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A single-blind controlled competition among tests for nonlinearity and chaos

非线性与混沌检验的单盲受控竞赛

Interest has been growing in testing for nonlinearity or chaos in economic data, but much controversy has arisen about the available results. This paper explores the reasons for these empirical difficulties. We designed and ran a single-blind controlled competition among five highly regarded tests for nonlinearity or chaos with ten simulated data series. The data generating mechanisms include linear processes, chaotic recursions, and nonchaotic stochastic processes; and both…

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Bispectral-Based Tests for the Detection of Gaussianity and Linearity in Time Series

基于双谱的时间序列高斯性与线性检测

Statistical techniques have been developed that use estimated bispectrum values to test whether a sample of a time series is consistent with the hypothesis that the observations are generated by a linear process. The magnitude of the test statistics indicates the amount of divergence between the observations and the linear model hypothesis. It is important to investigate such a divergence, since the usual linear model coefficients can be shown to be biased in the face of…

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Evidence of Nonlinearity in Daily Stock Returns

日度股票收益非线性的证据

This article applies a newly developed statistical technique to time series of daily rates of return of 15 common stocks. The technique involves estimating the bispectrum of the observed time series. The bispectrum is defined as the double Fourier transform of the third-order cumulant function. If the process generating rates of return is linear with independent innovations, then the skewness of the bispectrum will be constant. The article describes a test that can detect…

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A Method for Estimating Distributed Lags When Observations are Randomly Missing

观测随机缺失时分布滞后系数的估计方法

Abstract : This paper presents a frequency-domain technique for estimating distributed lag coefficients (the impulse-response function) when observations are randomly missed. The technique treats stationary processes with randomly missed observations as amplitude-modulated processes and estimates the transfer function accordingly. Estimates of the lag coefficients are obtained by taking the inverse transform of the estimated transfer function. Results with artificially…

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A Method for Estimating Distributed Lags when Observations are Randomly Missing

随机缺失观测下的分布滞后估计方法

This paper presents a frequency-domain technique for estimating distributed lag coefficients (the impulse-response function) when observations are randomly missed. The technique treats stationary processes with randomly missed observations as amplitude-modulated processes and estimates the transfer function accordingly. Estimates of the lag coefficients are obtained by taking the inverse transform of the estimated transfer function. Results with artificially created data…

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Estimating the Lag Structure of a Nonlinear Time Series Model

非线性时间序列模型滞后结构的估计

Suppose that the time series {Y(t)} is the output of a linear plus quadratic filter observed with additive noise. The relationship is a second-order approximation to a nonlinear distributed lag model. Assume that the input to the filter {X(t)} is a stationary Gaussian process. This article presents a relatively simple procedure for determining the values of the parameters of the quadratic filter by using the sample cross bispectrum between the two series. The asymptotic…

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A Simple Method for Robust Regression

一种简单的稳健回归方法

Estimates of the parameters of a linear model are usually obtained by the method of ordinary least-squares (OLS), which is sensitive to large values of the additive error term. By dividing the sample into nonoverlapping subsamples and computing the trimmed means of OLS subsample regression coefficients, we obtain a simple, consistent and asymptotically normal initial estimate of the coefficients, which protects the analyst from large values of ∈ i which are often hard to…

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A Test for a Shifting Slope Coefficient in a Linear Model

线性模型中斜率系数发生变化的检验

A locally most powerful test is developed for the hypothesis that a slope coefficient in a linear time series model is stable, against the alternative that the slope shifts exactly once somewhere in the series. Analysis of the procedure using artificial data indicates good power characteristics even when the ratio of the shift size to the error variance is moderate—especially if the shift does not occur very near either end of the series. Power also depends on the pattern of…

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