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An Investigation into Multivariate Variance Ratio Statistics and their Application to Stock Market Predictability

机译:多元方差比统计及其在股票市场可预测性中的应用研究

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We propose several multivariate variance ratio statistics for "testing" the weak form Efficient Market Hypothesis and for measuring the direction and magnitude of departures from this hypothesis. We derive the asymptotic distribution of the statistics and scalar functions thereof under the null hypothesis that returns are unpredictable after a constant mean adjustment. We propose asymptotic standard errors that are robust to departures from the "no leverage" assumption of Lo and MacKinlay (1988), but are relatively simple and in particular do not require the selection of a bandwidth parameter. We show the limiting behavior of the statistic under a multivariate fads model and under a moderately explosive bubble process: these alternative hypotheses give opposite predictions with regards to the long-run value of the statistics. We apply the methodology to weekly returns for Center for Research in Security Prices size-sorted portfolios from 1962 to 2013 in three subperiods. We find evidence of a reduction of linear predictability in the most recent period, for small and medium cap stocks, but we still reject the multivariate null hypothesis in the most recent period. The main findings are not substantially affected by allowing for a common factor time varying risk premium.
机译:我们提出了几种多元方差比率统计数据,用于“测试”弱形式的有效市场假说并测量偏离该假说的方向和幅度。我们在原假设下得出统计量和标量函数的渐近分布,该原假设是在均值调整后无法预测的。我们提出渐近标准误差,该误差对于抵制Lo和MacKinlay(1988)的“无杠杆”假设具有鲁棒性,但是相对简单,特别是不需要选择带宽参数。我们显示了在多元时尚模型和适度爆炸性泡沫过程下统计量的局限性:这些替代假设就统计量的长期价值给出了相反的预测。我们将该方法应用于1962年至2013年三个价格分时段的按价格分类的证券投资研究中心的每周收益。我们发现中小型股票最近期线性可预测性下降的证据,但我们仍拒绝最近期的多元零假设。主要因素并未因考虑公共因素随时间变化的风险溢价而受到实质性影响。

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