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Tests for Unit Roots and the Initial Condition

单位根检验与初始条件

The paper analyzes the impact of the initial condition on the problem of testing for unit roots. To this end, we derive a family of optimal tests that maximize a weighted average power criterion with respect to the initial condition. We then investigate the relationship of this optimal family to popular tests. We find that many unit root tests are closely related to specific members of the optimal family, but the corresponding members employ very different weightings for the…

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Bootstrap Methods for Markov Processes

马尔可夫过程的自助重抽样方法

The block bootstrap is the best known bootstrap method for time-series data when the analyst does not have a parametric model that reduces the data generation process to simple random sampling. However, the errors made by the block bootstrap converge to zero only slightly faster than those made by first-order asymptotic approximations. This paper describes a bootstrap procedure for data that are generated by a Markov process or a process that can be approximated by a Markov…

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Martingale Property of Exchange Rates and Central Bank Interventions

汇率的鞅性质与央行干预

the Richardson-Smith Wald test procedures to test for the martingale property of daily exchange rates of seven major currencies vis-a-vis the U.S. dollar. To allow for the possibility that exchange rates are not governed by a single process throughout the float, the test statistics are calculated and plotted for fixed-length moving subsample windows rather than being applied to the full sample. The results show that exchange rates do not always follow the martingale process.…

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Seasonality Tests

季节性检验

stochastic seasonality proposed by Canova and Hansen. A simplified form of the test statistic in which the nonparametric correction for serial correlation is based on estimates of the spectrum at the seasonal frequencies is considered and shown to have the same asymptotic distribution as the original formulation. Under the null hypothesis, the distribution of the seasonality test statistics is not affected by the inclusion of trends, even when modified to allow for…

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A new coincident index of business cycles based on monthly and quarterly series

基于月度与季度序列的新经济周期同步指数

Abstract Popular monthly coincident indices of business cycles, e.g. the composite index and the Stock–Watson coincident index, have two shortcomings. First, they ignore information contained in quarterly indicators such as real GDP. Second, they lack economic interpretation; hence the heights of peaks and the depths of troughs depend on the choice of an index. This paper extends the Stock–Watson coincident index by applying maximum likelihood factor analysis to a…

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Decomposability and selection of graphical models for multivariate time series

多元时间序列图模型的可分解性与模型选择

We derive conditions for decomposition and collapsibility of graphical interaction models for multivariate time series. These properties enable us to perform stepwise model selection under certain restrictions. For illustration, we apply the results to a multivariate time series describing the haemodynamic system as monitored in intensive care.

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SPRT and CUSUM in hidden Markov models

隐 Markov 模型中的 SPRT 与 CUSUM

In this paper, we study the problems of sequential probability ratio tests for parameterized hidden Markov models. We investigate in some detail the performance of the tests and derive corrected Brownian approximations for error probabilities and expected sample sizes. Asymptotic optimality of the sequential probability ratio test for testing simple hypotheses based on hidden Markov chain data is established. Next, we consider the cumulative sum (CUSUM) procedure for change…

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Dynamic panel estimation and homogeneity testing under cross section dependence

This paper deals with cross section dependence, homogeneity restrictions and small sample bias issues in dynamic panel regressions. To address the bias problem we develop a panel approach to median unbiased estimation that takes account of cross section dependence. The estimators given here considerably reduce the effects of bias and gain precision from estimating cross section error correlation. This paper also develops an asymptotic theory for tests of coefficient…

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Asymptotics for unit root tests under Markov regime‐switching

马尔可夫体制转换下单位根检验的渐近性质

processes observationally equivalent and that unit root tests virtually have no power to detect stationary processes around switching trends, although autocorrelation-robust unit root tests are not affected by size distortions. Conversely, Markov switches in the mean of the transitory components do not change the usual asymptotic properties of the tests. Finally, it is shown that in large samples Markov-switching variances cause neither size distortions nor inconsistency of…

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Generic consistency of the break‐point estimator under specification errors

模型设定错误下断点估计量的一般一致性

This paper considers the asymptotic behavior of the break-point estimator when some or all of the variables in a structural-break model are misspecified. An obvious example is misspecifying a linear model as a log--log model. The results given here cover a large number of data transformations, including transformation of the independent variables, dependent variable and transformation of both variables at the same time. The true data generating process can be stationary or…

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Exploring economic time series: a Bayesian graphical approach

探索经济时间序列:贝叶斯图形方法

Many macroeconomic time series exhibit non-stationary behaviour. When modelling such series an important problem is to assess the nature of this non-stationary behaviour. Initial interest centred on two types of linear non-stationary models, namely those for which the removal of a trend induces stationarity and those for which taking the first difference produces a stationary series. The latter are referred to as unit root models. More recently, other models such as state…

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An I(2) cointegration analysis of small‐country import price determination

小国进口价格决定机制的I(2)协整分析

This paper develops a procedure for testing hypotheses on the full set of cointegration parameters of the I(2) model. It applies this procedure to the analysis of small-country import price determination, extending the standard empirical framework to allow for variables integrated of order two. The empirical analysis of Danish data for 1975--1995 yields a fully specified long-run structure of the I(2) model in terms of stationary pricing-to-market and inventory relations, a…

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Surveillance of a Simple Linear Regression

简单线性回归的序贯监测

This article considers an important aspect of the general sequential analysis problem where a process is in control up to some unknown point i = ν − 1, after which the distribution from which the observations are generated changes. An extensive sequential analytic literature assumes that the change in distribution is abrupt, for example, from N(0,1) to N(μ,1). There is also an extensive literature that deals with a gradual change in the case where the decision (whether or…

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Nonlinear State-Space Models With State-Dependent Variances

具有状态依赖方差的非线性状态空间模型

Nonlinear state-space models with state-dependent variances (SDVs) are commonly used in financial time series. Important examples include stochastic volatility (SV) and affine term structure models. We propose a methodology for state smoothing in this class of models. Our smoothing technique is simulation based and uses an auxiliary mixture model. Key features of the auxiliary mixture model are the use of state-dependent weights and efficient block sampling algorithms to…

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J. DENIS SARGAN AND THE ORIGINS OF LSE ECONOMETRIC METHODOLOGY

丹尼斯·萨根与 LSE 计量经济学方法论的起源

I review the part played by John Denis Sargan in the formation of the “LSE approach” to dynamic econometric modeling. Despite his unassuming demeanor and his location at LSE—which had earlier dismissed a substantive role for econometric evidence—Sargan nevertheless radically altered the econometric approach of a generation, establishing a powerful approach to empirical modeling of economic time series. His main contributions to econometric methodology, and the subsequent…

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Diagnostics for Dependence within Time Series Extremes

时间序列极端值相依性的诊断

Summary The analysis of extreme values within a stationary time series entails various assumptions concerning its long- and short-range dependence. We present a range of new diagnostic tools for assessing whether these assumptions are appropriate and for identifying structure within extreme events. These tools are based on tail characteristics of joint survivor functions but can be implemented by using existing estimation methods for extremes of univariate independent and…

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Using Difference-Based Methods for Inference in Nonparametric Regression with Time Series Errors

时间序列误差下非参数回归推断的差分方法

Summary We show that difference-based methods can be used to construct simple and explicit estimators of error covariance and autoregressive parameters in nonparametric regression with time series errors. When the error process is Gaussian our estimators are efficient, but they are available well beyond the Gaussian case. As an illustration of their usefulness we show that difference-based estimators can be used to produce a simplified version of time series…

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Data Tilting for Time Series

时间序列的数据倾斜方法

Summary We develop a general methodology for tilting time series data. Attention is focused on a large class of regression problems, where errors are expressed through autoregressive processes. The class has a range of important applications and in the context of our work may be used to illustrate the application of tilting methods to interval estimation in regression, robust statistical inference and estimation subject to constraints. The method can be viewed as ‘empirical…

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Inference for Clusters of Extreme Values

极端值簇的统计推断

Summary Inference for clusters of extreme values of a time series typically requires the identification of independent clusters of exceedances over a high threshold. The choice of declustering scheme often has a significant effect on estimates of cluster characteristics. We propose an automatic declustering scheme that is justified by an asymptotic result for the times between threshold exceedances. The scheme relies on the extremal index, which we show may be estimated…

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Higher-order kernel semiparametric M-estimation of long memory

长记忆参数的高阶核半参数 M 估计

Econometric interest in the possibility of long memory has developed as a flexible alternative to, or compromise between, the usual short memory or unit root prescriptions, for example in the context of modelling cointegrating or other relationships and in describing the dependence structure of nonlinear functions of financial returns. Semiparametric methods of estimating the memory parameter can avoid bias incurred by misspecification of the short memory component. We…

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Real-Exchange-Rate Uncertainty and Private Investment in LDCs

发展中国家的实际汇率不确定性与私人投资

This paper examines empirically the link between real-exchange-rate uncertainty and private investment in developing countries, using a large cross-country time series data set. The paper builds a GARCH-based measure of real-exchange-rate volatility and finds that it has a strong negative effect on investment, after controlling for other standard investment determinants and taking into account their potential endogeneity. The effect of uncertainty is not uniform, however.…

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Testing for Forward-Rate Unbiasedness: On Regression in Levels and in Returns

远期汇率无偏性检验:水平回归与收益率回归

Several recent empirical studies have been forced to reject exact 1:1 cointegration between spot and forward exchange rates. Theoretically, this is shown to provide a possible explanation for the puzzling negative estimates reported from spot-return-forward-premium regressions. In particular, the coefficient in this regression has a unit root component in its limit distribution that imparts a bias and skewness to the estimator. Simulations are used to demonstrate how even…

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Residual-Based Block Bootstrap for Unit Root Testing

单位根检验的残差分块自助法

A nonparametric, residual-based block bootstrap procedure is proposed in the context of testing for integrated (unit root) time series. The resampling procedure is based on weak assumptions on the dependence structure of the stationary process driving the random walk and successfully generates unit root integrated pseudo-series retaining the important characteristics of the data. It is more general than previous bootstrap approaches to the unit root problem in that it allows…

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