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Title: Residual-based nodewise regression in factor models with ultra-high dimensions Authors:  Marcelo Medeiros - PUC-Rio (Brazil) [presenting]
Mehmet Caner - North Carolina State University (United States)
Abstract: A new theory is provided for nodewise regression when the residuals from a fitted factor model are used to apply our results to the analysis of the maximum Sharpe ratio when the number of assets in a portfolio is larger than its time span. We introduce a new hybrid model where factor models are combined with feasible nodewise regression. Returns are generated from an increasing number of factors plus idiosyncratic components (errors). The precision matrix of the idiosyncratic terms is assumed to be sparse, but the respective covariance matrix can be non-sparse. Since the nodewise regression is not feasible due to the unknown nature of errors, we provide a feasible-residual-based nodewise regression to estimate the precision matrix of errors as a new method. Next, we show that the residual-based nodewise regression provides a consistent estimate for the precision matrix of errors. In another new development, we also show that the precision matrix of returns can be estimated consistently, even with an increasing number of factors.