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

针对二元时间序列存在唯一的共同随机波动率而不存在特殊波动率因子的原假设，提出了拉格朗日乘子检验。检验统计量是通过在线性状态空间形式中表示模型而得到的，假设平方测量误差的对数是正态分布的。

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.