A test for independence based on the correlation dimension
提出一种适用于任何可转化为独立同分布误差驱动的时间序列模型残差的独立性检验方法，其渐近分布不受估计误差影响，可用于模型选择和设定检验。
This paper presents a test of independence that can be applied to the estimated residuals of any time series model that can be transformed into a model driven by independent and identically distributed errors. The first order asymptotic distribution of the test statistic is independent of estimation error provided that the parameters of the model under test can be estimated -consistently. Because of this, our method can be used as a model selection tool and as a specification test. Widely used software1 written by Dechert and LeBaron can be used to implement the test. Also, this software is fast enough that the null distribution of our test statistic can be estimated with bootstrap methods. Our method can be viewed as a nonlinear analog of the Box-Pierce Q statistic used in ARIMA analysis.