This paper proposes a novel methodology for the online detection of changepoints in the factor structure of large matrix time series. Our approach is based on the well-known fact that, in the presence of a changepoint, a factor model can be rewritten as a model with a larger number of common factors. In turn, this entails that, in the presence of a changepoint, the number of spiked eigenvalues in the second moment matrix of the data increases. Based on this, we propose two families of procedures - one based on the fluctuations of partial sums, and one based on extreme value theory - to monitor whether the first non-spiked eigenvalue diverges after a point in time in the monitoring horizon, thereby indicating the presence of a changepoint. Our procedure is based only on rates; at each point in time, we randomise the estimated eigenvalue, thus obtaining a normally distributed sequence which is $i.i.d.$ with mean zero under the null of no break, whereas it diverges to positive infinity in the presence of a changepoint. We base our monitoring procedures on such sequence. Extensive simulation studies and empirical analysis justify the theory.
翻译:本文提出了在线检测大型矩阵时间序列要素结构变化点的新方法。我们的方法基于众所周知的事实,即当出现一个变化点时,可以将一个要素模型改写为具有更多共同因素的模型。反过来,这意味着,在出现变化点时,数据增长第二时刻矩阵中高涨的eigen值数量将随数据增长而变化。在此基础上,我们建议两个程序组----一个基于部分金额波动,一个基于极端价值理论----以监测在监测地平线上一个时间点后第一个非斯皮奇亚值差异,从而显示存在一个变化点。我们的程序仅以费率为基础;在每一个时间点上,我们随机测算估计的eigen值数量,从而获得正常分布的顺序,即$.i.d.d.,零在不中断状态下为零,而在出现变化点时则有正数。我们把我们的监测程序建立在这种顺序上,广泛的模拟研究和实证分析证明理论是正确的。