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Distributions of error correction tests for cointegration

协整误差修正检验的分布

This paper provides densities and finite sample critical values for the single-equation error correction statistic for testing cointegration. Graphs and response surfaces summarize extensive Monte Carlo simulations and highlight simple dependencies of the statistic's quantiles on the number of variables in the error correction model, the choice of deterministic components, and the sample size. The response surfaces provide a convenient way for calculating finite sample…

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Maximum likelihood estimates for the Hildreth–Houck random coefficients model

Hildreth–Houck 随机系数模型的极大似然估计

We explore maximum likelihood (ML) estimation of the Hildreth-Houck random coefficients model. We show that the global ML estimator can be inconsistent. We develop an alternative LML (local ML) estimator and prove that it is consistent and asymptotically efficient for points in the interior of the parameters. Properties of the LML and comparisons with common method of moments (MM) estimates are done via Monte Carlo. Boundary parameters lead to nonstandard asymptotic…

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Estimation of the mean of a univariate normal distribution with known variance

已知方差的一元正态分布均值估计

We consider the estimation of the unknown mean "&eegr;" of a univariate normal distribution N("&eegr;", 1) given a single observation "x". We wish to obtain an estimator which is admissible and has good risk (and regret) properties. We first argue that the "usual" estimator "t" ("x") = "x" is not necessarily suitable. Next, we show that the traditional pretest estimator of the mean has many undesirable properties. Thus motivated, we suggest the Laplace estimator, based on a…

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Forecasting autoregressive time series in the presence of deterministic components

This paper studies the error in forecasting an autoregressive process with a deterministic component. We show that when the data are strongly serially correlated, forecasts based on a model that detrends the data using OLS before estimating the autoregressive parameters are much less precise than those based on an autoregression that includes the deterministic components, and the asymptotic distribution of the forecast errors under the two‐step procedure exhibits bimodality.…

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On LM type tests for seasonal unit roots in quarterly data

In this paper the application of the score principle to test for unit roots in seasonal processes is analysed. In particular, tests based on the procedure proposed by Hylleberg et al.(1990, Journal of Econometrics, 44, 215–38) (HEGY) are introduced and the respective limit distributions derived in a local‐to‐unity context. It is shown that these statistics converge to distributions already tabulated in the literature. A Monte Carlo investigation contrasting the conventional…

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Consistency of kernel variance estimators for sums of semiparametric linear processes

半参数线性过程之和的核方差估计量的一致性

Conditions are derived for the consistency of kernel estimators of the variance of a sum of dependent heterogeneous random variables, with a representation as moving averages of near-epoch dependent functions of a mixing process. Fourth moments are not generally required. The conditions permit more dependence than a purely non-parametric representation allows, and may be close to those of the best-known conditions for the functional central limit theorem. The class of…

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The tapered block bootstrap for general statistics from stationary sequences

In this paper, we define and study a new block bootstrap variation, the taperedblock bootstrap, that is applicable in the general case of approximately linear statistics, and constitutes an improvement over the original block bootstrap of Künsch (1989). The asymptotic validity, and the favorable bias properties of the tapered block bootstrap are shown in two important cases: smooth functions of means, and M‐estimators. The important practical issues of optimally choosing the…

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Model selection tests for nonlinear dynamic models

非线性动态模型的模型选择检验

This paper generalizes Vuong (1989) asymptotically normal tests for model selection in several important directions. First, it allows for incompletely parametrized models such as econometric models defined by moment conditions. Second, it allows for a broad class of estimation methods that includes most estimators currently used in practice. Third, it considers model selection criteria other than the models" likelihoods such as the mean squared errors of prediction. Fourth,…

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Testing linear restrictions in linear models with empirical likelihood

利用经验似然检验线性模型中的线性约束

In this paper we analyse the higher order asymptotic behaviour of a profiled empirical likelihood ratio which can be used to test a set of linear restrictions in linear regression models. We show that the resulting profiled empirical likelihood ratio admits a Bartlett correction which can be used to improve to third order the accuracy of commonly used tests in applied research without any distributional assumptions about the error process. Copyright Royal Economic Society…

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Exact interpretation of dummy variables in semilogarithmic equations

半对数方程中虚拟变量的精确解释

This paper considers the percentage impact of a dummy variable regressor on the level of the dependent variable in a semilogarithmic regression equation with normal disturbances. We derive an exact unbiased estimator, its variance, and an exact unbiased estimator of the variance. The main practical contribution lies in a convenient approximation for the unbiased estimator of the variance, which can be reported together with Kennedy"s approximate unbiased estimator of the…

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Progress from forecast failure-the Norwegian consumption function

After a forecast failure, a respecification is usually necessary to account for the data ex post, in which case there is a gain in knowledge as a result of the forecast failure. Using Norwegian consumption as an example, we show that the financial deregulation in the mid‐1980s led to forecast failure both for consumption functions (CFs) and Euler equations (EEs). We argue in the paper that such forecast failures would appear to be at odds with an underlying DGP belonging to…

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On Monte Carlo estimation of relative power

相对检验功效的蒙特卡洛估计

This paper derives standard errors for Monte Carlo (MC) estimators of (relative) power of tests when the critical values under the null have also been estimated. This situation is common, for example, in unit root and cointegration (CI) tests. The associated issue of MC design is discussed. The results are illustrated on likelihood-based tests for CI rank determination. Copyright Royal Economic Society 2002

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Testing for optimality in job search models

求职搜寻模型中的最优性检验

Models of search in labor markets are potentially of great use for policy analy-sis since their parameters are structural. However, a common feature of these models is that an assumption of optimal behavior on the part of agents is necessary to achieve identifica-tion. From a classical econometric perspective, this means the assumption of optimality is untestable and, if optimality is not imposed, it is impossible to learn about the unidentified parameters. This paper argues…

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A Gaussian approach for continuous time models of the short-term interest rate

短期利率连续时间模型的高斯估计方法

This paper proposes a Gaussian estimator for nonlinear continuous time models of the short-term interest rate. The approach is based on a stopping time argument that produces a normalizing transformation facilitating the use of a Gaussian likelihood. A Monte Carlo study shows that the finite-sample performance of the proposed procedure offers an improvement over the discrete approximation method proposed by Nowman (1997). An em-pirical application to US and British interest…

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Maximum eigenvalue versus trace tests for the cointegrating rank of a VAR process

The properties of a range of maximum eigenvalue and trace tests for the cointegrating rank of a vector autoregressive process are compared. The tests are all likelihood ratio-type tests and operate under different assumptions regarding the deterministic part of the data generation process. The asymptotic distributions under local alternatives are given and the local power is derived. It is found that the local power of corresponding maximum eigenvalue and trace tests is very…

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The limiting distribution of the t-ratio for the unit root test in an AR(1)

AR(1) 单位根检验 t 比率的极限分布

We consider the limiting distribution of the t -statistic for testing the random walk hypothesis in the classical Gaussian AR(1) model. Abadir (1995, Econometric Theory, 11, 775�793) derived the first derives a closed (i.e. integration-free) expression for the limit-ing distribution function. This paper derives an alternative closed expression. Abadir�s and the new expression are valid only for negative arguments and each involve two infinite summa-tions. To enable a…

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Asymptotic approximations in the near‐integrated model with a non‐zero initial condition

非零初始条件下近单整模型的渐近近似

This paper considers various asymptotic approximations in the near-integrated first-order autoregressive model with a non-zero initial condition. We first extend the work of Knight and Satchell (1993), who considered the random walk case with a zero initial con-dition, to derive the expansion of the relevant joint moment generating function in this more general framework. We also consider, as alternative approximations, the stochastic expansion of Phillips (1987c) and the…

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Likelihood‐based cointegration tests in heterogeneous panels

异质面板中基于似然的协整检验

This paper presents a maximum likelihood panel test of the cointegrating rank in heterogeneous panel models based on the mean of the individual rank trace statistics. The existence of the first two moments of the asymptotic distribution of the individual trace statistic is established. Based on this, the asymptotic distribution of the test statistic is shown to be normal. The small-sample size and power properties are investigated using Monte Carlo simulations. An empirical…

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Testing the unit root hypothesis using generalized range statistics

使用广义极差统计量检验单位根假设

The application of rescaled range statistics in econometrics is restricted to long memory detection in economic and financial time series. However, in this paper it is shown how such statistics can be generalized and used to test the unit root hypothesis. The proposed generalizations lead to testing procedures that are found to be consistent against I (0 , I (2 as well as against fractional integration and misspecification of the deterministic trend. A Monte Carlo simulation…

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Are apparent findings of nonlinearity due to structural instability in economic time series?

经济时间序列表观非线性是否源于结构不稳定?

Many modelling issues and policy debates in macroeconomics depend on whether macroeconomic time series are best characterized as linear or nonlinear. If departures from linearity exist, it is important to know whether these are endogenously generated (as in, e.g. a threshold autoregressive model) or whether they merely reflect changing structure over time. In this paper, we discuss a model comparison methodology which addresses these issues. We advocate a Bayesian approach…

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An automatic leading indicator of economic activity: forecasting GDP growth for European countries*

经济活动的自动先行指标:欧洲国家GDP增长预测

In the construction of a leading indicator model of economic activity, economists must select among a pool of variables which lead output growth. Usually the pool of variables is large and a selection of a subset must be carried out. This paper proposes an automatic leading indicator model which, rather than preselection, uses a dynamic factor model to summarize the information content of a pool of variables. Results using quarterly data for France, Germany, Italy and the…

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Forecasting with difference-stationary and trend-stationary models

Although difference-stationary (DS) and trend-stationary (TS) processes have been subject to considerable analysis, there are no direct comparisons for each being the datageneration process (DGP).We examine incorrect choice between these models for forecasting for both known and estimated parameters. Three sets of Monte Carlo simulations illustrate the analysis, to evaluate the biases in conventional standard errors when each model is misspecified, compute the relative…

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Estimation of AR(1) models with unequally spaced pseudo‐panels

不等间隔伪面板中AR(1)模型的估计

Surveys in developing countries are often taken at unequally spaced intervals. This paper provides for the estimation of dynamic pseudo-panel models with such data. Non-linear least squares, minimum distance, and one-step estimators are used to impose the non-linear parameter restrictions which occur in dynamic models over unequally spaced periods. Consistency and asymptotic normality of the estimators is established. A small-scale Monte Carlo simulation study corroborates…

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Graphical conditional moment tests

图形化条件矩检验

Tests of misspecification or other defects in microeconometric models are usually numerical and based on an average over the sample. In this paper, it is shown that certain types of misspecification can be concealed by averaging, and a framework is developed which allows the specification to be checked in the near neighbourhood of each sample point, rather than for the sample as a whole. The framework involves the application of a scatter-plot smoothing technique to a pair…

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