Nonnegative Elastic Net and application in index tracking

This paper deals with the model selection consistency of Nonnegative Elastic Net (proposed by imposing nonnegative constraint to the regression parameters) in general setting where p (the number of predictors), q (the number of predictors with non-zero coefficients in the true linear model) and n (sample size) all go to infinity. We prove that this method has nice property of variable selection consistency under NEIC condition. Comparing with Nonnegative-lasso, Nonnegative Elastic Net can select the true variables even when Nonnegative-lasso cannot. In Empirical Part, this method is applied to the constrained index tracking problem in stock market without short sales, i.e. tracking CSI 300 Index1 and SSE 180 Index2 by selecting about 30 stocks. The results indicate that Nonnegative Elastic Net outperforms Nonnegative-lasso in asset selection. A two-step method, Nonnegative Elastic Net combined with OLS produce better results than simple Nonnegative Elastic Net method.