Limit theorems for locally stationary processes - Rafael Kawka (Statistical Papers, 2020)
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.
Keywords: 510; Locally stationary process; Central limit theorem; Law of large numbers; Law of the iterated logarithm