weeks
107-.51004 .01314 (107*2π)/2983 weeks
108-.38524 .07065 (108*2π)/2983 weeks
109-.54549 .07625 (109*2π)/2983 weeks
110-.40438 .23034 (110*2π)/2983 weeks
111-.16667 .36173 (111*2π)/2983 weeks
112-.02468 .07562 (112*2π)/2983 weeks
113.05762 -.12515 (113*2π)/2983 weeks
114-.07899 -.42294 (114*2π)/2983 weeks
115-.27735 -.20144 (115*2π)/2983 weeks
116-.16779 -.32191 (116*2π)/2983 weeks
117-.49128 -.35087 (117*2π)/2983 weeks
118-.24861 -.37758 (118*2π)/2983 weeks
119-.60533 -.27999 (119*2π)/2983 weeks
120-.47473 -.02267 (120*2π)/2982 weeks
121-.22712 .05164 (121*2π)/2982 weeks
122.03365 -.18071 (122*2π)/2982 weeks
123-.23569 -.38587 (123*2π)/2982 weeks
124-.36693 -.35967 (124*2π)/2982 weeks
125-.46329 -.2383 (125*2π)/2982 weeks
126-.59736 -.38549 (126*2π)/2982 weeks
127-.28341 -.37894 (127*2π)/2982 weeks
128-.54094 -.35412 (128*2π)/2982 weeks
129-.73439 -.36876 (129*2π)/2982 weeks
130-.95149 -.13001 (130*2π)/2982 weeks
131-.84301 .27528 (131*2π)/2982 weeks
132-.52315 .26204 (132*2π)/2982 weeks
133-.63437 .345 (133*2π)/2982 weeks
134-.44197 .36881 (134*2π)/2982 weeks
135-.50017 .53392 (135*2π)/2982 weeks
136.03999 .58935 (136*2π)/2982 weeks
137.13996 .2222 (137*2π)/2982 weeks
138.25504 .00866 (138*2π)/2982 weeks
139-.18578 -.25092 (139*2π)/2982 weeks
140-.37571 .02173 (140*2π)/2982 weeks
141-.21168 .12486 (141*2π)/2982 weeks
142-.22396 .29537 (142*2π)/2982 weeks
143.04568 -.06276 (143*2π)/2982 weeks
144-.37655 -.04307 (144*2π)/2982 weeks
145-.23598 .00769 (145*2π)/2982 weeks
146-.45471 .02265 (146*2π)/2982 weeks
147-.34199 .31685 (147*2π)/2982 weeks
148-.15149 .12518 (148*2π)/2982 weeks
149-.06087   (149*2π)/2982 weeks
150-.15149 -.12518 (150*2π)/2982 weeks
151-.34199 -.31685 (151*2π)/2982 weeks
152-.45471 -.02265 (152*2π)/2982 weeks
153-.23598 -.00769 (153*2π)/2982 weeks
154-.37655 .04307 (154*2π)/2982 weeks
155.04568 .06276 (155*2π)/2982 weeks
156-.22396 -.29537 (156*2π)/2982 weeks
157-.21168 -.12486 (157*2π)/2982 weeks
158-.37571 -.02173 (158*2π)/2982 weeks
159-.18578 .25092 (159*2π)/2982 weeks
160.25504 -.00866 (160*2π)/2982 weeks
161.13996 -.2222 (161*2π)/2982 weeks
162.03999 -.58935 (162*2π)/2982 weeks
163-.50017 -.53392 (163*2π)/2982 weeks
164-.44197 -.36881 (164*2π)/2982 weeks
165-.63437 -.345 (165*2π)/2982 weeks
166-.52315 -.26204 (166*2π)/2982 weeks
167-.84301 -.27528 (167*2π)/2982 weeks
168-.95149 .13001 (168*2π)/2982 weeks
169-.73439 .36876 (169*2π)/2982 weeks
170-.54094 .35412 (170*2π)/2982 weeks
171-.28341 .37894 (171*2π)/2982 weeks
172-.59736 .38549 (172*2π)/2982 weeks
173-.46329 .2383 (173*2π)/2982 weeks
174-.36693 .35967 (174*2π)/2982 weeks
175-.23569 .38587 (175*2π)/2982 weeks
176.03365 .18071 (176*2π)/2982 weeks
177-.22712 -.05164 (177*2π)/2982 weeks
178-.47473 .02267 (178*2π)/2982 weeks
179-.60533 .27999 (179*2π)/2982 weeks
180-.24861 .37758 (180*2π)/2982 weeks
181-.49128 .35087 (181*2π)/2982 weeks
182-.16779 .32191 (182*2π)/2982 weeks
183-.27735 .20144 (183*2π)/2982 weeks
184-.07899 .42294 (184*2π)/2982 weeks
185.05762 .12515 (185*2π)/2982 weeks
186-.02468 -.07562 (186*2π)/2982 weeks
187-.16667 -.36173 (187*2π)/2982 weeks
188-.40438 -.23034 (188*2π)/2982 weeks
189-.54549 -.07625 (189*2π)/2982 weeks
190-.38524 -.07065 (190*2π)/2982 weeks
191-.51004 -.01314 (191*2π)/2982 weeks
192-.22464 -.00172 (192*2π)/2982 weeks
193-.61648 .04906 (193*2π)/2982 weeks
194-.55205 .28254 (194*2π)/2982 weeks
195-.32196 .43799 (195*2π)/2982 weeks
196-.45011 .15773 (196*2π)/2982 weeks
197-.24778 .26338 (197*2π)/2982 weeks
198-.15505 .08487 (198*2π)/2982 weeks
199-.2653 .23293 (199*2π)/2981 weeks
200-.25066 .06125 (200*2π)/2981 weeks
201-.09631 .30436 (201*2π)/2981 weeks
202-.07135 .25448 (202*2π)/2981 weeks
203-.01562 -.02225 (203*2π)/2981 weeks
204-.28011 .00013 (204*2π)/2981 weeks
205-.58747 .18595 (205*2π)/2981 weeks
206-.26936 .03276 (206*2π)/2981 weeks
207-.561 .43887 (207*2π)/2981 weeks
208-.21543 .25973 (208*2π)/2981 weeks
209-.1438 .21732 (209*2π)/2981 weeks
210.00609 .03879 (210*2π)/2981 weeks
211-.33216 .08572 (211*2π)/2981 weeks
212-.27822 -.21858 (212*2π)/2981 weeks
213-.46483 -.07306 (213*2π)/2981 weeks
214-.60423 .04477 (214*2π)/2981 weeks
215-.65326 -.01506 (215*2π)/2981 weeks
216-.5562 -.17802 (216*2π)/2981 weeks
217-.73422 .04879 (217*2π)/2981 weeks
218-.77733 .1209 (218*2π)/2981 weeks
219-.58841 .06395 (219*2π)/2981 weeks
220-1.0794 .08324 (220*2π)/2981 weeks
221-.99845 .27697 (221*2π)/2981 weeks
222-.84603 .21094 (222*2π)/2981 weeks
223-.98689 .30478 (223*2π)/2981 weeks
224-.95869 .91021 (224*2π)/2981 weeks
225-.91884 .38471 (225*2π)/2981 weeks
226-.71558 .91548 (226*2π)/2981 weeks
227-.8238 .75358 (227*2π)/2981 weeks
228-.64697 1.29658 (228*2π)/2981 weeks
229-.38654 .89713 (229*2π)/2981 weeks
230-.53497 1.14124 (230*2π)/2981 weeks
231-.28319 .91993 (231*2π)/2981 weeks
232-.10451 1.09485 (232*2π)/2981 weeks
233.14075 1.05405 (233*2π)/2981 weeks
234.37019 .46724 (234*2π)/2981 weeks
235.22174 .46754 (235*2π)/2981 weeks
236.20439 .23229 (236*2π)/2981 weeks
237-.20654 .38382 (237*2π)/2981 weeks
238.52637 .27389 (238*2π)/2981 weeks
239-.10476 -.10864 (239*2π)/2981 weeks
240-.19825 .02733 (240*2π)/2981 weeks
241-.81693 .20847 (241*2π)/2981 weeks
242-.67385 .7009 (242*2π)/2981 weeks
243-.30579 .34748 (243*2π)/2981 weeks
244-.3389 .7035 (244*2π)/2981 weeks
245-.22397 .40308 (245*2π)/2981 weeks
246-.37941 .34083 (246*2π)/2981 weeks
247-.57316 .79045 (247*2π)/2981 weeks
248-.02957 .22825 (248*2π)/2981 weeks
249-.71723 .13819 (249*2π)/2981 weeks
250-.62768 .16239 (250*2π)/2981 weeks
251-1.78612 .08065 (251*2π)/2981 weeks
252-1.10661 1.27883 (252*2π)/2981 weeks
253-1.13737 1.24674 (253*2π)/2981 weeks
254-1.05015 1.41279 (254*2π)/2981 weeks
255-.82937 1.30236 (255*2π)/2981 weeks
256-.72324 1.47584 (256*2π)/2981 weeks
257-.72203 1.71256 (257*2π)/2981 weeks
258.15452 1.82238 (258*2π)/2981 weeks
259.65658 1.36989 (259*2π)/2981 weeks
260-.42349 .97989 (260*2π)/2981 weeks
261-.10879 1.34378 (261*2π)/2981 weeks
262.02788 1.64011 (262*2π)/2981 weeks
263.4891 1.55895 (263*2π)/2981 weeks
264.30706 1.4114 (264*2π)/2981 weeks
265.60794 .69844 (265*2π)/2981 weeks
266.34892 1.10726 (266*2π)/2981 weeks
267.55828 .7375 (267*2π)/2981 weeks
268.8105 1.0238 (268*2π)/2981 weeks
269.95727 .28023 (269*2π)/2981 weeks
270-.17139 .53704 (270*2π)/2981 weeks
271-.46322 .72005 (271*2π)/2981 weeks
272-.05464 1.18088 (272*2π)/2981 weeks
273-.36028 1.31677 (273*2π)/2981 weeks
274.32222 .58134 (274*2π)/2981 weeks
275-1.03784 .76385 (275*2π)/2981 weeks
276-1.07116 .76594 (276*2π)/2981 weeks
277-1.29019 1.97008 (277*2π)/2981 weeks
278.03505 1.68945 (278*2π)/2981 weeks
279.10701 1.22275 (279*2π)/2981 weeks
280-.13567 -.10185 (280*2π)/2981 weeks
281-2.35114 1.88325 (281*2π)/2981 weeks
282-1.12114 1.29241 (282*2π)/2981 weeks
283-2.24006 2.45791 (283*2π)/2981 weeks
284-2.2813 2.91667 (284*2π)/2981 weeks
285-.59741 2.45265 (285*2π)/2981 weeks
286-1.45454 2.22602 (286*2π)/2981 weeks
287-3.52737 5.68252 (287*2π)/2981 weeks
288-1.20431 5.25926 (288*2π)/2981 weeks
289-.04916 4.88996 (289*2π)/2981 weeks
290-.80762 3.91759 (290*2π)/2981 weeks
291-2.93322 5.80764 (291*2π)/2981 weeks
2922.90368 8.08833 (292*2π)/2981 weeks
293-1.4905 10.69855 (293*2π)/2981 weeks
2945.34533 14.8685 (294*2π)/2981 weeks
2954.96549 15.59678 (295*2π)/2981 weeks
29615.05064 18.38748 (296*2π)/2981 weeks