Multivariate fractional integration tests allowing for conditional heteroskedasticity with an application to return volatility and trading volume
允许条件异方差的多变量分数积分检验：收益波动率与成交量应用AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要直接研究多变量分数积分时间序列检验，并用于股票收益波动率和成交量的持久性分析，支持时间序列与金融波动率分类。
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允许条件异方差的多变量分数积分检验：收益波动率与成交量应用
- 研究问题
- 在条件异方差及条件二阶矩相关存在时，如何联合检验多变量序列的分数积分阶数，并比较股票收益波动率与成交量的持久性？
- 方法与思路
- 作者在原假设下以可行 GLS 估计 FIVAR 模型，构造采用异方差稳健方差矩阵的 LM 联合检验，允许鞅差创新的条件二阶矩相关。
- 材料陈述的贡献
- 摘要称检验在较弱创新条件下具有标准卡方极限分布，模拟中缓解异方差导致的尺寸膨胀；股票应用发现波动率通常更持久。
- 阅读关注点
- 核对鞅差及矩条件、平稳与非平稳区域的处理、稳健方差估计的一致性，以及不同波动率代理如何影响积分阶数比较。
- 阅读边界
- 允许条件二阶矩的时序相关，并不表示允许任意创新自相关；摘要未列出全部正则条件，应用中的持久性排序也取决于波动率代理。
原文摘要
Summary We introduce a new joint test for the order of fractional integration of a multivariate fractionally integrated vector autoregressive (FIVAR) time series based on applying the Lagrange multiplier principle to a feasible generalised least squares estimate of the FIVAR model obtained under the null hypothesis. A key feature of the test we propose is that it is constructed using a heteroskedasticity‐robust estimate of the variance matrix. As a result, the test has a standard χ 2 limiting null distribution under considerably weaker conditions on the innovations than are permitted in the extant literature. Specifically, we allow the innovations driving the FIVAR model to follow a vector martingale difference sequence allowing for both serial and cross‐sectional dependence in the conditional second‐order moments. We also do not constrain the order of fractional integration of each element of the series to lie in a particular region, thereby allowing for both stationary and non‐stationary dynamics, nor do we assume any particular distribution for the innovations. A Monte Carlo study demonstrates that our proposed tests avoid the large oversizing problems seen with extant tests when conditional heteroskedasticity is present in the data. We report an empirical case study for a sample of major US stocks investigating the order of fractional integration in trading volume and different measures of volatility in returns, including realised variance. Our results suggest that both return volatility and trading volume are fractionally integrated, but with the former generally found to be more persistent (having a higher fractional exponent) than the latter, when more reliable proxies for volatility such as the range or realised variance are used.