A New Test of the Martingale Difference Hypothesis

In this paper we propose a new class of tests for the martingale difference hypothesis based on the moment conditions derived by Bierens (1982). In contrast with the existing consistent tests, the proposed test has a standard limiting distribution and is easy to implement. Comparing with the commonly used autocorrelation- and spectrum-based tests, it has power against a much larger class of alternatives that may be serially correlated or uncorrelated. Moreover, this test does not rely on the assumption of conditional homoskedasticity and requires a weaker moment condition. Our simulations confirm that the proposed test is powerful against various linear and nonlinear alternatives and is quite robust to the failure of higher-order moments. Our empirical study on exchange rate returns also shows that the conclusion resulted from the proposed test is different from that of the conventional tests.autocorrelation-based test, Bierens’ equivalence result, martingale difference sequence, multivariate exponential distribution, spectrum-based test

Insider patent holder licensing in an oligopoly market with different cost structures: Fixed-fee, royalty, and auction

The issue of the optimal licensing contract in firms having different cost structures is studied when the innovator is a producing patent holder who has three alternative licensing strategies, namely, the fixed-fee, royalty rate, and auction strategies. We conclude that the auction licensing strategy is not the best strategy when the innovator is a producing patent holder. This finding differs from that of Kabiraj (2004) where the auction licensing method is the optimal licensing strategy when the innovator is a non-producing patent holder. However, when we only compare two of the licensing methods, namely, the fixed-fee licensing method and the royalty licensing method, we conclude that if the inside innovator licenses to only some of the firms, then the royalty licensing method will be the best strategy. This result is different from that of Fosfuri and Roca (2004), who concluded that if only some of the licensees obtain a licensing contract, then the fixed-fee licensing method will be the best choice for a producing patent holder.Licensing strategy, Cost structure, Auction

Testing Over-Identifying Restrictions without Consistent Estimation of the Asymptotic Covariance Matrix

We extend the KVB approach of Kiefer, Vogelsang, and Bunzel (2000, Econometrica) and Kiefer and Vogelsang (2002b, Econometric Theory) to construct a class of robust tests for over-identifying restrictions in the context of GMM. The proposed test does not require consistent estimation of the asymptotic covariance matrix but relies on kernel-based normalizing matrices to eliminate the nuisance parameters in the limit. Moreover, the proposed test is valid for any consistent GMM estimator, in contrast with the conventional test that requires the optimal GMM estimator, and hence is easy to implement. Our simulations show that the proposed test is properly sized and may even be more powerful than the conventional test computed with an inappropriate user-chosen parameter.generalized method of moments, kernel function, KVB approach, overidentifying restrictions, robust test

Artificial Neural Networks

Artificial neural networks (ANNs) constitute a class of flexible nonlinear models designed to mimic biological neural systems. In this entry, we introduce ANN using familiar econometric terminology and provide an overview of ANN modeling approach and its implementation methods.

Breakdown of local convertibility through Majorana modes in a quantum quench

The local convertibility of quantum states, measured by the R\'enyi entropy, is concerned with whether or not a state can be transformed into another state, using only local operations and classical communications. We found that in the one-dimensional Kitaev chain with quenched chemical potential $\mu$, the convertibility between the state for $\mu$ and that for $\mu+\delta\mu$, depends on the quantum phases of the system ($\delta\mu$ is a perturbation). This is similar to the adiabatic case where the ground state is considered. Specifically, when the quenched system has edge modes and the subsystem size for the partition is much larger than the correlation length of the Majorana fermions which forms the edge modes, the quenched state is locally inconvertible. We give a physical interpretation for the result, based on analyzing the interactions between the two subsystems for various partitions. Our work should help to better understand the many-body phenomena in topological systems and also the entanglement properties in the Majorana fermionic quantum computation.Comment: 8 pages, 5 figures, accepted by Physical Review