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条件分布函数的估计方法AI 解读

Motivated by the problem of setting prediction intervals in time series analysis, we suggest two new methods for conditional distribution estimation. The first method is based on locally fitting a logistic model and is in the spirit of recent work on locally parametric techniques in density estimation. It produces distribution estimators that may be of arbitrarily high order but nevertheless always lie between 0 and 1. The second method involves an adjusted form of the…

混沌 Logistic 映射的不变分布与 Lyapunov 指数性质AI 解读

SUMMARY Statistical scientists have recently focused sharp attention on properties of iterated chaotic maps, with a view to employing such processes to model naturally occurring phenomena. In the present paper we treat the logistic map, which has earlier been studied in the context of modelling biological systems. We derive theory describing properties of ‘invariant’ or ‘stationary’ distributions under logistic maps and apply those results in conjunction with numerical work…

时间序列存在时相关积分行为的一则注记AI 解读

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…

时间序列情形下相关积分的行为AI 解读

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…