Abstract
The problem of detecting change points in the mean of high dimensional panel data with potentially strong cross–sectional dependence is considered. Under the assumption that the cross–sectional dependence is captured by an unknown number of common factors, a new CUSUM type statistic is proposed. We derive its asymptotic properties under three scenarios depending on to what extent the common factors are asymptotically dominant. With panel data consisting of N cross sectional time series of length T, the asymptotic results hold under the mild assumption that min {N, T} → ∞, with an otherwise arbitrary relationship between N and T, allowing the results to apply to most panel data examples. Bootstrap procedures are proposed to approximate the sampling distribution of the test statistics. A Monte Carlo simulation study showed that our test outperforms several other existing tests in finite samples in a number of cases, particularly when N is much larger than T. The practical application of the proposed results are demonstrated with real data applications to detecting and estimating change points in the high dimensional FRED-MD macroeconomic data set.
Application of High-Dimensional Statistics and Network Based Visualization Techniques on Arab Diabetes and Obesity Data
