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Fourier Analysis of PEI (Pennsylvania Real Estate Invest)


PEI (Pennsylvania Real Estate Invest) appears to have interesting cyclic behaviour every 228 weeks (1.2481*sine), 152 weeks (1.0032*sine), and 207 weeks (.5961*sine).

PEI (Pennsylvania Real Estate Invest) has an average price of 6.92 (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 5/3/1973 to 1/9/2017 for PEI (Pennsylvania Real Estate Invest), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
06.91865   0 
11.81047 -6.661 (1*2π)/22802,280 weeks
2-.7469 -2.29156 (2*2π)/22801,140 weeks
31.56366 -.34879 (3*2π)/2280760 weeks
42.27498 -2.34054 (4*2π)/2280570 weeks
5-.23152 -3.21238 (5*2π)/2280456 weeks
6-1.0634 -1.33673 (6*2π)/2280380 weeks
7-.2269 -.23034 (7*2π)/2280326 weeks
8.35164 -.53624 (8*2π)/2280285 weeks
9.51896 -.98613 (9*2π)/2280253 weeks
10-.22892 -1.24812 (10*2π)/2280228 weeks
11-.40247 -.59612 (11*2π)/2280207 weeks
12-.29678 -.2747 (12*2π)/2280190 weeks
13.27151 -.06296 (13*2π)/2280175 weeks
14.4607 -.55307 (14*2π)/2280163 weeks
15.03947 -1.00321 (15*2π)/2280152 weeks
16-.41936 -.63574 (16*2π)/2280143 weeks
17-.39248 -.18361 (17*2π)/2280134 weeks
18-.06279 -.03863 (18*2π)/2280127 weeks
19.16075 -.1457 (19*2π)/2280120 weeks
20.0969 -.29623 (20*2π)/2280114 weeks
21.06134 -.30457 (21*2π)/2280109 weeks
22.17408 -.18252 (22*2π)/2280104 weeks
23.15239 -.43578 (23*2π)/228099 weeks
24.0016 -.39315 (24*2π)/228095 weeks
25-.01013 -.31051 (25*2π)/228091 weeks
26.10349 -.35194 (26*2π)/228088 weeks
27-.00103 -.40426 (27*2π)/228084 weeks
28-.16055 -.41066 (28*2π)/228081 weeks
29-.09468 -.17229 (29*2π)/228079 weeks
30.01199 -.22836 (30*2π)/228076 weeks
31-.00807 -.37259 (31*2π)/228074 weeks
32-.12123 -.27138 (32*2π)/228071 weeks
33-.12544 -.32858 (33*2π)/228069 weeks
34-.23758 -.18554 (34*2π)/228067 weeks
35-.13602 -.03792 (35*2π)/228065 weeks
36.03493 -.0643 (36*2π)/228063 weeks
37.0837 -.22034 (37*2π)/228062 weeks
38-.12221 -.23862 (38*2π)/228060 weeks
39-.07582 -.15096 (39*2π)/228058 weeks
40-.03339 -.12913 (40*2π)/228057 weeks
41-.00391 -.18743 (41*2π)/228056 weeks
42-.08408 -.19787 (42*2π)/228054 weeks
43-.17795 -.15297 (43*2π)/228053 weeks
44-.0617 .05675 (44*2π)/228052 weeks
45.07084 -.02462 (45*2π)/228051 weeks
46.14494 -.19462 (46*2π)/228050 weeks
47.03189 -.2744 (47*2π)/228049 weeks
48-.12959 -.28336 (48*2π)/228048 weeks
49-.17507 -.09247 (49*2π)/228047 weeks
50-.05666 -.07511 (50*2π)/228046 weeks
51-.08625 -.11296 (51*2π)/228045 weeks
52-.05945 -.04132 (52*2π)/228044 weeks
53.02011 -.10191 (53*2π)/228043 weeks
54-.05685 -.13014 (54*2π)/228042 weeks
55-.10813 -.11612 (55*2π)/228041 weeks
56-.03462 .00808 (56*2π)/228041 weeks
57.02643 -.11423 (57*2π)/228040 weeks
58-.06651 -.1514 (58*2π)/228039 weeks
59-.11735 -.06809 (59*2π)/228039 weeks
60-.0458 .05963 (60*2π)/228038 weeks
61.06528 -.07803 (61*2π)/228037 weeks
62-.01172 -.07617 (62*2π)/228037 weeks
63-.00917 -.07298 (63*2π)/228036 weeks
64.02358 -.09452 (64*2π)/228036 weeks
65-.01928 -.14384 (65*2π)/228035 weeks
66-.08855 -.08826 (66*2π)/228035 weeks
67-.07655 -.01873 (67*2π)/228034 weeks
68.01009 -.06782 (68*2π)/228034 weeks
69-.07259 -.03953 (69*2π)/228033 weeks
70-.01787 .01374 (70*2π)/228033 weeks
71.0814 .01645 (71*2π)/228032 weeks
72.11961 -.1244 (72*2π)/228032 weeks
73-.01472 -.20916 (73*2π)/228031 weeks
74-.12489 -.10227 (74*2π)/228031 weeks
75-.07927 .00739 (75*2π)/228030 weeks
76.01652 -.00087 (76*2π)/228030 weeks
77.01475 -.08427 (77*2π)/228030 weeks
78-.0202 -.03975 (78*2π)/228029 weeks
79.02375 -.0237 (79*2π)/228029 weeks
80.04506 -.0887 (80*2π)/228029 weeks
81-.00838 -.13933 (81*2π)/228028 weeks
82-.10065 -.07998 (82*2π)/228028 weeks
83-.06277 .02035 (83*2π)/228027 weeks
84.05141 .02721 (84*2π)/228027 weeks
85.05832 -.0747 (85*2π)/228027 weeks
86.02966 -.10251 (86*2π)/228027 weeks
87-.04225 -.07038 (87*2π)/228026 weeks
88-.00151 -.0544 (88*2π)/228026 weeks
89-.00003 -.04304 (89*2π)/228026 weeks
90.02903 -.09379 (90*2π)/228025 weeks
91-.01244 -.09841 (91*2π)/228025 weeks
92-.01761 -.08085 (92*2π)/228025 weeks
93-.0634 -.07949 (93*2π)/228025 weeks
94-.0396 -.03823 (94*2π)/228024 weeks
95-.01374 -.05716 (95*2π)/228024 weeks
96-.06762 -.06658 (96*2π)/228024 weeks
97-.06625 -.00865 (97*2π)/228024 weeks
98-.01956 .02403 (98*2π)/228023 weeks
99.00237 -.00972 (99*2π)/228023 weeks
100-.01549 -.0118 (100*2π)/228023 weeks
101.02953 -.00387 (101*2π)/228023 weeks
102-.00048 -.03588 (102*2π)/228022 weeks
103-.0111 .00271 (103*2π)/228022 weeks
104.04397 .00021 (104*2π)/228022 weeks
105.04581 -.03056 (105*2π)/228022 weeks
106.02386 -.05315 (106*2π)/228022 weeks
107-.01446 -.03971 (107*2π)/228021 weeks
108.0152 .03253 (108*2π)/228021 weeks
109.09474 -.00868 (109*2π)/228021 weeks
110.08687 -.08749 (110*2π)/228021 weeks
111.02568 -.09874 (111*2π)/228021 weeks
112-.00026 -.06704 (112*2π)/228020 weeks
113.00007 -.03664 (113*2π)/228020 weeks
114.03537 -.04411 (114*2π)/228020 weeks
115.04085 -.06258 (115*2π)/228020 weeks
116.01122 -.07258 (116*2π)/228020 weeks
117.01146 -.03801 (117*2π)/228019 weeks
118.05246 -.03975 (118*2π)/228019 weeks
119.06014 -.08348 (119*2π)/228019 weeks
120.02146 -.09949 (120*2π)/228019 weeks
121.00842 -.11466 (121*2π)/228019 weeks
122-.02189 -.09356 (122*2π)/228019 weeks
123-.02448 -.05034 (123*2π)/228019 weeks
124.00405 -.04173 (124*2π)/228018 weeks
125.02095 -.05982 (125*2π)/228018 weeks
126.02373 -.08618 (126*2π)/228018 weeks
127-.00589 -.09779 (127*2π)/228018 weeks
128-.02982 -.08196 (128*2π)/228018 weeks
129-.0252 -.05784 (129*2π)/228018 weeks
130-.01397 -.05481 (130*2π)/228018 weeks
131.00999 -.04955 (131*2π)/228017 weeks
132.00796 -.08909 (132*2π)/228017 weeks
133-.02926 -.09237 (133*2π)/228017 weeks
134-.06711 -.06361 (134*2π)/228017 weeks
135-.01929 .00017 (135*2π)/228017 weeks
136.03913 -.04884 (136*2π)/228017 weeks
137.00915 -.11073 (137*2π)/228017 weeks
138-.07903 -.10729 (138*2π)/228017 weeks
139-.07493 -.01338 (139*2π)/228016 weeks
140-.02828 -.00295 (140*2π)/228016 weeks
141.0108 .00054 (141*2π)/228016 weeks
142.0378 -.05917 (142*2π)/228016 weeks
143-.00069 -.09206 (143*2π)/228016 weeks
144-.06153 -.07562 (144*2π)/228016 weeks
145-.0343 -.01193 (145*2π)/228016 weeks
146-.00723 -.01862 (146*2π)/228016 weeks
147.01174 -.05448 (147*2π)/228016 weeks
148-.02904 -.06124 (148*2π)/228015 weeks
149-.02507 -.04161 (149*2π)/228015 weeks
150-.0365 -.02013 (150*2π)/228015 weeks
151-.00335 -.01533 (151*2π)/228015 weeks
152.01238 -.0398 (152*2π)/228015 weeks
153-.00538 -.05621 (153*2π)/228015 weeks
154-.02325 -.05159 (154*2π)/228015 weeks
155-.02216 -.03643 (155*2π)/228015 weeks
156-.01896 -.03612 (156*2π)/228015 weeks
157-.01434 -.02534 (157*2π)/228015 weeks
158-.00105 -.04851 (158*2π)/228014 weeks
159-.03647 -.05084 (159*2π)/228014 weeks
160-.04423 -.01995 (160*2π)/228014 weeks
161-.01409 .00967 (161*2π)/228014 weeks
162.02545 -.01142 (162*2π)/228014 weeks
163.00765 -.04739 (163*2π)/228014 weeks
164-.0113 -.05134 (164*2π)/228014 weeks
165-.01793 -.0305 (165*2π)/228014 weeks
166-.01009 -.02234 (166*2π)/228014 weeks
167.00018 -.02288 (167*2π)/228014 weeks
168.01363 -.04137 (168*2π)/228014 weeks
169-.01283 -.04714 (169*2π)/228013 weeks
170-.00988 -.04146 (170*2π)/228013 weeks
171-.02992 -.03725 (171*2π)/228013 weeks
172-.03699 .01014 (172*2π)/228013 weeks
173.04868 .01168 (173*2π)/228013 weeks
174.03553 -.06288 (174*2π)/228013 weeks
175-.00938 -.0642 (175*2π)/228013 weeks
176-.01029 -.0293 (176*2π)/228013 weeks
177.01464 -.02647 (177*2π)/228013 weeks
178.02152 -.07251 (178*2π)/228013 weeks
179-.03113 -.05998 (179*2π)/228013 weeks
180-.02382 -.02791 (180*2π)/228013 weeks
181-.00644 -.02116 (181*2π)/228013 weeks
182.00753 -.03203 (182*2π)/228013 weeks
183.00859 -.04726 (183*2π)/228012 weeks
184.00113 -.05579 (184*2π)/228012 weeks
185-.01899 -.06237 (185*2π)/228012 weeks
186-.01783 -.04269 (186*2π)/228012 weeks
187-.01749 -.03839 (187*2π)/228012 weeks
188-.01499 -.05721 (188*2π)/228012 weeks
189-.03711 -.04722 (189*2π)/228012 weeks
190-.03113 -.01746 (190*2π)/228012 weeks
191-.00735 -.02826 (191*2π)/228012 weeks
192-.0074 -.04451 (192*2π)/228012 weeks
193-.02079 -.04662 (193*2π)/228012 weeks
194-.03918 -.04553 (194*2π)/228012 weeks
195-.05043 -.02625 (195*2π)/228012 weeks
196-.04592 -.00432 (196*2π)/228012 weeks
197-.01142 .01502 (197*2π)/228012 weeks
198.00079 -.01605 (198*2π)/228012 weeks
199-.01848 -.01784 (199*2π)/228011 weeks
200.00431 .01543 (200*2π)/228011 weeks
201.0405 -.01563 (201*2π)/228011 weeks
202.01517 -.05941 (202*2π)/228011 weeks
203-.01341 -.04884 (203*2π)/228011 weeks
204-.00538 -.0359 (204*2π)/228011 weeks
205-.01824 -.03283 (205*2π)/228011 weeks
206.00008 -.03864 (206*2π)/228011 weeks
207-.0242 -.04089 (207*2π)/228011 weeks
208-.0322 -.0257 (208*2π)/228011 weeks
209-.01486 -.00792 (209*2π)/228011 weeks
210-.00178 -.01753 (210*2π)/228011 weeks
211-.00027 -.01761 (211*2π)/228011 weeks
212.00187 -.03285 (212*2π)/228011 weeks
213-.00415 -.02762 (213*2π)/228011 weeks
214.00783 -.027 (214*2π)/228011 weeks
215.00479 -.04806 (215*2π)/228011 weeks
216-.00468 -.06026 (216*2π)/228011 weeks
217-.04361 -.0533 (217*2π)/228011 weeks
218-.03289 -.01746 (218*2π)/228010 weeks
219-.01604 -.01346 (219*2π)/228010 weeks
220-.00482 -.03603 (220*2π)/228010 weeks
221-.02463 -.03668 (221*2π)/228010 weeks
222-.02679 -.02255 (222*2π)/228010 weeks
223-.02398 -.00339 (223*2π)/228010 weeks
224.0175 -.02467 (224*2π)/228010 weeks
225-.01156 -.06045 (225*2π)/228010 weeks
226-.04204 -.03798 (226*2π)/228010 weeks
227-.02439 -.00384 (227*2π)/228010 weeks
228-.01189 -.02912 (228*2π)/228010 weeks
229-.015 -.02388 (229*2π)/228010 weeks
230-.01524 -.03704 (230*2π)/228010 weeks
231-.02443 -.04474 (231*2π)/228010 weeks
232-.05474