因子模型门槛效应的LM和Wald检验及其统计性质研究

门槛因子模型可以有效地刻画高维度时间序列的共变特征和区制转换行为,具有良好的可解释性和预测能力。针对因子载荷矩阵存在的门槛效应,本文提出了拉格朗日乘子和沃尔德检验方法,并给出了渐近分布,相关结果表明以上检验统计量具有良好的大样本性质和有限样本表现。在实证部分,以我国股市的行业指数作为研究对象,通过构建门槛因子模型来刻画我国股票市场波动的共变性特征和非对称效应。实证结果表明基于门槛因子模型可以很好地刻画中国股市行业收益率波动的共变特征和区制转换行为。

LM and Wald Tests of Threshold Effect in Factor Model and Their Statistical Properties

Threshold factor model is an effective method to describe the co-movement and regime shift of high-dimensional time series, and has high interpretability and predictability. In this paper, we propose the Lagrange Multiplier and Wald tests to test the threshold effect. We also study the asymptotic properties, and the results show that the above tests have good large-sample property and finite sample performance. In the empirical part, threshold factor models are constructed and applied to China’s stock sector indexes to reflect the co-movement and asymmetric effect of market volatility. The empirical results provide clear evidence that the threshold factor model best describes co-movement and regime shift in the volatility of stock market returns.