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Asymptotically Optimal Smoothing with Arch Models

利用 ARCH 模型进行渐近最优平滑

Suppose an observed time series is generated by a stochastic volatility model. As shown by D. B. Nelson (1992) and D. B. Nelson and D. P. Foster (1994), a misspecified ARCH model will often be able to consistently (as a continuous time limit is approached) estimate the unobserved volatility process using information in the lagged residuals. This paper shows how to more efficiently estimate such a volatility process using information in both lagged and led residuals. In…

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Testing for Parameter Constancy in Linear Regressions: An Empirical Distribution Function Approach

线性回归中的参数恒定性检验:经验分布函数方法

This paper proposes some tests for parameter constancy in linear regressions. The tests use weighted empirical distribution functions of estimated residuals and are asymptotically distribution free. The proposed tests have nontrivial local power against a wide range of alternatives. In particular, the tests are capable of detecting error heterogeneity that is not necessarily manifested in the form of changing variances. The model allows for both dynamic and trending…

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Regime switching as a test for exchange rate bubbles

以区制转换检验汇率投机泡沫

This paper develops a new test for speculative bubbles, which is applied to data for the Japanese yen, the German mark and the Canadian dollar exchange rates from 1977 to 1991. The test assumes that bubbles display a particular kind of regime-switching behaviour, which is shown to imply coefficient restrictions on a simple switching-regression model of exchange rate innovations. Test results are sensitive to the specification of exchange rate fundamentals and other factors.…

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On a double-threshold autoregressive heteroscedastic time series model

双阈值自回归条件异方差时间序列模型

Tong's threshold models have been found useful in modelling nonlinearities in the conditional mean of a time series. The threshold model is extended to the so-called double-threshold ARCH(DTARCH) model, which can handle the situation where both the conditional mean and the conditional variance specifications are piecewise linear given previous information. Potential applications of such models include financial data with different (asymmetric) behaviour in a visiting versus…

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Function estimation via wavelet shrinkage for long-memory data

长记忆数据的小波收缩函数估计

In this article we study function estimation via wavelet shrinkage for data with long-range dependence. We propose a fractional Gaussian noise model to approximate nonparametric regression with long-range dependence and establish asymptotics for minimax risks. Because of long-range dependence, the minimax risk and the minimax linear risk converge to 0 at rates that differ from those for data with independence or short-range dependence. Wavelet estimates with best selection…

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Why Are Some Industries More Cyclical Than Others?

为什么有些行业的周期性更强?

This paper is an empirical examination of why some industries are far more cyclical than others. Using highly disaggregate panel data, the authors examine which elements of technology and market structure appear to be most closely associated with differences in cyclicality across industries. They find that durable goods industries are approximately three times more cyclical than nondurable goods industries. Within durable goods industries, the proportion of variable and…

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The Persistence of Shocks to Macroeconomic Time Series: Some Evidence From Economic Theory

宏观时间序列冲击的持续性:来自经济理论的若干证据

This paper presents new estimates of persistence of shocks to quarterly labor income, monthly Treasury bill yields, and annual real common stock dividends. The authors replace orthogonality conditions involving near unit root instruments with restrictions on innovation variances implied by a generalized version of the permanent income hypothesis, a term structure model, and constant discount rate efficient markets model. Conditional on these theories, they obtain precise…

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Testing Identifiability of Cointegrating Vectors

协整向量可识别性的检验

This paper analyzes the identification and normalization of cointegrating vectors. Normalizing a cointegrating relation with respect to one of the relevant variables is with loss of generality; and restrictions which are supposed to identify a vector may fail to do so for particular parameter values. The author proposes to tackle both problems by testing whether particular rank conditions are violated. He shows that S. Johansen and K. Juselius's (1992) class of likelihood…

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The Level and Power of the Bootstrap t Test in the AR(1) Model with Trend

含趋势的AR(1)模型中自助t检验的水平与功效

This paper considers a first-order autoregressive model which may include an intercept and trend where the innovations are independently and identically distributed. The innovation distribution is assumed unknown. The autoregressive parameter is tested using the conventional t statistic. The paper presents Monte Carlo estimates of the rejection probability of the test with bootstrap-based critical values. The results show that the test with the bootstrap-based critical value…

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The Level and Power of the Bootstrap t Test in the AR(1) Model With Trend

含趋势 AR(1) 模型中 Bootstrap t 检验的水平与功效

This paper considers a first-order autoregressive model which may include an intercept and trend where the innovations are independently and identically distributed. The innovation distribution is assumed unknown. The autoregressive parameter is tested using the conventional t statistic. The paper presents Monte Carlo estimates of the rejection probability of the test with bootstrap-based critical values. The results show that the test with the bootstrap-based critical value…

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Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems

非线性动力系统的条件密度与敏感度度量估计

Using locally polynomial regression, we develop nonparametric estimators for the conditional density function and its square root, and their partial derivatives. Two measures of sensitivity to initial conditions in nonlinear stochastic dynamic systems are proposed, one of which relates Fisher information with initial-value sensitivity in dynamical systems. We propose estimators for these, and show asymptotic normality for one of them. We further propose a simple method for…

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Estimation of the Generalized Prediction Error Variance of a Multiple Time Series

多元时间序列广义预测误差方差的估计

For a multivariate stationary time series, we propose a nonparametric estimator for its generalized prediction error variance using a multivariate analog of the Szegö-Kolmogorov formula, replacing the integral by a sum and replacing the unknown spectral density matrix by a consistent estimator. Asymptotic normality of this estimator is established, and its small-sample behavior is assessed through simulation and application to two real data sets. These examples show that the…

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A Review of the Development and Application of Recursive Residuals in Linear Models

线性模型中递归残差的发展与应用综述

Recursive residuals have been shown to be useful in a variety of applications in linear models. Unlike the more familiar ordinary least squares residuals or studentized residuals, recursive residuals are independent as well as homoscedastic under the model. Their independence is particularly appealing for use in developing test statistics. They are not uniquely defined; their values depend on the order in which they are calculated, although their properties do not. In some…

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Discrimination of Time Series by Parametric Filtering

通过参数滤波区分时间序列

A new approach to time series discrimination is discussed. The approach, called parametric filtering, combines a parametric filter bank with an analysis of first-order autocorrelation from the filtered time series. As a function of the filter parameter, the first-order autocorrelation is shown to uniquely characterize the correlation structure of the original stationary time series. It is also shown to produce a diagnostic that not only characterizes correlation structures,…

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Quasi-Likelihood for Median Regression Models

中位数回归模型的拟似然

This article proposes quasi-likelihood equations for median regression models. The quasi-likelihood can be used for dependent observations such as repeated measurements or time series data. To construct a quasi-likelihood equation, we need to specify the relation between the median and the dispersion and also specify the dependency of the observations. If a monotone transformation of the original observation has a Laplace distribution, then the quasi-likelihood is the exact…

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Robust Bayesian Model Selection for Autoregressive Processes with Additive Outliers

存在加性异常值的自回归过程的稳健贝叶斯模型选择

Autoregressive (AR) models of order k are often used for forecasting and control of time series, as well as for the estimation of functionals such as the spectrum. Here we propose a method that consists of calculating the posterior probabilities of the competing AR(k) models in a way that is robust to outliers, and then obtaining the predictive distributions of quantities of interest, such as future observations and the spectrum, as a weighted average of the predictive…

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Estimation of the Generalized Prediction Error Variance of a Multiple Time Series

多元时间序列广义预测误差方差的估计

For a multivariate stationary time series, we propose a nonparametric estimator for its generalized prediction error variance using a multivariate analog of the Szegö-Kolmogorov formula, replacing the integral by a sum and replacing the unknown spectral density matrix by a consistent estimator. Asymptotic normality of this estimator is established, and its small-sample behavior is assessed through simulation and application to two real data sets. These examples show that the…

AI 解读阅读原文 ↗BibTeX ↓

Discrimination of Time Series by Parametric Filtering

通过参数滤波区分时间序列

A new approach to time series discrimination is discussed. The approach, called parametric filtering, combines a parametric filter bank with an analysis of first-order autocorrelation from the filtered time series. As a function of the filter parameter, the first-order autocorrelation is shown to uniquely characterize the correlation structure of the original stationary time series. It is also shown to produce a diagnostic that not only characterizes correlation structures,…

AI 解读阅读原文 ↗BibTeX ↓

Robust Bayesian Model Selection for Autoregressive Processes With Additive Outliers

含加性异常值的自回归过程稳健贝叶斯模型选择

Autoregressive (AR) models of order k are often used for forecasting and control of time series, as well as for the estimation of functionals such as the spectrum. Here we propose a method that consists of calculating the posterior probabilities of the competing AR(k) models in a way that is robust to outliers, and then obtaining the predictive distributions of quantities of interest, such as future observations and the spectrum, as a weighted average of the predictive…

AI 解读阅读原文 ↗BibTeX ↓

A Review of the Development and Application of Recursive Residuals in Linear Models

线性模型中递归残差的发展与应用综述

Recursive residuals have been shown to be useful in a variety of applications in linear models. Unlike the more familiar ordinary least squares residuals or studentized residuals, recursive residuals are independent as well as homoscedastic under the model. Their independence is particularly appealing for use in developing test statistics. They are not uniquely defined; their values depend on the order in which they are calculated, although their properties do not. In some…

AI 解读阅读原文 ↗BibTeX ↓