We analyzed six stock exchange markets through the nonlinear dynamics concept. We used daily data from the Toronto Stock Exchange, NYSE, London Stock Exchange, Hong Kong Stock Market, Tokyo Stock Exchange, and the Singapore Stock Exchange. The period studied is from January 1, 1988 to June 30, 1999. We performed Local Principal Components Analysis in order to estimate the dimension of each underlying attractor. Our main interest is the noise level estimation of each time series. The results indicate weak determinism and strong noise influence. The noise-to-signal ratio for almost all time series is above 50%. Noise is leptokurtic in the eastern stock markets, and mesokurtic in western ones.