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.

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

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

Predicting appliance ownership using logit, neural network, and regression tree models

Includes bibliographical references (p. 36-37)

A recurrent Newton algorithm and its convergence properties

Includes bibliographic references (p. 13-15)

A Generalized Jarque-Bera Test of Conditional Normality

We consider testing normality in a general class of models that admits nonlinear conditional mean and conditional variance functions. We derive the asymptotic distribution of the skewness and kurtosis coefficients of the model’s standardized residuals and propose an asymptotic x2 test of normality. This test simplifies to the Jarque-Bera test only when: (i) the conditional mean function contains an intercept term but does not depend on past errors, and (ii) the errors are conditionally homoskedastic. Beyond this context, it is shown that the Jarque-Bera test has size distortion but the proposed test does not.conditional heteroskedsaticity, conditional normality, Jarque-Bera test

Re-Examining the Profitability of Technical Analysis with White’s Reality Check

In this paper, we re-examine the profitability of technical analysis using the Reality Check of White (2000, Econometrica) that corrects the data snooping bias. Comparing to previous studies, we study a more complete “universe” of trading techniques, including not only simple trading rules but also investor’s strategies, and we test the profitability of these rules and strategies with four main indices from both relatively mature and young markets. It is found that profitable simple rules and investor’s strategies do exist with statistical significance for NASDAQ Composite and Russell 2000 but not for DJIA and S&P 500. Moreover, the best rules for NASDAQ Composite and Russell 2000 outperform the buy-and-hold strategy in most in- and out-of-sample periods, even when transaction costs are taken into account. We also find that investor’s strategies are able to improve on the profits of simple rules and may even generate significant profits from unprofitable simple rules.data snooping, investor’s strategies, stationary bootstrap, technical analysis, trading rules, White’s Reality Check.

Change-Point Estimation of Nonstationary I(d) Processes

We examine the least-squares estimator of change point for nonstationary I(d) data with 0.5least-squares estimator, change point, nonstationary I(d) process, spurious change

Improved HAC Covariance Matrix Estimation Based on Forecast Errors

We propose computing HAC covariance matrix estimators based on one-stepahead forecasting errors. It is shown that this estimator is consistent and has smaller bias than other HAC estimators. Moreover, the tests that rely on this estimator have more accurate sizes without sacrificing its power.forecast error, HAC estimator, kernel estimator, recursive residual, robust test

Algebraic Quantum Error-Correction Codes

Based on the group structure of a unitary Lie algebra, a scheme is provided to systematically and exhaustively generate quantum error correction codes, including the additive and nonadditive codes. The syndromes in the process of error-correction distinguished by different orthogonal vector subspaces, the coset subspaces. Moreover, the generated codes can be classified into four types with respect to the spinors in the unitary Lie algebra and a chosen initial quantum state