Specification testing in the state space model and its identification condition

在本研究中，我们提出了状态空间模型的规范测试和识别条件。在动态因子模型中，采用格兰杰非因果关系检验、线性依赖检验和省略解释变量检验。所有的测试都可以构建为用于计算平滑矩的程序的自然副产品，并且它们不需要估计额外的参数。这些检验应用于收益率曲线的期限结构模型。此外，我们还证明了我们的约束条件解决了识别问题。在随机波动模型中，我们对二元时间序列只有一个共同的随机波动因子而没有特殊波动因子的零假设提出了拉格朗日乘数检验。我们将该测试应用于亚洲股票市场指数。

In this research, we proposed specification tests and identification conditions of the state-space model. In dynamic factor models, the Granger non-causality, linear dependency, and omitted explanatory variables tests were presented. All of the tests could be constructed as a natural byproduct of the routine used to calculate the smoothed moments, and they did not require the estimation of additional parameters. The tests were applied to the term structure model of a yield curve. In addition, we showed our restriction conditions solve the identification problem. In stochastic volatility models, we proposed the Lagrange multiplier test for the null hypothesis that the bivariate time series had only a single common stochastic volatility factor and no idiosyncratic volatility factor. We applied the test to the Asian stock market indices.