A Note on the Behaviour of the Correlation Integral in the Presence of a Time Series
研究了简单混沌和纯随机噪声下相关积分的已知行为，并考察了弱结构噪声（如自回归和移动平均模型）下该积分的预期行为，对理解时间序列的维数估计有帮助。
The behaviour of the correlation integral is well known when applied to simple chaotic regimes and to pure random noise. The asymptotic behaviour of a chaotic system is represented by an infinite set of points called an attractor, the dimension of which can be estimated by the correlation integral. Essentially, the correlation integral of a time series is a normalized count of the number of close pairs of points of the series lying in phase space. We examine the expected behaviour of the integral for some stochastic process models which place a weak structure on the noise, such as simple autoregressive and moving average formulations.