Noise in unspecified, non-linear time series

In this paper a method is developed which allows the determination of the noise level (the size of external shocks) which is present in a linear or non-linear autoregressive time series. Nothing need to be known about the functional form or about the lag structure of the underlying model. The technique regards the time series as a hypersurface, lying in a higher dimensional embedding space, and makes use of the correlation integral, as introduced in the physical sciences. Uniformly distributed noise is considered at first, then the technique is generalized to normal and other distributions. And even if the distribution of the noise is unknown, one can still make comparisons between the intensities of noise in different time series. The method is put to a test with empirically assessed stock market data.