Hypothesis testing of the dimension of state variables in the state space model

对于二元时间序列只有共同的随机波动和没有特殊波动因子的零假设，提出了拉格朗日乘数检验。在假设测量误差平方的对数为正态分布的情况下，将模型表示为线性状态空间形式，得到检验统计量。

The Lagrange multiplier test is proposed for the null hypothesis that the bivariate time series has the only common stochastic volatility and no idiosyncratic volatility factor. The test statistic is derived by representing the model in the linear state-space form under the assumption that the log of squared measurement error is normally distributed.