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# Fourier Analysis of PEI (Pennsylvania Real Estate Invest)

PEI (Pennsylvania Real Estate Invest) appears to have interesting cyclic behaviour every 229 weeks (1.1711*sine), 153 weeks (.968*sine), and 164 weeks (.6766*sine).

PEI (Pennsylvania Real Estate Invest) has an average price of 6.87 (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 3/20/2017 for PEI (Pennsylvania Real Estate Invest), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
06.87164   0
11.76835 -6.62146 (1*2π)/22902,290 weeks
2-.71677 -2.25049 (2*2π)/22901,145 weeks
31.61334 -.4577 (3*2π)/2290763 weeks
42.12924 -2.50125 (4*2π)/2290573 weeks
5-.46596 -3.14734 (5*2π)/2290458 weeks
6-1.11572 -1.17532 (6*2π)/2290382 weeks
7-.16189 -.1899 (7*2π)/2290327 weeks
8.3542 -.59664 (8*2π)/2290286 weeks
9.40832 -1.05854 (9*2π)/2290254 weeks
10-.38155 -1.17114 (10*2π)/2290229 weeks
11-.42866 -.47868 (11*2π)/2290208 weeks
12-.2416 -.20384 (12*2π)/2290191 weeks
13.33452 -.14436 (13*2π)/2290176 weeks
14.35887 -.67657 (14*2π)/2290164 weeks
15-.17797 -.96803 (15*2π)/2290153 weeks
16-.5091 -.45604 (16*2π)/2290143 weeks
17-.32418 -.04146 (17*2π)/2290135 weeks
18.04079 -.03054 (18*2π)/2290127 weeks
19.1944 -.22031 (19*2π)/2290121 weeks
20.06477 -.34644 (20*2π)/2290115 weeks
21.02508 -.33448 (21*2π)/2290109 weeks
22.14581 -.26414 (22*2π)/2290104 weeks
23.01753 -.48744 (23*2π)/2290100 weeks
24-.11136 -.37033 (24*2π)/229095 weeks
25-.08519 -.29027 (25*2π)/229092 weeks
26-.01071 -.36406 (26*2π)/229088 weeks
27-.14395 -.35163 (27*2π)/229085 weeks
28-.26509 -.27401 (28*2π)/229082 weeks
29-.09256 -.09521 (29*2π)/229079 weeks
30-.03951 -.21294 (30*2π)/229076 weeks
31-.13305 -.30799 (31*2π)/229074 weeks
32-.18419 -.14915 (32*2π)/229072 weeks
33-.19281 -.18528 (33*2π)/229069 weeks
34-.193 -.00765 (34*2π)/229067 weeks
35-.01785 .02885 (35*2π)/229065 weeks
36.08327 -.10935 (36*2π)/229064 weeks
37.00272 -.24311 (37*2π)/229062 weeks
38-.1715 -.12645 (38*2π)/229060 weeks
39-.05885 -.08096 (39*2π)/229059 weeks
40-.02191 -.09673 (40*2π)/229057 weeks
41-.04376 -.15025 (41*2π)/229056 weeks
42-.10936 -.09388 (42*2π)/229055 weeks
43-.11642 -.01058 (43*2π)/229053 weeks
44.09961 .04147 (44*2π)/229052 weeks
45.10032 -.14232 (45*2π)/229051 weeks
46.00809 -.2794 (46*2π)/229050 weeks
47-.13692 -.20368 (47*2π)/229049 weeks
48-.21256 -.07488 (48*2π)/229048 weeks
49-.07771 .07018 (49*2π)/229047 weeks
50.01485 -.03177 (50*2π)/229046 weeks
51-.03917 -.04365 (51*2π)/229045 weeks
52.02546 -.02393 (52*2π)/229044 weeks
53.01701 -.11681 (53*2π)/229043 weeks
54-.05953 -.06205 (54*2π)/229042 weeks
55-.05124 -.02297 (55*2π)/229042 weeks
56.07592 -.01704 (56*2π)/229041 weeks
57-.0041 -.13749 (57*2π)/229040 weeks
58-.07307 -.05962 (58*2π)/229039 weeks
59-.00618 .01635 (59*2π)/229039 weeks
60.11161 -.00757 (60*2π)/229038 weeks
61.03555 -.17355 (61*2π)/229038 weeks
62-.01807 -.0789 (62*2π)/229037 weeks
63-.00827 -.08417 (63*2π)/229036 weeks
64-.01222 -.10882 (64*2π)/229036 weeks
65-.06345 -.07727 (65*2π)/229035 weeks
66-.02809 .00352 (66*2π)/229035 weeks
67.03685 -.01061 (67*2π)/229034 weeks
68.03031 -.10783 (68*2π)/229034 weeks
69.00913 -.02432 (69*2π)/229033 weeks
70.07308 -.07688 (70*2π)/229033 weeks
71.06685 -.155 (71*2π)/229032 weeks
72-.06593 -.19319 (72*2π)/229032 weeks
73-.14723 -.05874 (73*2π)/229031 weeks
74-.03617 .0567 (74*2π)/229031 weeks
75.07425 -.00346 (75*2π)/229031 weeks
76.05737 -.10688 (76*2π)/229030 weeks
77-.02824 -.11123 (77*2π)/229030 weeks
78.00645 -.05445 (78*2π)/229029 weeks
79.0162 -.09532 (79*2π)/229029 weeks
80-.04636 -.11145 (80*2π)/229029 weeks
81-.07557 -.05017 (81*2π)/229028 weeks
82-.01085 .02591 (82*2π)/229028 weeks
83.07997 -.03614 (83*2π)/229028 weeks
84.05669 -.13999 (84*2π)/229027 weeks
85-.05957 -.13084 (85*2π)/229027 weeks
86-.06129 -.0725 (86*2π)/229027 weeks
87-.03162 -.01107 (87*2π)/229026 weeks
88-.00349 -.06661 (88*2π)/229026 weeks
89-.01228 -.06128 (89*2π)/229026 weeks
90-.04906 -.08325 (90*2π)/229025 weeks
91-.04069 -.0271 (91*2π)/229025 weeks
92-.01142 -.023 (92*2π)/229025 weeks
93-.01059 -.0018 (93*2π)/229025 weeks
94.03138 -.03899 (94*2π)/229024 weeks
95.00592 -.05881 (95*2π)/229024 weeks
96.00297 -.01643 (96*2π)/229024 weeks
97.05887 -.04391 (97*2π)/229024 weeks
98.05452 -.09437 (98*2π)/229023 weeks
99-.0005 -.10316 (99*2π)/229023 weeks
100-.00412 -.08094 (100*2π)/229023 weeks
101-.0002 -.1106 (101*2π)/229023 weeks
102-.03328 -.07184 (102*2π)/229022 weeks
103.00204 -.07495 (103*2π)/229022 weeks
104-.02106 -.1191 (104*2π)/229022 weeks
105-.05548 -.08802 (105*2π)/229022 weeks
106-.05676 -.05772 (106*2π)/229022 weeks
107-.02811 -.04385 (107*2π)/229021 weeks
108.00521 -.09102 (108*2π)/229021 weeks
109-.07713 -.1271 (109*2π)/229021 weeks
110-.1211 -.05695 (110*2π)/229021 weeks
111-.07503 .00476 (111*2π)/229021 weeks
112-.02718 -.00578 (112*2π)/229020 weeks
113-.01886 -.03192 (113*2π)/229020 weeks
114-.04522 -.0584 (114*2π)/229020 weeks
115-.05722 -.03666 (115*2π)/229020 weeks
116-.048 -.01007 (116*2π)/229020 weeks
117-.02219 -.02881 (117*2π)/229020 weeks
118-.05078 -.0492 (118*2π)/229019 weeks
119-.07916 -.01423 (119*2π)/229019 weeks
120-.05533 .02715 (120*2π)/229019 weeks
121-.03576 .01983 (121*2π)/229019 weeks
122.00433 .01936 (122*2π)/229019 weeks
123.02059 -.01112 (123*2π)/229019 weeks
124-.00993 -.03484 (124*2π)/229018 weeks
125-.03505 -.02271 (125*2π)/229018 weeks
126-.03721 -.00165 (126*2π)/229018 weeks
127-.01334 .0212 (127*2π)/229018 weeks
128.01388 .00933 (128*2π)/229018 weeks
129.01775 -.01876 (129*2π)/229018 weeks
130.00041 -.02759 (130*2π)/229018 weeks
131-.0076 -.02986 (131*2π)/229017 weeks
132-.02328 -.00013 (132*2π)/229017 weeks
133.01498 .01436 (133*2π)/229017 weeks
134.04032 -.00983 (134*2π)/229017 weeks
135.02812 -.07258 (135*2π)/229017 weeks
136-.04707 -.04518 (136*2π)/229017 weeks
137-.02477 .02379 (137*2π)/229017 weeks
138.04691 .02799 (138*2π)/229017 weeks
139.07364 -.0659 (139*2π)/229016 weeks
140-.00233 -.08534 (140*2π)/229016 weeks
141-.02993 -.06543 (141*2π)/229016 weeks
142-.05766 -.02093 (142*2π)/229016 weeks
143-.00764 .01776 (143*2π)/229016 weeks
144.03913 -.00054 (144*2π)/229016 weeks
145.03342 -.07073 (145*2π)/229016 weeks
146-.01891 -.05152 (146*2π)/229016 weeks
147-.02989 -.02701 (147*2π)/229016 weeks
148.00871 -.00643 (148*2π)/229015 weeks
149.01383 -.04237 (149*2π)/229015 weeks
150.00801 -.04239 (150*2π)/229015 weeks
151-.02324 -.05383 (151*2π)/229015 weeks
152-.03093 -.02526 (152*2π)/229015 weeks
153-.00719 -.0076 (153*2π)/229015 weeks
154.00913 -.02058 (154*2π)/229015 weeks
155.00626 -.03861 (155*2π)/229015 weeks
156-.00521 -.03717 (156*2π)/229015 weeks
157-.00604 -.03792 (157*2π)/229015 weeks
158-.01876 -.02721 (158*2π)/229014 weeks
159.01063 -.02067 (159*2π)/229014 weeks
160.00651 -.05542 (160*2π)/229014 weeks
161-.02502 -.06481 (161*2π)/229014 weeks
162-.05197 -.02985 (162*2π)/229014 weeks
163-.02498 .0078 (163*2π)/229014 weeks
164.00022 -.01183 (164*2π)/229014 weeks
165.0039 -.03336 (165*2π)/229014 weeks
166-.01375 -.03376 (166*2π)/229014 weeks
167-.02118 -.025 (167*2π)/229014 weeks
168-.02086 -.01375 (168*2π)/229014 weeks
169.00527 -.00791 (169*2π)/229014 weeks
170-.0002 -.03055 (170*2π)/229013 weeks
171.00258 -.02964 (171*2π)/229013 weeks
172-.01003 -.05053 (172*2π)/229013 weeks
173-.06661 -.03522 (173*2π)/229013 weeks
174-.02659 .04312 (174*2π)/229013 weeks
175.02807 .00412 (175*2π)/229013 weeks
176.01352 -.03545 (176*2π)/229013 weeks
177-.01293 -.02049 (177*2π)/229013 weeks
178-.00382 .00533 (178*2π)/229013 weeks
179.04232 -.01787 (179*2π)/229013 weeks
180.0057 -.05148 (180*2π)/229013 weeks
181-.01574 -.03244 (181*2π)/229013 weeks
182-.01484 -.01406 (182*2π)/229013 weeks
183.0004 -.00761 (183*2π)/229013 weeks
184.01426 -.01449 (184*2π)/229012 weeks
185.0198 -.02463 (185*2π)/229012 weeks
186.01128 -.04674 (186*2π)/229012 weeks
187.00115 -.03521 (187*2π)/229012 weeks
188-.00334 -.02976 (188*2π)/229012 weeks
189.01091 -.04512 (189*2π)/229012 weeks
190-.0113 -.05521 (190*2π)/229012 weeks
191-.02842 -.02903 (191*2π)/229012 weeks
192-.00664 -.02136 (192*2π)/229012 weeks
193.00551 -.03296 (193*2π)/229012 weeks
194-.00041 -.04284 (194*2π)/229012 weeks
195-.01601 -.05543 (195*2π)/229012 weeks
196-.03862 -.04946 (196*2π)/229012 weeks
197-.05281 -.03044 (197*2π)/229012 weeks
198-.03639 .00749 (198*2π)/229012 weeks
199-.01113 -.00893 (199*2π)/229012 weeks
200-.02709 -.02025 (200*2π)/229011 weeks
201-.02329 .02217 (201*2π)/229011 weeks
202.02468 .01696 (202*2π)/229011 weeks
203.02615 -.03223 (203*2π)/229011 weeks
204-.0016 -.03872 (204*2π)/229011 weeks
205.00082 -.02648 (205*2π)/229011 weeks
206-.01337 -.02765 (206*2π)/229011 weeks
207.0061 -.02786 (207*2π)/229011 weeks
208-.01486 -.03884 (208*2π)/229011 weeks
209-.02986 -.02889 (209*2π)/229011 weeks
210-.02101 -.00594 (210*2π)/229011 weeks
211-.0061 -.00932 (211*2π)/229011 weeks
212-.00356 -.00753 (212*2π)/229011 weeks
213.00297 -.02145 (213*2π)/229011 weeks
214-.00352 -.01821 (214*2π)/229011 weeks
215.00849 -.01431 (215*2π)/229011 weeks
216.0111 -.03525 (216*2π)/229011 weeks
217.00556 -.05097 (217*2π)/229011 weeks
218-.03477 -.05304 (218*2π)/229011 weeks
219-.03238 -.01669 (219*2π)/229010 weeks
220-.01725 -.00842 (220*2π)/229010 weeks
221-.00286 -.02858 (221*2π)/229010 weeks
222-.02202 -.03195 (222*2π)/229010 weeks
223-.02619 -.01831 (223*2π)/229010 weeks
224-.02547 .00188 (224*2π)/229010 weeks
225.01734 -.01571 (225*2π)/229010 weeks
226