Time Series Reconstruction from Unequally Spaced Natural Archive Data

Some natural substrates record environmental information and, as such, provide a means to reconstruct the environmental conditions from the period these substrates were formed. Samples from environmental archives are not always equally spaced in distance. When a periodic time series model is estimated from these unequally spaced proxy records, the search for reasonable starting values is the main difficulty. In this work, a non-parametric method based on the regressive Fourier series is first presented, which reduces averaging errors starting from unequally spaced records. The method is applied to synthetic data and generally performs well in all circumstances. Secondly, a parametric method for the construction of a time base and the elimination of averaging errors from unequally spaced records is presented. This parametric method uses the non-parametric method to produce starting values for the parameters. The method is compared with the time series construction method with the averaging effect taken into account and it is observed that only the current method produces acceptable results. The statistical performance of the method is verified with a Monte Carlo simulation and the estimator is proven to be an efficient estimator. The applicability of the method is demonstrated on the vessel density measurement in a mangrove tree, Rizophora mucronata, which is a proxy for the rainfall in tropical coastal regions.