We present limit theorems for locally stationary processes that have a one sided time-varying moving average representation. In particular, we prove a central limit theorem (CLT), a weak and a strong law of large numbers (WLLN, SLLN) and a law of the iterated logarithm (LIL) under mild assumptions using a time-varying Beveridge–Nelson decomposition.

中文翻译：

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局部平稳过程的极限定理

我们提出了具有单边时变移动平均表示的局部平稳过程的极限定理。特别是，我们在温和的假设下使用时变 Beveridge-Nelson 分解证明了中心极限定理 (CLT)、弱和强大数定律 (WLLN、SLLN) 和迭代对数定律 (LIL)。