Estimation and Testing of Structural Changes in Possibly Misspecified High-Dimensional Factor Models: A Singularity Approach

Description

While high-dimensional factor models are useful tools for big data processing andmachine learning, practitioners should be cautious when interpreting the estimationresults of a factor model because the factor loading coefficients may undergo structuralchanges. In our preliminary study, we propose a quasi-maximum likelihood (QML)estimator for a single unknown break date. The new estimator can be applied under abroader context by allowing more types of breaks than existing methods. Ourpreliminary study also proposes a likelihood ratio (LR) test for breaks in loadings basedon the QML estimator. We show that underlying structural changes in factor loading matrix leads to singularsubsample covariance matrices of pseudo-factors. Our preliminary work proves that thissingularity results in the QML estimator equal to the true break point with a probabilityapproaching one in large samples under circumstances where existing estimators do notwork. In addition, the superior performance of the QML estimator under the singularityalso makes our LR test more powerful than existing tests, so it can detect structuralbreaks with a higher probability. Given the good properties of our QML estimator and LR test, we would like to extendthe results to a more general setting. First, we will consider a more realistic setup withpossibly multiple breaks in the sample. The project will establish the conditions underwhich the QML estimator can maintain its accuracy for multiple break points. Also, theproject plans to generalize the LR test and study its sensitivity to multiple breaks (i.e.,the power properties). We will propose a test for m breaks versus m+1 breaks, whichrequires us to investigate the properties of the QML estimator when the number ofbreaks is underestimated. Third, we will consider the robustness of the QML estimatorunder the case where the number of factors is possibly overestimated. Preliminarysimulation supports the robustness property and we plan to further investigate thisconjecture.