We demonstrate by using simulations that spatial embedding of single-v
ariable time series data does not reliably reconstruct state-space dyn
amics. Instead, correlation dimension estimated from spatially embedde
d data is largely a measure of linear cross-correlation in the data se
t. For actual electroencephalographic (EEC) data, we demonstrate a hig
h negative correlation between spatial correlation dimension and the a
verage amount of lag-zero crosscorrelation between ''nearest-neighbor'
' embedding channels (the greater the cross-correlation, the lower the
dimension). We also show that the essential results obtained from spa
tially embedding EEG data are also obtained when one spatially embeds
across a set of highly cross-correlated stochastic (second-order autor
egressive) processes. Although, with appropriate surrogate data, corre
lation dimension estimated from spatially embedded data detects nonlin
earity, its use is not recommended because correlation dimension estim
ated from temporally embedded data both reconstructs state-spate dynam
ics and, with appropriate surrogate data, detects nonlinearity as well
.