Linear state space models (LSSMs) provide a very general framework for multiple time series analysis. We propose a novel statistical procedure for testing validity of a LSSM which is focused on the detection of changes in parameters of the given LSSM. We derive the moments as well as the asymptotic distribution of the test statistic, and investigate the test size and the test power for changes in means, variances, and autoregressive coefficients. In the empirical application we test the validity of LSSMs applied to daily realized volatility time series.

中文翻译：

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测试线性状态空间模型中的参数变化

线性状态空间模型 (LSSM) 为多时间序列分析提供了一个非常通用的框架。我们提出了一种新的统计程序来测试 LSSM 的有效性，该程序专注于检测给定 LSSM 参数的变化。我们推导了检验统计量的矩和渐近分布，并研究了检验量和均值、方差和自回归系数变化的检验功效。在实证应用中，我们测试了应用于每日实际波动率时间序列的 LSSM 的有效性。