In this paper, we propose a kernel-type estimator for the local characteristic function of locally stationary processes. Under weak moment conditions, we prove joint asymptotic normality for local empirical characteristic functions. For time-varying linear processes, we establish a central limit theorem under the assumption of finite absolute first moments of the process. Additionally, we prove weak convergence of the local empirical characteristic process. We apply our asymptotic results to parameter estimation. Furthermore, by extending the notion of distance correlation of Szekely, Rizzo and Bakirov (2007) to locally stationary processes, we are able to provide asymptotic theory for local empirical distance correlations. Finally, we provide a simulation study on minimum distance estimation for a-stable distributions and illustrate the pairwise dependence structure over time of log returns of German stock prices via local empirical distance correlations.

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基于经验特征函数的局部平稳过程估计和距离相关

在本文中，我们提出了一种用于局部平稳过程的局部特征函数的核型估计器。在弱矩条件下，我们证明了局部经验特征函数的联合渐近正态性。对于时变线性过程，我们在过程的绝对一阶矩有限的假设下建立了中心极限定理。此外，我们证明了局部经验特征过程的弱收敛性。我们将渐近结果应用于参数估计。此外，通过将 Szekely、Rizzo 和 Bakirov (2007) 的距离相关性概念扩展到局部平稳过程，我们能够为局部经验距离相关性提供渐近理论。最后，