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A bootstrap algorithm for testing cointegration rank in VAR models in the presence of stationary variables

含平稳变量的 VAR 模型中协整秩检验的自助法算法

In this paper, a bootstrap algorithm for a reduced rank vector autoregressive (VAR) model which also includes stationary regressors, is analyzed. It is shown that the bootstrap distribution for estimating the rank converges to the distribution derived from the usual asymptotic framework. Because the asymptotic distribution will typically depend on unknown parameters, bootstrap distributions are of considerable interest in this context. The result of an application and some…

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Bootstrap Algorithms for Testing and Determining the Cointegration Rank in VAR Models

VAR 模型中协整秩检验与选择的自助法算法

In this paper a bootstrap algorithm for a reduced rank vector autoregressive model with a restricted linear trend and independent, identically distributed errors is analyzed. For testing the cointegration rank, the asymptotic distribution under the hypothesis is the same as for the usual likelihood ratio test, so that the bootstrap is consistent. It is furthermore shown that a bootstrap procedure for determining the rank is asymptotically consistent in the sense that the…

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More on testing exact rational expectations in cointegrated vector autoregressive models: Restricted constant and linear term

协整向量自回归中精确理性预期的进一步检验:受限常数项与线性项

In this note we develop the likelihood-ratio test for some linear restrictions implied by rational expectations hypotheses in a cointegrated vector autoregressive model for I(1) variables, when the constant or linear term is restricted to the cointegration space. Copyright Royal Economic Socciety 2004

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A NOTE ON THE POWER OF BOOTSTRAP UNIT ROOT TESTS

关于自助法单位根检验功效的说明

In this note we consider the asymptotic power functions of some bootstrap unit root tests under local alternatives and show that they are in fact the same as for ordinary unit root tests. This is regardless of whether the differences of the observations, i.e., the so-called restricted residuals, or the ordinary least squares residuals are used to construct the resampled observations. We also consider models containing a constant and a linear trend and the DF-GLS tests…

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A Note on Asymptotic Power Calculations in Nearly Nonstationary Time Series

近非平稳时间序列渐近功效计算的一点说明

In the AR(2) model, with a double root at unity, we consider the asymptotic distribution of the likelihood ratio with respect to a nearly nonstationary alternative. It is shown how the distribution can be represented as a Radon-Nikodym derivative of an Ito process with respect to Brownian motion. Using this result, we point out how standard contiguity arguments can be applied to obtain a representation of the asymptotic power function in nearly nonstationary alternatives.

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