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Fourier Analysis of PGAL (Global X MSCI Portugal ETF)


PGAL (Global X MSCI Portugal ETF) appears to have interesting cyclic behaviour every 14 weeks (.1613*sine), 19 weeks (.1447*cosine), and 12 weeks (.1194*cosine).

PGAL (Global X MSCI Portugal ETF) has an average price of 11.11 (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 11/13/2013 to 7/17/2017 for PGAL (Global X MSCI Portugal ETF), this program was able to calculate the following Fourier Series:
Sequence #Cosine Coefficients Sine Coefficients FrequenciesPeriod
011.10888   0 
11.70612 1.90019 (1*2π)/193193 weeks
2.45758 1.33181 (2*2π)/19397 weeks
3-.26975 .92276 (3*2π)/19364 weeks
4-.27524 -.1809 (4*2π)/19348 weeks
5.10872 -.03975 (5*2π)/19339 weeks
6-.08658 .08477 (6*2π)/19332 weeks
7.01646 -.11312 (7*2π)/19328 weeks
8.06331 .20566 (8*2π)/19324 weeks
9.01035 .00233 (9*2π)/19321 weeks
10-.14471 .00291 (10*2π)/19319 weeks
11.00939 .08568 (11*2π)/19318 weeks
12.04173 .06195 (12*2π)/19316 weeks
13.03483 .04503 (13*2π)/19315 weeks
14.02814 .16135 (14*2π)/19314 weeks
15-.03881 .09106 (15*2π)/19313 weeks
16-.11942 .04675 (16*2π)/19312 weeks
17.01167 -.13846 (17*2π)/19311 weeks
18.05707 .14231 (18*2π)/19311 weeks
19.08357 .07291 (19*2π)/19310 weeks
20-.02537 .03287 (20*2π)/19310 weeks
21-.00387 -.02443 (21*2π)/1939 weeks
22.03054 .01409 (22*2π)/1939 weeks
23.0882 .02092 (23*2π)/1938 weeks
24.03597 .02678 (24*2π)/1938 weeks
25.07182 -.00226 (25*2π)/1938 weeks
26.0275 -.01185 (26*2π)/1937 weeks
27.06696 .05263 (27*2π)/1937 weeks
28-.01135 .07539 (28*2π)/1937 weeks
29-.0184 .04544 (29*2π)/1937 weeks
30.00848 .01533 (30*2π)/1936 weeks
31-.03457 -.03103 (31*2π)/1936 weeks
32.05247 .05515 (32*2π)/1936 weeks
33.0366 .04844 (33*2π)/1936 weeks
34-.06259 .03088 (34*2π)/1936 weeks
35.03574 .03791 (35*2π)/1936 weeks
36-.05676 -.02678 (36*2π)/1935 weeks
37-.02277 -.04663 (37*2π)/1935 weeks
38.01918 -.01655 (38*2π)/1935 weeks
39-.01287 .00722 (39*2π)/1935 weeks
40.01903 -.00835 (40*2π)/1935 weeks
41-.03418 -.00001 (41*2π)/1935 weeks
42.02591 -.00602 (42*2π)/1935 weeks
43.01842 .02236 (43*2π)/1934 weeks
44-.01496 .07669 (44*2π)/1934 weeks
45-.02496 .00423 (45*2π)/1934 weeks
46.00073 -.051 (46*2π)/1934 weeks
47.08323 .00487 (47*2π)/1934 weeks
48.01127 .02162 (48*2π)/1934 weeks
49.04795 .03349 (49*2π)/1934 weeks
50.00306 .00929 (50*2π)/1934 weeks
51-.02459 .02532 (51*2π)/1934 weeks
52-.02511 -.03664 (52*2π)/1934 weeks
53.01438 .00955 (53*2π)/1934 weeks
54.01985 -.00299 (54*2π)/1934 weeks
55-.00653 .01438 (55*2π)/1934 weeks
56-.0391 .00067 (56*2π)/1933 weeks
57-.02745 .00003 (57*2π)/1933 weeks
58.01234 -.03575 (58*2π)/1933 weeks
59.02552 -.00881 (59*2π)/1933 weeks
60.02112 -.00637 (60*2π)/1933 weeks
61-.03475 .02372 (61*2π)/1933 weeks
62.01187 -.01163 (62*2π)/1933 weeks
63.02154 -.02316 (63*2π)/1933 weeks
64.01394 .01068 (64*2π)/1933 weeks
65.00027 .02109 (65*2π)/1933 weeks
66.02306 .00811 (66*2π)/1933 weeks
67-.0056 .01725 (67*2π)/1933 weeks
68-.0363 -.04637 (68*2π)/1933 weeks
69.02515 -.00392 (69*2π)/1933 weeks
70.04068 -.00943 (70*2π)/1933 weeks
71.0122 .00612 (71*2π)/1933 weeks
72.00626 .01353 (72*2π)/1933 weeks
73-.01463 -.02272 (73*2π)/1933 weeks
74.02688 .00387 (74*2π)/1933 weeks
75.01609 .02151 (75*2π)/1933 weeks
76.0176 .00102 (76*2π)/1933 weeks
77.01166 .01722 (77*2π)/1933 weeks
78-.00536 -.01043 (78*2π)/1932 weeks
79.02759 -.00042 (79*2π)/1932 weeks
80.00565 -.01698 (80*2π)/1932 weeks
81.01681 .01524 (81*2π)/1932 weeks
82.01135 .00224 (82*2π)/1932 weeks
83.00924 -.00266 (83*2π)/1932 weeks
84-.00808 -.0141 (84*2π)/1932 weeks
85.01344 .00889 (85*2π)/1932 weeks
86-.01297 .00093 (86*2π)/1932 weeks
87.02762 -.00133 (87*2π)/1932 weeks
88.01019 .0051 (88*2π)/1932 weeks
89.00542 .02385 (89*2π)/1932 weeks
90.01638 -.00373 (90*2π)/1932 weeks
91-.01406 -.01907 (91*2π)/1932 weeks
92.02825 .02875 (92*2π)/1932 weeks
93.0329 -.02892 (93*2π)/1932 weeks
94.0365 -.00707 (94*2π)/1932 weeks
95.02662 .00609 (95*2π)/1932 weeks
96.01822 .00701 (96*2π)/1932 weeks
97.01822 -.00701 (97*2π)/1932 weeks
98.02662 -.00609 (98*2π)/1932 weeks
99.0365 .00707 (99*2π)/1932 weeks
100.0329 .02892 (100*2π)/1932 weeks
101.02825 -.02875 (101*2π)/1932 weeks
102-.01406 .01907 (102*2π)/1932 weeks
103.01638 .00373 (103*2π)/1932 weeks
104.00542 -.02385 (104*2π)/1932 weeks
105.01019 -.0051 (105*2π)/1932 weeks
106.02762 .00133 (106*2π)/1932 weeks
107-.01297 -.00093 (107*2π)/1932 weeks
108.01344 -.00889 (108*2π)/1932 weeks
109-.00808 .0141 (109*2π)/1932 weeks
110.00924 .00266 (110*2π)/1932 weeks
111.01135 -.00224 (111*2π)/1932 weeks
112.01681 -.01524 (112*2π)/1932 weeks
113.00565 .01698 (113*2π)/1932 weeks
114.02759 .00042 (114*2π)/1932 weeks
115-.00536 .01043 (115*2π)/1932 weeks
116.01166 -.01722 (116*2π)/1932 weeks
117.0176 -.00102 (117*2π)/1932 weeks
118.01609 -.02151 (118*2π)/1932 weeks
119.02688 -.00387 (119*2π)/1932 weeks
120-.01463 .02272 (120*2π)/1932 weeks
121.00626 -.01353 (121*2π)/1932 weeks
122.0122 -.00612 (122*2π)/1932 weeks
123.04068 .00943 (123*2π)/1932 weeks
124.02515 .00392 (124*2π)/1932 weeks
125-.0363 .04637 (125*2π)/1932 weeks
126-.0056 -.01725 (126*2π)/1932 weeks
127.02306 -.00811 (127*2π)/1932 weeks
128.00027 -.02109 (128*2π)/1932 weeks
129.01394 -.01068 (129*2π)/1931 weeks
130.02154 .02316 (130*2π)/1931 weeks
131.01187 .01163 (131*2π)/1931 weeks
132-.03475 -.02372 (132*2π)/1931 weeks
133.02112 .00637 (133*2π)/1931 weeks
134.02552 .00881 (134*2π)/1931 weeks
135.01234 .03575 (135*2π)/1931 weeks
136-.02745 -.00003 (136*2π)/1931 weeks
137-.0391 -.00067 (137*2π)/1931 weeks
138-.00653 -.01438 (138*2π)/1931 weeks
139.01985 .00299 (139*2π)/1931 weeks
140.01438 -.00955 (140*2π)/1931 weeks
141-.02511 .03664 (141*2π)/1931 weeks
142-.02459 -.02532 (142*2π)/1931 weeks
143.00306 -.00929 (143*2π)/1931 weeks
144.04795 -.03349 (144*2π)/1931 weeks
145.01127 -.02162 (145*2π)/1931 weeks
146.08323 -.00487 (146*2π)/1931 weeks
147.00073 .051 (147*2π)/1931 weeks
148-.02496 -.00423 (148*2π)/1931 weeks
149-.01496 -.07669 (149*2π)/1931 weeks
150.01842 -.02236 (150*2π)/1931 weeks
151.02591 .00602 (151*2π)/1931 weeks
152-.03418 .00001 (152*2π)/1931 weeks
153.01903 .00835 (153*2π)/1931 weeks
154-.01287 -.00722 (154*2π)/1931 weeks
155.01918 .01655 (155*2π)/1931 weeks
156-.02277 .04663 (156*2π)/1931 weeks
157-.05676 .02678 (157*2π)/1931 weeks
158.03574 -.03791 (158*2π)/1931 weeks
159-.06259 -.03088 (159*2π)/1931 weeks
160.0366 -.04844 (160*2π)/1931 weeks
161.05247 -.05515 (161*2π)/1931 weeks
162-.03457 .03103 (162*2π)/1931 weeks
163.00848 -.01533 (163*2π)/1931 weeks
164-.0184 -.04544 (164*2π)/1931 weeks
165-.01135 -.07539 (165*2π)/1931 weeks
166.06696 -.05263 (166*2π)/1931 weeks
167.0275 .01185 (167*2π)/1931 weeks
168.07182 .00226 (168*2π)/1931 weeks
169.03597 -.02678 (169*2π)/1931 weeks
170.0882 -.02092 (170*2π)/1931 weeks
171.03054 -.01409 (171*2π)/1931 weeks
172-.00387 .02443 (172*2π)/1931 weeks
173-.02537 -.03287 (173*2π)/1931 weeks
174.08357 -.07291 (174*2π)/1931 weeks
175.05707 -.14231 (175*2π)/1931 weeks
176.01167 .13846 (176*2π)/1931 weeks
177-.11942 -.04675 (177*2π)/1931 weeks
178-.03881 -.09106 (178*2π)/1931 weeks
179.02814 -.16135 (179*2π)/1931 weeks
180.03483 -.04503 (180*2π)/1931 weeks
181.04173 -.06195 (181*2π)/1931 weeks
182.00939 -.08568 (182*2π)/1931 weeks
183-.14471 -.00291 (183*2π)/1931 weeks
184.01035 -.00233 (184*2π)/1931 weeks
185.06331 -.20566 (185*2π)/1931 weeks
186.01646 .11312 (186*2π)/1931 weeks
187-.08658 -.08477 (187*2π)/1931 weeks
188.10872 .03975 (188*2π)/1931 weeks
189-.27524 .1809 (189*2π)/1931 weeks
190-.26975 -.92276 (190*2π)/1931 weeks
191.45758 -1.33181 (191*2π)/1931 weeks



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