Keywords: big data, conditional dependence, graphical lasso, sparse portfolio selection
In the time of big data, the conditional dependence structure of the high-dimensional data is important in computing the covariance estimators and constructing the sparse portfolios. It has applications in the contagion analysis of the market downside movement. Regarding China's special market conditions in the stock market performance, negatively correlated to the overall economic performance, we investigate several estimators of the conditional dependence structure including threshold estimator, non-stationary threshold estimator, shrinkage estimator, quantile regression estimator and compute the sparsity of precision matrix by using graphical lasso model. The empirical results indicate that the less dependence structure of the market is, the more market prices move downside, opposite to the situations in other markets. We embed the non-stationary covariance matrix into the iterative threshold algorithm to construct sparse portfolio. The sparse portfolios constructed from index component stocks enhance the performance of Exchange Traded Fund (ETF) based on the same index.