Calculating Lyapunov exponents for short and/or noisy data sets

We present a technique for calculating the Lyapunov spectrum from a scalar time series. The technique is particularly useful when the data set is short and/or noisy. The method is based on an orthogonal polynomial expansion of the dynamics. For comparison purposes we test the new technique to two previous methods. We find that the global method performs as well as, or better than, either of the previous techniques.