Weak Identification of Long Memory with Implications for Volatility Modeling
研究了金融资产波动率建模中长记忆模型与粗糙模型之间的弱识别问题，发现两者在渐近上近乎观测等价，标准方法难以区分，并提出了识别稳健的置信集方法。实证表明两种模型可能共存。
Abstract This paper explores implications of weak identification in common ‘long memory’ and recent ‘rough’ approaches to modeling volatility dynamics of financial assets. We unveil an asymptotic near-observational equivalence between a long memory model with weak autoregressive dynamics and a rough model with a near-unit autoregressive root. Standard methods struggle to distinguish them, and conventional asymptotics are invalid. We propose an identification-robust approach to construct confidence sets that reveal the uncertainty and aid inference. Empirical studies based on realized volatility and trading volume often fail to statistically reject either model, thereby providing evidence of their potential coexistence.