An application of the maximum noise fraction method to filtering noisy time series

We propose a tool for filtering multivariate time series that was initially developed for analysing multi-spectral satellite imagery. The basic technique, known as the maximum noise fraction (MNF) method (Green et al. 1988), may be used to provide a subspace decomposition of a multivariate time series in terms of basis vectors which contain maximum noise (or maximum signal). We demonstrate the utility of the method for filtering nonsmooth multivariate data that includes high variance bands such as climate data. The methodology is applied to the reduction of data on noisy manifolds. A comparison of the approach to independent component analysis (ICA) is also provided.