Specification testing in the state space model and its identification condition

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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.