Chung-Ming Kuan

Artificial neural networks: an econometric perspective ∗

(1994). Artificial neural networks: an econometric perspective. Econometric Reviews: Vol. 13, No. 1, pp. 1-91.

Convergence of learning algorithms with constant learning rates

The behavior of neural network learning algorithms with a small, constant learning rate, epsilon, in stationary, random input environments is investigated. It is rigorously established that the sequence of weight estimates can be approximated by a certain ordinary differential equation, in the sense of weak convergence of random processes as epsilon tends to zero. As applications, backpropagation in feedforward architectures and some feature extraction algorithms are studied in more detail.

The generalized fluctuation test: A unifying view

In this paper, a general principle of constructing tests for parameter constancy without assuming a specific alternative is introduced. A unified asymptotic result is established to analyze this class of tests. As applications, tests based on the range of recursive and moving estimates are considered, and their asymptotic distributions are characterized analytically. Our simulations show that different tests have quite different behavior under various alternatives and that no test uniformly dominates the other tests.

Original Contribution: Convergence analysis of local feature extraction algorithms

We investigate the asymptotic behavior of a general class of on-line Principal Component Analysis (PCA) learning algorithms, focusing our attention on the analysis of two algorithms which have recently been proposed and are based on strictly local learning rules. We rigorously establish that the behavior of the algorithms is intimately related to an ordinary differential equation (ODE) which is obtained by suitably averaging over the training patterns, and study the equilibria of these ODEs and their local stability properties. Our results imply, in particular, that local PCA algorithms should always incorporate hierarchical rather than more competitive, symmetric decorrelation, for reasons of superior performance of the algorithms.

MONITORING STRUCTURAL CHANGES WITH THE GENERALIZED FLUCTUATION TEST

In this paper we introduce the generalized fluctuation test for monitoring structural changes and establish a result characterizing the limiting behavior of this class of tests. As applications of the generalized fluctuation test, tests based on the maximum and range of the fluctuation of moving estimates are proposed. We also derive the boundary functions for the proposed tests and tabulate simulated critical values. Our simulations indicate that these tests compare favorably with the recursive-estimates-based test considered by Chu, Stinchcombe, and White (1996, Econometrica 64, 1045–1065) when a change occurs late.

Change‐Point Estimation of Fractionally Integrated Processes

In this paper we analyze the least‐squares estimator of the change point for fractionally integrated processes with fractionally differencing parameter −0.5

The Moving-Estimates Test for Parameter Stability

In this paper a new class of tests for parameter stability, the moving-estimates (ME) test, is proposed. It is shown that in the standard situation the ME test asymptotically equivalent to the maximal likelihood ratio test under the alternative of a temporary parameter shift. It is also shown that the asymptotic null distribution of the ME test is determined by the increments of a vector Brownian bridge and that under a broad class of alternatives the ME test is consistent and has nontrivial local power in general. Our simulations also demonstrate that the proposed test has power superior to other competing tests when parameters are temporarily instable.

Testing time reversibility without moment restrictions

In this paper we propose a class of new tests for time reversibility. It is shown that this test has an asymptotic normal distribution under the null hypothesis and non-trivial power under local alternatives. A novel feature of this test is that it does not have any moment restriction, in contrast with other time reversibility and linearity tests. Our simulations also confirm that the proposed test is very robust when data do not possess proper moments. An empirical study of stock market indices is also included to illustrate the usefulness of the new test.

ADAPTIVE LEARNING WITH NONLINEAR DYNAMICS DRIVEN BY DEPENDENT PROCESSES

The authors provide a convergence theory for adaptive learning algorithms useful for the study of learning by economic agents. Their results extend the framework of L. Ljung previously utilized by A. Marcet-T. J. Sargent and M. Woodford by permitting nonlinear laws of motion driven by stochastic processes that may exhibit moderate dependence, such as mixing and mixingale processes. The authors draw on previous work by H. J. Kushner and D. S. Clark to provide readily verifiable and/or interpretable conditions ensuring algorithm convergence, chosen for their suitability in the context of adaptive learning. Copyright 1994 by The Econometric Society.

A convergence result for learning in recurrent neural networks

We give a rigorous analysis of the convergence properties of a backpropagation algorithm for recurrent networks containing either output or hidden layer recurrence. The conditions permit data generated by stochastic processes with considerable dependence. Restrictions are offered that may help assure convergence of the network parameters to a local optimum, as some simulations illustrate.