Limit Theorems for the Symbolic Correlation Integral and the Renyi-2 Entropy under Short-range Dependence
短程依赖下符号相关积分与 Rényi 二阶熵的极限定理
The symbolic correlation integral provides a way to measure the complexity of time series and dynamical systems. In the present article we prove limit results for an estimator of this quantity which is based on U-statistics under the assumption of short-range dependence. To this end, we slightly generalize classical limit results in the framework of 1-approximating functionals. Furthermore, we carefully analyze the limit variance. A simulation study with ARMA and ARCH time…