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A drawback of many voice conversion algorithms is that they rely on linear models and/or require a lot of tuning. In addition, many of them ignore the inherent time-dependency between speech features. To address these issues, we propose to use dynamic kernel partial least squares (DKPLS) technique to model nonlinearities as well as to capture the dynamics in the data. The method is based on a kernel transformation of the source features to allow non-linear modeling and concatenation of previous and next frames to model the dynamics. Partial least squares regression is used to find a conversion function that does not overfit to the data. The resulting DKPLS algorithm is a simple and efficient algorithm and does not require massive tuning. Existing statistical methods proposed for voice conversion are able to produce good similarity between the original and the converted target voices but the quality is usually degraded. The experiments conducted on a variety of conversion pairs show that DKPLS, being a statistical method, enables successful identity conversion while achieving a major improvement in the quality scores compared to the state-of-the-art Gaussian mixture-based model. In addition to enabling better spectral feature transformation, quality is further improved when aperiodicity and binary voicing values are converted using DKPLS with auxiliary information from spectral features.