Near-Optimal Unit Root Tests with Stationary Covariates with Better Finite Sample Size

Numerous tests for integration and cointegration have been proposed in the literature. Since Elliott, Rothemberg and Stock (1996) the search for tests with better power has moved in the direction of finding tests with some optimality properties both in univariate and multivariate models. Although the optimal tests constructed so far have asymptotic power that is indistinguishable from the power envelope, it is well known that they can have severe size distortions in finite samples. This paper proposes a simple and powerful test that can be used to test for unit root or for no cointegration when the cointegration vector is known. Although this test is not optimal in the sense of Elliott and Jansson (2003), it has better finite sample size properties while having asymptotic power curves that are indistinguishable from the power curves of optimal tests. Similarly to Hansen (1995), Elliott and Jansson (2003), Zivot (2000), and Elliott, Jansson and Pesavento (2005) the proposed test achieves higher power by using additional information contained in covariates correlated with the variable being tested. The test is constructed by applying Hansen’s test to variables that are detrended under the alternative in a regression augmented with leads and lags of the stationary covariates. Using local to unity parametrization, the asymptotic distribution of the test under the null and the local alternative is analytically computed.Unit Root Test, GLS detrending.

A Parallel Best-Response Algorithm with Exact Line Search for Nonconvex Sparsity-Regularized Rank Minimization

In this paper, we propose a convergent parallel best-response algorithm with the exact line search for the nondifferentiable nonconvex sparsity-regularized rank minimization problem. On the one hand, it exhibits a faster convergence than subgradient algorithms and block coordinate descent algorithms. On the other hand, its convergence to a stationary point is guaranteed, while ADMM algorithms only converge for convex problems. Furthermore, the exact line search procedure in the proposed algorithm is performed efficiently in closed-form to avoid the meticulous choice of stepsizes, which is however a common bottleneck in subgradient algorithms and successive convex approximation algorithms. Finally, the proposed algorithm is numerically tested.Comment: Submitted to IEEE ICASSP 201

A Unified Successive Pseudo-Convex Approximation Framework

In this paper, we propose a successive pseudo-convex approximation algorithm to efficiently compute stationary points for a large class of possibly nonconvex optimization problems. The stationary points are obtained by solving a sequence of successively refined approximate problems, each of which is much easier to solve than the original problem. To achieve convergence, the approximate problem only needs to exhibit a weak form of convexity, namely, pseudo-convexity. We show that the proposed framework not only includes as special cases a number of existing methods, for example, the gradient method and the Jacobi algorithm, but also leads to new algorithms which enjoy easier implementation and faster convergence speed. We also propose a novel line search method for nondifferentiable optimization problems, which is carried out over a properly constructed differentiable function with the benefit of a simplified implementation as compared to state-of-the-art line search techniques that directly operate on the original nondifferentiable objective function. The advantages of the proposed algorithm are shown, both theoretically and numerically, by several example applications, namely, MIMO broadcast channel capacity computation, energy efficiency maximization in massive MIMO systems and LASSO in sparse signal recovery.Comment: submitted to IEEE Transactions on Signal Processing; original title: A Novel Iterative Convex Approximation Metho

Impulse Response Confidence Intervals for Persistent Data: What Have We Learned?

This paper is a comprehensive comparison of existing methods for constructing confidence bands for univariate impulse response functions in the presence of high persistence. Monte Carlo results show that Kilian (1998a), Wright (2000), Gospodinov (2004) and Pesavento and Rossi (2005) have favorable coverage properties, although they differ in terms of robustness at various horizons, median unbiasedness, and reliability in the possible presence of a unit or mildly explosive root. On the other hand, methods like Runkleís (1987) bootstrap, Andrews and Chen (1994), and regressions in levels or first differences (even when based on pre-tests) may not have accurate coverage properties. The paper makes recommendations as to the appropriateness of each method in empirical work.Local to unity asymptotics, persistence, impulse response functions

Do Technology Shocks Drive Hours Up or Down? A Little Evidence From an Agnostic Procedure

This paper analyzes the robustness of the estimate of a positive productivity shock on hours to the presence of a possible unit root in hours. Estimations in levels or in first differences provide opposite conclusions. We rely on an agnostic procedure in which the researcher does not have to choose between a specification in levels or in first differences. We find that a positive productivity shock has a negative impact effect on hours, as in Francis and Ramey (2001), but the effect is much more short-lived, and disappears after two quarters. The effect becomes positive at business cycle frequencies, as in Christiano et al. (2003), although it is not significant.Technology shocks, persistence, impulse response functions, Real Business Cycle Theory

Interference Exploitation-based Hybrid Precoding with Robustness Against Phase Errors

Hybrid analog-digital precoding significantly reduces the hardware costs in massive MIMO transceivers when compared to fully-digital precoding at the expense of increased transmit power. In order to mitigate the above shortfall, we use the concept of constructive interference-based precoding, which has been shown to offer significant transmit power savings when compared with the conventional interference suppression-based precoding in fully-digital multiuser MIMO systems. Moreover, in order to circumvent the potential quality-of-service degradation at the users due to the hardware impairments in the transmitters, we judiciously incorporate robustness against such vulnerabilities in the precoder design. Since the undertaken constructive interference-based robust hybrid precoding problem is nonconvex with infinite constraints and thus difficult to solve optimally, we decompose the problem into two subtasks, namely, analog precoding and digital precoding. In this paper, we propose an algorithm to compute the optimal constructive interference-based robust digital precoders. Furthermore, we devise a scheme to facilitate the implementation of the proposed algorithm in a low-complexity and distributed manner. We also discuss block-level analog precoding techniques. Simulation results demonstrate the superiority of the proposed algorithm and its implementation scheme over the state-of-the-art methods

Do Technology Shocks Drive Hours Up or Down?

This paper analyzes the robustness of the estimate of a positive productivity shock on hours to the presence of a possible unit root in hours. Estimations in levels or in first differences provide opposite conclusions. We rely on an agnostic procedure in which the researcher does not have to choose between a specification in levels or in first differences. The method uses alternative approximations based on local-to-unity asymptotic theory and allows the lead-time of the impulse response function to be a fixed fraction of the sample size. These devices provide better approximations in small samples and give confidence bands that have better coverage properties at medium and long horizons than existing methods. We find that a positive productivity shock has a negative effect on hours, as in Francis and Ramey (2001), but the effect is much more short-lived, and disappears after two quarters. The effect becomes positive at business cycle frequencies, as in Christiano et al. (2003)Technology shocks, persistence, impulse response functions, Real Business Cycle.

Impulse Response Confidence Intervals for Persistent Data: What Have We Learned?

This paper is a comprehensive comparison of existing methods for constructing confidence bands for univariate impulse response functions in the presence of high persistence. Monte Carlo results show that Kilian (1998a), Wright (2000), Gospodinov (2004) and Pesavento and Rossi (2005) have favorable coverage properties, although they differ in terms of robustness at various horizons, median unbiasedness, and reliability in the possible presence of a unit or mildly explosive root. On the other hand, methods like Runkle’s (1987) bootstrap, Andrews and Chen (1994), and regressions in levels or first differences (even when based on pre-tests) may not have accurate coverage properties. The paper makes recommendations as to the appropriateness of each method in empirical work.Local to unity asymptotics, persistence, impulse response functions

Small Sample Confidence Intervals for Multivariate Impulse Response Functions at Long Horizons

Existing methods for constructing confidence bands for multivatiate impulse response functions depend on auxiliary assumptions on the order of integration of the variables. Thus, they may have poor coverage at long lead times when variables are highly persistent. Solutions that have been proposed in the literature may be computationally challenging. The goal of this paper is to propose a simple method for constructing confidence bands for impulse response functions that are robust to the presence of highly persistent processes. The method uses alternative approximations based on local-to-unity asymptotic theory and allows the lead time of the impulse response function to be a fixed fraction of the sample size. Monte Carlo simulations show that our method has better coverage properties than existing methods. We also investigate the properties of the various methods in terms of the length of their confidence bands. Finally, we show, with empirical applications, that our method may provide different economic interpretations of the data. Applications to real GDP and to nominal versus real sources of fluctuations in exchange rates are discussed.