On LASSO for High Dimensional Predictive Regression

This paper examines LASSO, a widely-used $L_{1}$-penalized regression method, in high dimensional linear predictive regressions, particularly when the number of potential predictors exceeds the sample size and numerous unit root regressors are present. The consistency of LASSO is contingent upon two key components: the deviation bound of the cross product of the regressors and the error term, and the restricted eigenvalue of the Gram matrix. We present new probabilistic bounds for these components, suggesting that LASSO's rates of convergence are different from those typically observed in cross-sectional cases. When applied to a mixture of stationary, nonstationary, and cointegrated predictors, LASSO maintains its asymptotic guarantee if predictors are scale-standardized. Leveraging machine learning and macroeconomic domain expertise, LASSO demonstrates strong performance in forecasting the unemployment rate, as evidenced by its application to the FRED-MD database

Boosting the Hodrick-Prescott Filter

The Hodrick-Prescott (HP) filter is one of the most widely used econometric methods in applied macroeconomic research. The technique is nonparametric and seeks to decompose a time series into a trend and a cyclical component unaided by economic theory or prior trend specification. Like all nonparametric methods, the HP filter depends critically on a tuning parameter that controls the degree of smoothing. Yet in contrast to modern nonparametric methods and applied work with these procedures, empirical practice with the HP filter almost universally relies on standard settings for the tuning parameter that have been suggested largely by experimentation with macroeconomic data and heuristic reasoning about the form of economic cycles and trends. As recent research has shown, standard settings may not be adequate in removing trends, particularly stochastic trends, in economic data. This paper proposes an easy-to-implement practical procedure of iterating the HP smoother that is intended to make the filter a smarter smoothing device for trend estimation and trend elimination. We call this iterated HP technique the boosted HP filter in view of its connection to L_2-boosting in machine learning. The paper develops limit theory to show that the boosted HP filter asymptotically recovers trend mechanisms that involve unit root processes, deterministic polynomial drifts, and polynomial drifts with structural breaks – the most common trends that appear in macroeconomic data and current modeling methodology. In doing so, the boosted filter provides a new mechanism for consistently estimating multiple structural breaks. A stopping criterion is used to automate the iterative HP algorithm, making it a data-determined method that is ready for modern data-rich environments in economic research. The methodology is illustrated using three real data examples that highlight the differences between simple HP filtering, the data-determined boosted filter, and an alternative autoregressive approach. These examples show that the boosted HP filter is helpful in analyzing a large collection of heterogeneous macroeconomic time series that manifest various degrees of persistence, trend behavior, and volatility

Adaptive Sliding Control for a Class of Fractional Commensurate Order Chaotic Systems

This paper proposes adaptive sliding mode control design for a class of fractional commensurate order chaotic systems. We firstly introduce a fractional integral sliding manifold for the nominal systems. Secondly we prove the stability of the corresponding fractional sliding dynamics. Then, by introducing a Lyapunov candidate function and using the Mittag-Leffler stability theory we derive the desired sliding control law. Furthermore, we prove that the proposed sliding manifold is also adapted for the fractional systems in the presence of uncertainties and external disturbances. At last, we design a fractional adaptation law for the perturbed fractional systems. To verify the viability and efficiency of the proposed fractional controllers, numerical simulations of fractional Lorenz’s system and Chen’s system are presented

Nickell Bias in Panel Local Projection: Financial Crises Are Worse Than You Think

Local Projection is widely used for impulse response estimation, with the Fixed Effect (FE) estimator being the default for panel data. This paper highlights the presence of Nickell bias for all regressors in the FE estimator, even if lagged dependent variables are absent in the regression. This bias is the consequence of the inherent panel predictive specification. We recommend using the split-panel jackknife estimator to eliminate the asymptotic bias and restore the standard statistical inference. Revisiting three macro-finance studies on the linkage between financial crises and economic contraction, we find that the FE estimator substantially underestimates the post-crisis economic losses

Visibility-Aware Pixelwise View Selection for Multi-View Stereo Matching

The performance of PatchMatch-based multi-view stereo algorithms depends heavily on the source views selected for computing matching costs. Instead of modeling the visibility of different views, most existing approaches handle occlusions in an ad-hoc manner. To address this issue, we propose a novel visibility-guided pixelwise view selection scheme in this paper. It progressively refines the set of source views to be used for each pixel in the reference view based on visibility information provided by already validated solutions. In addition, the Artificial Multi-Bee Colony (AMBC) algorithm is employed to search for optimal solutions for different pixels in parallel. Inter-colony communication is performed both within the same image and among different images. Fitness rewards are added to validated and propagated solutions, effectively enforcing the smoothness of neighboring pixels and allowing better handling of textureless areas. Experimental results on the DTU dataset show our method achieves state-of-the-art performance among non-learning-based methods and retrieves more details in occluded and low-textured regions.Comment: 8 page