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Fourier Analysis of NCO (Nuveen California Municipal Mar)


NCO (Nuveen California Municipal Mar) appears to have interesting cyclic behaviour every 10 weeks (4.0318*sine), 10 weeks (3.9627*cosine), and 2 weeks (3.3159*cosine).

NCO (Nuveen California Municipal Mar) has an average price of 7.97 (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 1/2/2007 to 9/17/2012 for NCO (Nuveen California Municipal Mar), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
07.96825   0 
1.64679 -1.23209 (1*2π)/125125 weeks
2-.03558 -3.09361 (2*2π)/12563 weeks
31.3541 1.39875 (3*2π)/12542 weeks
4-2.5357 -1.85486 (4*2π)/12531 weeks
52.52244 -.60829 (5*2π)/12525 weeks
6-.77819 .93581 (6*2π)/12521 weeks
7.24091 -2.31881 (7*2π)/12518 weeks
81.39064 2.00624 (8*2π)/12516 weeks
9-3.19468 -.7886 (9*2π)/12514 weeks
101.79701 -2.07767 (10*2π)/12513 weeks
11-.50733 1.75112 (11*2π)/12511 weeks
12-1.61203 -4.03176 (12*2π)/12510 weeks
133.96269 .54726 (13*2π)/12510 weeks
14-2.51364 .23452 (14*2π)/1259 weeks
152.6334 -1.96192 (15*2π)/1258 weeks
16-.38518 2.55501 (16*2π)/1258 weeks
17-1.17517 -2.93804 (17*2π)/1257 weeks
182.6654 .6042 (18*2π)/1257 weeks
19-1.32646 .82097 (19*2π)/1257 weeks
20.74895 -1.43617 (20*2π)/1256 weeks
21-.04563 1.78567 (21*2π)/1256 weeks
22-1.34913 -2.60275 (22*2π)/1256 weeks
232.88651 .33095 (23*2π)/1255 weeks
24-1.74705 2.01144 (24*2π)/1255 weeks
25-.10396 -3.35811 (25*2π)/1255 weeks
261.79303 2.56982 (26*2π)/1255 weeks
27-2.49849 -2.02288 (27*2π)/1255 weeks
282.95595 -.47761 (28*2π)/1254 weeks
29-.97399 1.87712 (29*2π)/1254 weeks
30.50643 -2.45095 (30*2π)/1254 weeks
311.08089 2.7377 (31*2π)/1254 weeks
32-1.78872 -1.49851 (32*2π)/1254 weeks
331.93712 .05644 (33*2π)/1254 weeks
34-1.21721 1.72543 (34*2π)/1254 weeks
35-.5226 -2.86616 (35*2π)/1254 weeks
362.4212 1.24976 (36*2π)/1253 weeks
37-1.85361 .3333 (37*2π)/1253 weeks
381.91912 -1.5084 (38*2π)/1253 weeks
39-.47908 3.00351 (39*2π)/1253 weeks
40-1.34864 -3.04319 (40*2π)/1253 weeks
413.0915 1.12969 (41*2π)/1253 weeks
42-2.8187 .93986 (42*2π)/1253 weeks
432.24805 -2.63459 (43*2π)/1253 weeks
44.02501 2.88584 (44*2π)/1253 weeks
45-.61792 -1.89111 (45*2π)/1253 weeks
461.78256 1.16619 (46*2π)/1253 weeks
47-2.34678 .54158 (47*2π)/1253 weeks
481.84264 -2.16779 (48*2π)/1253 weeks
49.22334 2.42419 (49*2π)/1253 weeks
50-1.72004 -1.5073 (50*2π)/1253 weeks
513.31593 -.6187 (51*2π)/1252 weeks
52-2.12193 3.48811 (52*2π)/1252 weeks
53-.49854 -3.17615 (53*2π)/1252 weeks
541.20274 1.52158 (54*2π)/1252 weeks
55-2.07967 -.90896 (55*2π)/1252 weeks
562.65254 -1.1865 (56*2π)/1252 weeks
57-1.84527 2.27281 (57*2π)/1252 weeks
58.78596 -3.19416 (58*2π)/1252 weeks
591.09619 2.52258 (59*2π)/1252 weeks
60-2.53179 -1.39033 (60*2π)/1252 weeks
612.69985 -1.82625 (61*2π)/1252 weeks
62-.04565 2.2625 (62*2π)/1252 weeks
63-.04565 -2.2625 (63*2π)/1252 weeks
642.69985 1.82625 (64*2π)/1252 weeks
65-2.53179 1.39033 (65*2π)/1252 weeks
661.09619 -2.52258 (66*2π)/1252 weeks
67.78596 3.19416 (67*2π)/1252 weeks
68-1.84527 -2.27281 (68*2π)/1252 weeks
692.65254 1.1865 (69*2π)/1252 weeks
70-2.07967 .90896 (70*2π)/1252 weeks
711.20274 -1.52158 (71*2π)/1252 weeks
72-.49854 3.17615 (72*2π)/1252 weeks
73-2.12193 -3.48811 (73*2π)/1252 weeks
743.31593 .6187 (74*2π)/1252 weeks
75-1.72004 1.5073 (75*2π)/1252 weeks
76.22334 -2.42419 (76*2π)/1252 weeks
771.84264 2.16779 (77*2π)/1252 weeks
78-2.34678 -.54158 (78*2π)/1252 weeks
791.78256 -1.16619 (79*2π)/1252 weeks
80-.61792 1.89111 (80*2π)/1252 weeks
81.02501 -2.88584 (81*2π)/1252 weeks
822.24805 2.63459 (82*2π)/1252 weeks
83-2.8187 -.93986 (83*2π)/1252 weeks
843.0915 -1.12969 (84*2π)/1251 weeks
85-1.34864 3.04319 (85*2π)/1251 weeks
86-.47908 -3.00351 (86*2π)/1251 weeks
871.91912 1.5084 (87*2π)/1251 weeks
88-1.85361 -.3333 (88*2π)/1251 weeks
892.4212 -1.24976 (89*2π)/1251 weeks
90-.5226 2.86616 (90*2π)/1251 weeks
91-1.21721 -1.72543 (91*2π)/1251 weeks
921.93712 -.05644 (92*2π)/1251 weeks
93-1.78872 1.49851 (93*2π)/1251 weeks
941.08089 -2.7377 (94*2π)/1251 weeks
95.50643 2.45095 (95*2π)/1251 weeks
96-.97399 -1.87712 (96*2π)/1251 weeks
972.95595 .47761 (97*2π)/1251 weeks
98-2.49849 2.02288 (98*2π)/1251 weeks
991.79303 -2.56982 (99*2π)/1251 weeks
100-.10396 3.35811 (100*2π)/1251 weeks
101-1.74705 -2.01144 (101*2π)/1251 weeks
1022.88651 -.33095 (102*2π)/1251 weeks
103-1.34913 2.60275 (103*2π)/1251 weeks
104-.04563 -1.78567 (104*2π)/1251 weeks
105.74895 1.43617 (105*2π)/1251 weeks
106-1.32646 -.82097 (106*2π)/1251 weeks
1072.6654 -.6042 (107*2π)/1251 weeks
108-1.17517 2.93804 (108*2π)/1251 weeks
109-.38518 -2.55501 (109*2π)/1251 weeks
1102.6334 1.96192 (110*2π)/1251 weeks
111-2.51364 -.23452 (111*2π)/1251 weeks
1123.96269 -.54726 (112*2π)/1251 weeks
113-1.61203 4.03176 (113*2π)/1251 weeks
114-.50733 -1.75112 (114*2π)/1251 weeks
1151.79701 2.07767 (115*2π)/1251 weeks
116-3.19468 .7886 (116*2π)/1251 weeks
1171.39064 -2.00624 (117*2π)/1251 weeks
118.24091 2.31881 (118*2π)/1251 weeks
119-.77819 -.93581 (119*2π)/1251 weeks
1202.52244 .60829 (120*2π)/1251 weeks
121-2.5357 1.85486 (121*2π)/1251 weeks
1221.3541 -1.39875 (122*2π)/1251 weeks
123-.03558 3.09361 (123*2π)/1251 weeks

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