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# Fourier Analysis of BRE (BRE Properties, Inc. Common Sto)

BRE (BRE Properties, Inc. Common Sto) appears to have interesting cyclic behaviour every 233 weeks (9.6832*cosine), 155 weeks (6.9386*sine), and 166 weeks (5.9988*sine).

BRE (BRE Properties, Inc. Common Sto) has an average price of 57.01 (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.

## Fourier Analysis

Using data from 6/1/1972 to 1/9/2017 for BRE (BRE Properties, Inc. Common Sto), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
057.00551   0
118.60036 -79.32625 (1*2π)/23262,326 weeks
2-25.32375 -33.95377 (2*2π)/23261,163 weeks
3-22.10794 -11.25559 (3*2π)/2326775 weeks
4-16.06347 -2.53054 (4*2π)/2326582 weeks
5-16.36676 -1.65021 (5*2π)/2326465 weeks
6-19.66491 9.0907 (6*2π)/2326388 weeks
7-9.05154 21.09361 (7*2π)/2326332 weeks
86.70994 20.23426 (8*2π)/2326291 weeks
916.37796 7.58158 (9*2π)/2326258 weeks
109.6832 -3.7421 (10*2π)/2326233 weeks
114.61378 -2.71288 (11*2π)/2326211 weeks
122.93026 -2.45319 (12*2π)/2326194 weeks
134.10023 -1.77003 (13*2π)/2326179 weeks
143.68602 -5.99879 (14*2π)/2326166 weeks
15-1.45575 -6.93864 (15*2π)/2326155 weeks
16-3.83097 -3.93622 (16*2π)/2326145 weeks
17-4.38891 -2.01313 (17*2π)/2326137 weeks
18-4.65223 -.14909 (18*2π)/2326129 weeks
19-4.05036 1.59298 (19*2π)/2326122 weeks
20-3.08103 3.33111 (20*2π)/2326116 weeks
21-.55845 3.99657 (21*2π)/2326111 weeks
22.73027 2.83066 (22*2π)/2326106 weeks
23.46152 2.22864 (23*2π)/2326101 weeks
241.41858 3.36757 (24*2π)/232697 weeks
254.04252 2.50852 (25*2π)/232693 weeks
265.18138 -.19389 (26*2π)/232689 weeks
274.11568 -3.56148 (27*2π)/232686 weeks
28.77097 -5.08514 (28*2π)/232683 weeks
29-2.17829 -3.18556 (29*2π)/232680 weeks
30-1.84201 -1.27176 (30*2π)/232678 weeks
31-1.78058 -1.02709 (31*2π)/232675 weeks
32-1.74656 -.41217 (32*2π)/232673 weeks
33-2.09278 -.70457 (33*2π)/232670 weeks
34-3.71162 .90106 (34*2π)/232668 weeks
35-1.97385 3.79642 (35*2π)/232666 weeks
36.97163 3.37457 (36*2π)/232665 weeks
371.90143 1.74082 (37*2π)/232663 weeks
381.64031 .47015 (38*2π)/232661 weeks
39.9686 .73813 (39*2π)/232660 weeks
402.08515 .7769 (40*2π)/232658 weeks
412.51703 -.90109 (41*2π)/232657 weeks
421.66589 -1.93293 (42*2π)/232655 weeks
43.67655 -2.64924 (43*2π)/232654 weeks
44-1.12807 -2.75253 (44*2π)/232653 weeks
45-2.31681 -1.23453 (45*2π)/232652 weeks
46-1.96728 .25811 (46*2π)/232651 weeks
47-1.15745 .46285 (47*2π)/232649 weeks
48-.97526 .67016 (48*2π)/232648 weeks
49-.95492 .52855 (49*2π)/232647 weeks
50-1.14289 1.46232 (50*2π)/232647 weeks
51-.0255 2.07207 (51*2π)/232646 weeks
521.08625 1.71465 (52*2π)/232645 weeks
531.63586 .93943 (53*2π)/232644 weeks
541.80065 -.08655 (54*2π)/232643 weeks
551.20529 -.65553 (55*2π)/232642 weeks
56.88677 -.76013 (56*2π)/232642 weeks
57.94824 -.88889 (57*2π)/232641 weeks
58.76343 -1.8774 (58*2π)/232640 weeks
59-.82232 -2.27465 (59*2π)/232639 weeks
60-2.00784 -1.07543 (60*2π)/232639 weeks
61-1.8531 .18165 (61*2π)/232638 weeks
62-1.19354 .69144 (62*2π)/232638 weeks
63-1.00822 .76257 (63*2π)/232637 weeks
64-.87744 1.23253 (64*2π)/232636 weeks
65-.09696 1.86509 (65*2π)/232636 weeks
661.03993 1.43538 (66*2π)/232635 weeks
671.24528 .45301 (67*2π)/232635 weeks
68.9022 .2336 (68*2π)/232634 weeks
691.3688 .08838 (69*2π)/232634 weeks
701.13493 -.86786 (70*2π)/232633 weeks
71.5991 -.93543 (71*2π)/232633 weeks
72.34458 -1.19719 (72*2π)/232632 weeks
73-.25155 -1.32269 (73*2π)/232632 weeks
74-.79606 -1.13676 (74*2π)/232631 weeks
75-1.44033 -.62211 (75*2π)/232631 weeks
76-1.38605 .22628 (76*2π)/232631 weeks
77-1.12545 .61212 (77*2π)/232630 weeks
78-.85292 1.1528 (78*2π)/232630 weeks
79-.28805 1.43445 (79*2π)/232629 weeks
80.54732 1.63101 (80*2π)/232629 weeks
811.50674 .76731 (81*2π)/232629 weeks
821.19672 -.27702 (82*2π)/232628 weeks
83.50686 -.42556 (83*2π)/232628 weeks
84.43895 -.08508 (84*2π)/232628 weeks
85.83792 -.28041 (85*2π)/232627 weeks
86.80737 -1.02965 (86*2π)/232627 weeks
87-.15419 -1.4602 (87*2π)/232627 weeks
88-.91547 -.92458 (88*2π)/232626 weeks
89-.97908 -.25902 (89*2π)/232626 weeks
90-.90172 .03395 (90*2π)/232626 weeks
91-.59721 .3714 (91*2π)/232626 weeks
92-.68375 .17857 (92*2π)/232625 weeks
93-.76262 .74079 (93*2π)/232625 weeks
94-.32658 1.13265 (94*2π)/232625 weeks
95.34464 1.39124 (95*2π)/232624 weeks
961.0871 .865 (96*2π)/232624 weeks
971.24474 .19478 (97*2π)/232624 weeks
981.12976 -.31449 (98*2π)/232624 weeks
99.85657 -.70646 (99*2π)/232623 weeks
100.5596 -.94664 (100*2π)/232623 weeks
101.08935 -1.21522 (101*2π)/232623 weeks
102-.53051 -1.19277 (102*2π)/232623 weeks
103-1.1563 -.75948 (103*2π)/232623 weeks
104-1.37962 .02482 (104*2π)/232622 weeks
105-1.01153 .79091 (105*2π)/232622 weeks
106-.14343 .92849 (106*2π)/232622 weeks
107.0119 .36418 (107*2π)/232622 weeks
108-.22199 .49144 (108*2π)/232622 weeks
109-.12635 .72069 (109*2π)/232621 weeks
110.34223 1.11648 (110*2π)/232621 weeks
1111.27365 .65585 (111*2π)/232621 weeks
1121.26692 -.3445 (112*2π)/232621 weeks
113.65808 -.79478 (113*2π)/232621 weeks
114.25342 -.657 (114*2π)/232620 weeks
115.21072 -.70129 (115*2π)/232620 weeks
116-.06769 -.98458 (116*2π)/232620 weeks
117-.67303 -.90833 (117*2π)/232620 weeks
118-1.17861 -.42623 (118*2π)/232620 weeks
119-1.22378 .3989 (119*2π)/232620 weeks
120-.62426 .99343 (120*2π)/232619 weeks
121.09405 .84177 (121*2π)/232619 weeks
122.17192 .45419 (122*2π)/232619 weeks
123.26092 .49592 (123*2π)/232619 weeks
124.38165 .24719 (124*2π)/232619 weeks
125.19953 .22483 (125*2π)/232619 weeks
126.46214 .44499 (126*2π)/232618 weeks
1271.00037 .00091 (127*2π)/232618 weeks
128.68293 -.72959 (128*2π)/232618 weeks
129.08808 -.73445 (129*2π)/232618 weeks
130-.00467 -.61475 (130*2π)/232618 weeks
131-.3542 -.67456 (131*2π)/232618 weeks
132-.54048 -.28778 (132*2π)/232618 weeks
133-.47888 -.20209 (133*2π)/232617 weeks
134-.65283 -.12806 (134*2π)/232617 weeks
135-.7823 .22488 (135*2π)/232617 weeks
136-.73674 .59611 (136*2π)/232617 weeks
137-.4754 1.23574 (137*2π)/232617 weeks
138.65241 1.45149 (138*2π)/232617 weeks
1391.45337 .41066 (139*2π)/232617 weeks
140.91503 -.58836 (140*2π)/232617 weeks
141.16879 -.5494 (141*2π)/232616 weeks
142.08496 -.11819 (142*2π)/232616 weeks
143.42265 -.11725 (143*2π)/232616 weeks
144.46696 -.61889 (144*2π)/232616 weeks
145-.06229 -.98719 (145*2π)/232616 weeks
146-.69242 -.7482 (146*2π)/232616 weeks
147-.96495 -.18557 (147*2π)/232616 weeks
148-.75884 .37501 (148*2π)/232616 weeks
149-.37597 .4765 (149*2π)/232616 weeks
150-.31826 .4453 (150*2π)/232616 weeks
151-.17577 .69905 (151*2π)/232615 weeks
152.24572 .72859 (152*2π)/232615 weeks
153.53788 .54653 (153*2π)/232615 weeks
154.78097 .20574 (154*2π)/232615 weeks
155.68162 -.21898 (155*2π)/232615 weeks
156.53933 -.37445 (156*2π)/232615 weeks
157.32353 -.70344 (157*2π)/232615 weeks
158-.1876 -.61023 (158*2π)/232615 weeks
159-.17747 -.37265 (159*2π)/232615 weeks
160-.34304 -.415 (160*2π)/232615 weeks
161-.47992 -.23729 (161*2π)/232614 weeks
162-.60333 -.05073 (162*2π)/232614 weeks
163-.60464 .29978 (163*2π)/232614 weeks
164-.33675 .53275 (164*2π)/232614 weeks
165-.04336 .57796 (165*2π)/232614 weeks
166.10253 .44256 (166*2π)/232614 weeks
167.18947 .50661 (167*2π)/232614 weeks
168.48625 .43124 (168*2π)/232614 weeks
169.67493 .19677 (169*2π)/232614 weeks
170.8269 -.17625 (170*2π)/232614 weeks
171.59846 -.66284 (171*2π)/232614 weeks
172.07673 -.86353 (172*2π)/232614 weeks
173-.28324 -.62287 (173*2π)/232613 weeks
174-.4952 -.56051 (174*2π)/232613 weeks
175-.86464 -.11611 (175*2π)/232613 weeks
176-.5635 .3919 (176*2π)/232613 weeks
177-.25729 .45107 (177*2π)/232613 weeks
178-.08256 .33637 (178*2π)/232613 weeks
179-.05651 .47183 (179*2π)/232613 weeks
180.32613 .36593 (180*2π)/232613 weeks
181.24951 .0111 (181*2π)/232613 weeks
182.06722 .15883 (182*2π)/232613 weeks
183.34495 .11933 (183*2π)/232613 weeks
184.22943 -.16195 (184*2π)/232613 weeks
185.08471 -.0058 (185*2π)/232613 weeks
186.29134 .00289 (186*2π)/232613 weeks
187.37201 -.27468 (187*2π)/232612 weeks
188.16539 -.5448 (188*2π)/232612 weeks
189-.23468 -.61896 (189*2π)/232612 weeks
190-.61157 -.33278 (190*2π)/232612 weeks
191-.52966 .10191 (191*2π)/232612 weeks
192-.43728 .15704 (192*2π)/232612 weeks
193-.43792 .45071 (193*2π)/232612 weeks
194-.05594 .65689 (194*2π)/232612 weeks
195.32414 .48145 (195*2π)/232612 weeks
196.39774 .19029 (196*2π)/232612 weeks
197.34898 .00815 (197*2π)/232612 weeks
198.24673 -.04727 (198*2π)/232612 weeks
199.26228 -.05892 (199*2π)/232612 weeks
200.2883 -.16453 (200*2π)/232612 weeks
201.24585 -.36656 (201*2π)/232612 weeks
202-.00137 -.46178 (202*2π)/232612 weeks
203-.29654 -.402 (203*2π)/232611 weeks
204-.33645 -.05424 (204*2π)/232611 weeks
205-.16337 -.08856 (205*2π)/232611 weeks
206-.43382 -.12747 (206*2π)/232611 weeks
207-.47654 .26031 (207*2π)/232611 weeks
208-.20988 .46326 (208*2π)/232611 weeks
209.02932 .51351 (209*2π)/232611 weeks
210.2872 .34875 (210*2π)/232611 weeks
211.31434 .17635 (211*2π)/232611 weeks