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Despite powerful advances in interest rate curve modeling for data-rich countries in the last 30 years, comparatively little attention has been paid to the key practical problem of estimation of the term structure of interest rates for emerging markets. This may be partly due to limited data availability. However, emerging bond markets are becoming increasingly important and liquid. It is, therefore, important to be understand whether conclusions drawn from developed countries carry over to emerging markets. We estimate model parameters of fully flexible Nelson-Siegel-Svensson term structures model which has become one of the most popular term structure model among academics, practitioners, and central bankers. We investigate four sets of bond data: U.S. Treasuries, and three major emerging market government bond data-sets (Brazil, Mexico and Turkey). By including both the very dense U.S. data and the comparatively sparse emerging market data, we ensure that are results are not specific to a particular data-set. We find that gradient and direct search methods perform poorly in estimating term structures of interest rates, while global optimization methods, particularly the hybrid particle swarm optimization introduced in this paper, do well. Our results are consistent across four countries, both in- and out-of-sample, and for perturbations in prices and starting values. For academics and practitioners interested in optimization methods, this study provides clear evidence of the practical importance of choice of optimization method and validates a method that works well for the NSS model. [ABSTRACT FROM AUTHOR]