Chart: WIG20 futures vs S&P500 futures over 10 years, stooq.com
The Polish and the US stock markets are undeniably connected, which is visible on the above chart, showing performance of the WIG20 futures against the S&P500 futures over 10 years (the realized correlation over the period is 0.7091).
However it doesn't mean that you can use this connection to predict short time price movements - the correlation between previous day change in the S&P500 futures and the current day WIG20 futures change is just 0.1380.
Since for the gaps between the closing on the previous day and the opening on the current you are unable to "catch" the whole daily change of the WIG20, the better value to compare is the change from the opening till close. In this case, the correlation with S&P500 futures changes to -0.1273 (minus).
> fw20c[1:10,]
Date Open High Low Close Volume OpenInt D_Change OC_Change
3 2000-01-05 1827 1839 1807 1811 5172 4694 -0.019683522 -0.0087960985
4 2000-01-06 1802 1849 1784 1848 5220 4801 0.020224794 0.0252068140
5 2000-01-07 1936 1998 1935 1982 5671 4918 0.070002463 0.0234824471
7 2000-01-11 2010 2070 1950 2042 5990 5622 -0.020359404 0.0157949977
8 2000-01-12 2015 2044 2010 2030 4312 5917 -0.005893927 0.0074165977
9 2000-01-13 2110 2148 2093 2135 5174 6033 0.050430854 0.0117786992
10 2000-01-14 2080 2137 2075 2115 5024 5716 -0.009411834 0.0166869188
13 2000-01-19 2035 2044 2005 2036 5719 5936 -0.005388208 0.0004912798
14 2000-01-20 2058 2068 2007 2053 5975 5839 0.008315039 -0.0024324994
15 2000-01-21 2043 2077 2043 2071 3672 6266 0.008729444 0.0136122666
(...)
>
> esfc[1:10,]
Date Open High Low Close Volume OpenInt D_Change
2 2000-01-04 1467.00 1468.75 1409.50 1411.75 61942 13967 -0.038218999
3 2000-01-05 1411.50 1427.25 1385.00 1413.50 64049 13007 0.001238829
4 2000-01-06 1411.00 1426.25 1395.75 1404.00 73127 13870 -0.006743593
6 2000-01-10 1459.75 1481.00 1455.25 1475.00 60548 15339 0.009879147
7 2000-01-11 1473.75 1475.00 1447.00 1454.25 59343 16080 -0.014167686
8 2000-01-12 1453.50 1459.50 1438.75 1442.00 70097 16982 -0.008459265
9 2000-01-13 1441.50 1466.75 1441.25 1458.50 62509 16832 0.011377471
11 2000-01-18 1478.00 1480.25 1462.00 1469.50 57421 16106 -0.005767616
12 2000-01-19 1468.75 1474.00 1450.25 1472.50 65454 16859 0.002039430
13 2000-01-20 1472.75 1485.00 1448.00 1457.00 57788 18126 -0.010582109
(...)
>
> cor(esfc$D_Change,fw20c$D_Change)
[1] 0.1380338
> cor(esfc$D_Change,fw20c$OC_Change)
[1] -0.1273032
> cor(fw20c$D_Change,fw20c$OC_Change)
[1] 0.8551321
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