In this major paper, we use high-dimensional models to analyze macroeconomic data which is in influenced by the break point. In particular, we consider to detect the break point and study the changes of the number of factors and the factor loadings with the structural instability.
Concretely, we propose two factor models which explain the processes of pre- and post- break periods. Then, we consider the break point as known or unknown. In both situations, we derive the shrinkage estimators by minimizing the penalized least square function and calculate the estimators of the numbers of pre- and post- break factors and the existence of the break point. After that, we present some results about the asymptotic performance of the penalty least square estimators with both the cross-section dimension and the time dimension tend to infinity.
In addition, we establish the Monte Carlo simulation to evaluate the performance of the procedure and we analyze the real dataset from 2007-2009 Great Recession. The theoretical results are confirmed by simulation that the break point can be properly detected. More than half proposed post model selection estimators domain the full sample estimators while the procedure performs relatively poor in estimating the number of pre- and post- factors.
Master of Science
Mathematics and Statistics
Major Research Paper