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Nonlinear econometric models with cointegrated and deterministically trending regressors

含协整与确定性趋势解释变量的非线性计量模型

This paper develops an asymptotic theory for a general class of nonlinear non-stationary regressions, extending earlier work by Phillips and Hansen (1990) on linear coin-tegrating regressions.The model considered accommodates a linear time trend and stationary regressors, as well as multiple I(1) regressors. We establish consistency and derive the limit distribution of the nonlinear least squares estimator. The estimator is consistent under fairly general conditions but the…

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Analysis of a panel of UK macroeconomic forecasts

英国宏观经济预测面板分析

This paper looks at unobserved components models and examines the implied weighting patterns for signal extraction. There are four main themes. The first concerns the implications of correlated disturbances driving the components, especially those cases in which the correlation is perfect. The second is about the way in which ARIMA-based methods for trend extraction relate to those based on unobserved components. The third explores the impact of heteroscedasticity and…

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Fiscal forecasting: The track record of the IMF, OECD and EC

财政预测:国际货币基金组织、经合组织与欧委会的历史表现

We analyse the relative performance of the IMF, OECD and EC in forecasting the government deficit, as a ratio to GDP, for the G7 countries. Interesting differences across countries emerge, sometimes supporting the hypothesis of an asymmetric loss function (i.e. of a preference for underprediction or overprediction), and potential benefits from forecast pooling.

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Determining the order of differencing in seasonal time series processes

In this paper we propose a sequential testing procedure to determine the order of differencing in seasonally observed time series processes, which builds upon existing approaches developed for nonseasonal series. We allow for the possible presence of multiple unit roots at both the zero and seasonal frequencies of the data. Multiple seasonal unit roots can be useful in circumstances where one does not wish to take logarithms of the data‐set at hand. Multiple unit roots at…

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Testing for stationarity in heterogeneous panel data

This paper proposes a residual-based Lagrange multiplier (LM) test for a null that the individual observed series are stationary around a deterministic level or around a deterministic trend against the alternative of a unit root in panel data. The tests which are asymptotically similar under the null, belong to the locally best invariant (LBI) test statistics. The asymptotic distributions of the statistics are derived under the null and are shown to be normally distributed.…

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Testing for linear autoregressive dynamics under heteroskedasticity

异方差下线性自回归动态的检验

A puzzling characteristic of asset returns for various frequencies is the often observed positive autocorrelation at lag one. To some extent this can be explained by standard asset pricing models when assuming time-varying risk premia. However, one often finds better results when directly fitting an autoregressive model, for which there is little economic foundation. One may ask whether the underlying process does in fact contain an autoregressive component. It is therefore…

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Prediction‐based estimating functions

A generalization of martingale estimating functions is presented which is useful when there are no natural or easily calculated martingales that can be used to construct a class of martingale estimating functions. An estimating function of the new type, which is based on linear predictors, is called a prediction‐based estimating functions. Special attention is given to classes of prediction‐based estimating functions given by a finite‐dimensional space of predictors. It is…

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The finite sample distribution of the KPSS test

KPSS 检验的有限样本分布

This paper gives numerical approximations of the finite sample distribution of the KPSS test statistic. We use two types of approximations depending on whether we estimate the long-run variance or not. In the known variance case we apply a very simple Laplace inversion formula, while in the unknown case we use saddlepoint approximation to calculate the right-hand tail of the distribution of the KPSS test statistic. In the unknown variance case, we also investigate the…

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Controlling the significance levels of prediction error tests for linear regression models

控制线性回归模型预测误差检验的显著性水平

This paper provides evidence on problems associated with using standard tests for predictive failure when the errors of a linear regression model are not normally distributed. The ability of a simple bootstrap procedure to give a useful degree of control over the significance levels is examined.

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Measuring business cycles with a dynamic Markov switching factor model: an assessment using Bayesian simulation methods

动态马尔可夫转换因子模型的商业周期测度:贝叶斯模拟评估

A Markov switching common factor is used to drive a dynamic factor model for important macroeconomic variables in eight countries. Bayesian estimation of the model is based on Markov chain Monte Carlo simulation methods which yield inferences about the unobservable path of the common factor, the latent variable of the state process and all model parameters. Additionally, simulation based filtering provides us with samples from the prediction density that can be used for…

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Behaviour of the standard and symmetric Dickey-Fuller-type tests when there is a break under the null hypothesis

We examine the behaviour of tests of the unit root null hypothesis when the true generating model is I (1) with a break. Asymptotic distributional results are derived predicting that the standard Dickey–Fuller test will in that case yield frequent rejections of the null for relatively early breaks. This phenomenon is most severe for lowest values of the break fraction under a break in level, and for a break in slope occurring about 15% of the way through the series. However,…

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Some tests for parameter constancy in cointegrated VAR‐models

协整VAR模型中的若干参数稳定性检验

Some methods for the evaluation of parameter constancy in cointegrated vector autoregressive (VAR) models are discussed. Two different ways of re-estimating the VAR-model are proposed; one in which all parameters are estimated recursively based upon the likelihood function for the first observations, and another in which the cointegrating relations are estimated recursively from a likelihood function, where the short-run parameters have been concentrated out. We suggest…

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Rank estimation of a transformation model with observed truncation

存在可观测截断时变换模型的秩估计

This paper introduces rank estimators for a general transformation model with observable truncation points. The estimators, which are modified versions of the rank estimators of Han (1987) and Cavanagh and Sherman (1998), are asymptotically normal and require no bandwidth choice. Log-concavity of the error disturbance?s survival function is a sufficient condition for the associated monotonicity conditions. Monte Carlo simulations investigate the estimators? behavior for…

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Cointegration rank inference with stationary regressors in VAR models

含平稳回归变量的VAR模型协整秩推断

The issue of including stationary explanatory variables is addressed in the vector autoregressive (VAR) model, when testing for cointegration rank. It is shown that simply in-cluding stationary explanatory variables as extra regressors will lead to nuisance parameters in the asymptotic distribution of the trace statistic for cointegration rank. The nuisance parame-ters are characterized as canonical correlations between the common trends (which in this case also involve the…

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Inference for Lorenz curve orderings

洛伦兹曲线排序的统计推断

In this paper we consider the issue of performing statistical inference for Lorenz curve orderings. This involves testing for an ordered relationship in a multivariate context and making comparisons among more than two population distributions. Our approach is to frame the hypotheses of interest as sets of linear inequality constraints on the vector of Lorenz curve ordinates, and apply order-restricted statistical inference to derive test statistics and their sampling…

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Simulated maximum likelihood estimation of multivariate mixed‐Poisson regression models, with application

多元混合泊松回归的模拟最大似然估计及应用

This paper proposes and implements simulated maximum likelihood estimation of bivariate count models with unrestricted correlation pattern of unobserved heterogeneity. The implementation incorporates both antithetic acceleration and adjustment for first-order simulation bias. Both the Monte Carlo simulation evidence and an application to health utilization data confirm that the method is reliable and feasible in data analysis.

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Degrees of freedom adjustment for disturbance variance estimators in dynamic regression models

动态回归模型中扰动方差估计量的自由度调整

In the classical regression model with fixed regressors the statistic S 2 , i.e. the sum of squared residuals (SSR) divided by the number of degrees of freedom, is an unbiased estimator of the variance of the disturbances. If the model is dynamic and contains lagged-dependent explanatory variables, then the least-squares coefficient estimators are biased in finite samples, and so is S 2 . By deriving the expectation of the initial terms in an expansion of the expression for…

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An ADF coefficient test for a unit root in ARMA models of unknown order with empirical applications to the US economy

This paper proposes an Augmented Dickey-Fuller (ADF) coefficient test for detecting the presence of a unit root in autoregressive moving average (ARMA) models of unknown order. Although the limit distribution of the coefficient estimate depends on nuisance parameters, a simple transformation can be applied to eliminate the nuisance parameter asymptotically, providing an ADF coefficient test for this case. When the time series has an unknown deterministic trend, we propose a…

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Distribution approximation of unit root tests in autoregressive models

自回归模型中单位根检验的分布近似

The present work applies saddlepoint approximation to calculate the left-hand tail of the distribution of the unit root t test and an asymptotic equivalent test under the null hypothesis of a unit root. (This is the tail of interest when testing against a stationary alternative.) The saddlepoint equation is solved numerically. Distribution approximations are obtained both in the asymptotic and finite-sample cases. In the finite-sample case, two slightly different methods are…

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A framework for economic forecasting

经济预测的一个分析框架

This paper proposes a tripartite framework of design, evaluation, and post-evaluation analysis for generating and interpreting economic forecasts. This framework?s value is illustrated by re-examining mean square forecast errors from dynamic models and nonlinearity biases from empirical forecasts of US external trade. Previous studies have examined properties such as nonlinearity bias and the possible nonmonotonicity and nonexistence of mean square forecast errors in…

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Computationally attractive stability tests for the efficient method of moments

This paper develops structural stability tests based on the Efficient Method of Moments for the case of a known breakpoint. Computationally attractive post-sample estimators and test-statistics for structural stability are proposed, which are modifications of the Lagrange Multiplier, Likelihood Ratio, Wald and Hansen tests for structural stability. The modifications retain the asymptotic optimality properties against certain local alternatives of those based on efficient…

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Simulation‐based likelihood inference for limited dependent processes

受限因变量过程的模拟似然推断

This paper looks at the problem of performing likelihood inference for limited dependent processes. Throughout we use simulation to carry out either classical inference through a simulated score method (simulated EM algorithm) or Bayesian analysis. A common theme is to develop computationally robust methods which are likely to perform well for any time series problem. The central tools we use to deal with the time series dimension of the models are the scan sampler and the…

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Estimating the Kronecker indices of cointegrated echelon‐form VARMA models

协整阶梯形 VARMA 模型的 Kronecker 指数估计

VARMA models can be parameterized by using the echelon form, which is characterized by the Kronecker indices. Three different methods for estimating the Kronecker indices of echelon-form VARMA models are discussed and compared. The three methods are expected to work even for non-stationary processes with cointegrated variables. They have the common feature of estimating the individual equations of the system separately and using order selection criteria. The small sample…

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Simulation‐based finite sample normality tests in linear regressions

线性回归中基于模拟的有限样本正态性检验

In the literature on tests of normality, much concern has been expressed over the problems associated with residual-based procedures. Indeed, the specialized tables of critical points which are needed to perform the tests have been derived for the location-scale model; hence, reliance on available significance points in the context of regression models may cause size distortions. We propose a general solution to the problem of controlling the size of normality tests for the…

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