High-dimensional Setups Research Articles

Lasso with long memory regression errors

Lasso is a computationally efficient approach to model selection and estimation, and its properties are well studied when the regression errors are independent and identically distributed. We study the case, where the regression errors form a long memory moving average process. We establish a finite sample oracle inequality for the Lasso solution. We then show the asymptotic sign consistency in this setup. These results are established in the high dimensional setup (p>n) where p can be increasing exponentially with n. Finally, we show the consistency, n1/2−d-consistency of Lasso, along with the oracle property of adaptive Lasso, in the case where p is fixed. Here d is the memory parameter of the stationary error sequence. The performance of Lasso is also analysed in the present setup with a simulation study.

Factor Multivariate Stochastic Volatility via Wishart Processes

This paper proposes a high dimensional factor multivariate stochastic volatility (MSV) model in which factor covariance matrices are driven by Wishart random processes. The framework allows for unrestricted specification of intertemporal sensitivities, which can capture the persistence in volatilities, kurtosis in returns, and correlation breakdowns and contagion effects in volatilities. The factor structure allows addressing high dimensional setups used in portfolio analysis and risk management, as well as modeling conditional means and conditional variances within the model framework. Owing to the complexity of the model, we perform inference using Markov chain Monte Carlo simulation from the posterior distribution. A simulation study is carried out to demonstrate the efficiency of the estimation algorithm. We illustrate our model on a data set that includes 88 individual equity returns and the two Fama–French size and value factors. With this application, we demonstrate the ability of the model to address high dimensional applications suitable for asset allocation, risk management, and asset pricing.