Robustness of alternative non‐linearity tests for SETAR models

In recent years there has been a growing interest in exploiting potential forecast gains from the non‐linear structure of self‐exciting threshold autoregressive (SETAR) models. Statistical tests have been proposed in the literature to help analysts check for the presence of SETAR‐type non‐linearities in an observed time series. It is important to study the power and robustness properties of these tests since erroneous test results might lead to misspecified prediction problems. In this paper we investigate the robustness properties of several commonly used non‐linearity tests. Both the robustness with respect to outlying observations and the robustness with respect to model specification are considered. The power comparison of these testing procedures is carried out using Monte Carlo simulation. The results indicate that all of the existing tests are not robust to outliers and model misspecification. Finally, an empirical application applies the statistical tests to stock market returns of the four little dragons (Hong Kong, South Korea, Singapore and Taiwan) in East Asia. The non‐linearity tests fail to provide consistent conclusions most of the time. The results in this article stress the need for a more robust test for SETAR‐type non‐linearity in time series analysis and forecasting. Copyright © 2004 John Wiley & Sons, Ltd.     

关于Dirichlet级数的一个注记

本文对一类Ｄｉｒｉｃｈｌｅｔ级教给出了的关系，此处Ｘ（Ｘ）＝Ｘｐ（Ｘ）是实数集合Ｐ的特征函数．     

冒泡排序算法的改进

本文作者对传统的冒泡排序算法进行了时间复杂性分析，指出其效率不高的缺陷，提出了双向同时浮沉的改进方法，并编程予以实现。其效率较传统的冒泡排序算法有一定程度的提高．     

The problem of time's arrow historico-critically reexamined

Responding to Hasok Chang's vision of the history and philosophy of science (HPS) as the continuation of science by other means, I illustrate the methods of HPS and their utility through a historico-critical examination of the problem of “time's arrow”, that is to say, the problem posed by the claim by Boltzmann and others that the temporal asymmetry of many physical processes and indeed the very possibility of identifying each of the two directions we distinguish in time must have a ground in the laws of nature. I claim that this problem has proved intractable chiefly because the standard mathematical representation of time employed in the formulation of the laws of nature “forgets” one of the connotations of the word ‘time’ as it is used in ordinary language and in experimental physics.     

Banach空间中的幂级数方程

本文考虑Banach空间中形如x=u+sum from k=1 to ∞(a_kx~k)的幂级数方程,建立了一个比较定理,并将其应用于一定的非线性积分方程.     

正项级数的广义Cauchy判别法

对正项级数的Cauchy,判别法作了推广,得出正项级数的广义Cauchy判别法.使原来的Cauchy判别法成为该判别之特例,从而扩大了它的使用范围.     

基于RBF网络的混沌时间序列的建模与多步预测

提出将RBF神经网络应用于混沌时间序列的建模与预测中 ,设计了一个三层RBF网络结构 ,说明了RBF网络用于混沌时间序列建模和预测时的基本性质。仿真结果表明 ,RBF网络模型对混沌时间序列有比较强的拟合能力和比较高的一步及多步预测精度。采用RBF网络进行混沌时间序列的建模和预测能够取得比其它方法好得多的效果。     

Dirichlet公式的简化证明及应用

本文给出了Ｄｉｒｉｃｈｌｅｔ公式的一个简化证明，极易掌握。利用这一公式导出了一个含双参数的级数及其和的表达式。适当选取参数，得出了几个新的收敛级数。     

A ground‐level ozone forecasting model for Santiago,Chile

A physically based model for ground‐level ozone forecasting is evaluated for Santiago, Chile. The model predicts the daily peak ozone concentration, with the daily rise of air temperature as input variable; weekends and rainy days appear as interventions. This model was used to analyse historical data, using the Linear Transfer Function/Finite Impulse Response (LTF/FIR) formalism; the Simultaneous Transfer Function (STF) method was used to analyse several monitoring stations together. Model evaluation showed a good forecasting performance across stations—for low and high ozone impacts—with power of detection (POD) values between 70 and 100%, Heidke's Skill Scores between 40% and 70% and low false alarm rates (FAR). The model consistently outperforms a pure persistence forecast. Model performance was not sensitive to different implementation options. The model performance degrades for two‐ and three‐days ahead forecast, but is still acceptable for the purpose of developing an environmental warning system at Santiago. Copyright © 2002 John Wiley & Sons, Ltd.     

Forecasting trend output in the Euro area

This paper is an applied study about forecasting trend output and the output gap in the Euro area. The need for trend output forecasts is justified by an analysis of the monetary strategy of the European Central Bank. Trend output serves as a direct inflation indicator and helps to determine the reference value for money. For both purposes, trend output has to be forecasted. A permanent–transitory decomposition based on cointegration restrictions gives an estimate of trend output in the Euro area. Ex‐ante point forecasts of trend output are computed and bootstrap simulation is employed to construct prediction intervals that take estimation uncertainty into consideration. The uncertainty of trend output and the output gap is quite large and raises questions about their usefulness as indicators for monetary policy. Copyright © 2002 John Wiley & Sons, Ltd.