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首页> 外文期刊>Journal of Time Series Analysis >A GENERALIZED PORTMANTEAU TEST FOR INDEPENDENCE OF TWO INFINITE-ORDER VECTOR AUTOREGRESSIVE SERIES
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A GENERALIZED PORTMANTEAU TEST FOR INDEPENDENCE OF TWO INFINITE-ORDER VECTOR AUTOREGRESSIVE SERIES

机译：两个无穷向量自回归序列的独立性的广义Portmanteau检验

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摘要

In many situations, we want to verify the existence of a relationship between multivariate time series. Here, we propose a semiparametric approach for testing the independence between two infinite-order vector autoregressive (VAR(∞)) series, which is an extension of Hong's [Biometrika (1996c) vol. 83, 615-625] univariate results. We first filter each series by a finite-order autoregression and the test statistic is a standardized version of a weighted sum of quadratic forms in the residual cross-correlation matrices at all possible lags. The weights depend on a kernel function and on a truncation parameter. Using a result of Lewis and Reinsel [Journal of Multivariate Analysis (1985) Vol. 16, pp. 393- 411], the asymptotic distribution of the test statistic is derived under the null hypothesis and its consistency is also established for a fixed alternative of serial cross-correlation of unknown form. Apart from standardization factors, the multivariate portmanteau statistic proposed by Bouhaddioui and Roy [Statistics and Probability Letters (2006) vol. 76, pp. 58-68] that takes into account a fixed number of lags can be viewed as a special case by using the truncated uniform kernel. However, many kernels lead to a greater power, as shown in an asymptotic power analysis and by a small simulation study in finite samples. A numerical example with real data is also presented.
机译：在许多情况下，我们要验证多元时间序列之间是否存在关系。在这里，我们提出了一种半参数方法来测试两个无限阶向量自回归（VAR（∞））系列之间的独立性，这是Hong [Biometrika（1996c）vol。 83，615-625]单变量结果。我们首先通过有限阶自回归对每个序列进行过滤，检验统计量是所有可能滞后残差互相关矩阵中二次形式的加权和的标准形式。权重取决于内核函数和截断参数。使用Lewis和Reinsel的结果[Multivariate Analysis（1985）Vol。 [16，pp。393-411]，检验统计量的渐近分布是在原假设下得出的，并且其一致性也可用于未知形式的序列互相关的固定选择。除标准化因素外，Bouhaddioui和Roy提出的多元portmanteau统计量[Statistics and Probability Letters（2006）vol。 [76，pp。58-68]，考虑到固定滞后数，可以通过使用截短的均匀核将其视为特殊情况。但是，如渐近幂分析和有限样本中的小型仿真研究所示，许多内核会产生更大的幂。还给出了带有实际数据的数值示例。

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