AI 中文总结
本文研究因果非因果状态空间模型，证明其可与理性预期股票价格模型一致，探讨该模型的状态与参数推断方法，以互联网泡沫规模估计验证其有效性。
AI 中文摘要
本文研究因果非因果状态空间模型，以建模具有局部爆炸性增长后急剧下降特征的时间序列，如股票价格。为论证使用因果非因果状态空间模型的合理性，我们证明了Gourieroux和Zakoian（2017）提出的因果非因果卷积自回归模型可与理性预期股票价格模型一致。与因果状态空间模型类似，核心问题是如何在因果非因果状态空间模型中进行状态与参数推断，本文对此展开讨论。我们还更深入研究了因果非因果卷积自回归模型，提供了该模型的一些新结果。为说明因果非因果状态空间模型的实用性，我们使用该模型实时和事后估计互联网泡沫的规模，并以Gourieroux和Zakoian（2017）考虑的稳定非因果自回归模型作为基准。
英文摘要
In this paper, we study causal non-causal state space models to model time series characterised by a local explosive increase followed by a sharp decrease such as stock prices. To motivate the use of causal non-causal state space models, we show that the causal non-causal convolution autoregressive model introduced by Gourieroux and Zakoian (2017) can be consistent with the rational expectations stock price model. As in a causal state space model, a central question is how to perform state and parameter inference in the causal non-causal state space model, which we discuss in the paper. We also study the causal non-causal convolution autoregressive model in more detail, providing some new results for the model. To illustrate the usefulness of causal non-causal state space models, we use the causal non-causal convolution autoregressive model to estimate the size of the dot-com bubble in both real time and a posteriori with the stable non-causal autoregressive model considered also by Gourieroux and Zakoian (2017) as a benchmark.
