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  • George Kapetanios (a1) and Andrew P. Blake (a2)

The martingale difference restriction is an outcome of many theoretical analyses in economics and finance. A large body of econometric literature deals with tests of that restriction. We provide new tests based on radial basis function (RBF) neural networks. Our work is based on the test design of Blake and Kapetanios (2000, 2003a, 2003b). However, unlike that work we provide a formal theoretical justification for the validity of these tests and present some new general theoretical results. These results take advantage of the link between the algorithms of Blake and Kapetanios (2000, 2003a, 2003b) and boosting. We carry out a Monte Carlo study of the properties of the new tests and find that they have very good power performance. A simplified implementation of boosting is found to have desirable properties and small computational cost. An empirical application to the S&P 500 constituents illustrates the usefulness of our new test.

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*Address correspondence to George Kapetanios, Department of Economics, Queen Mary, University of London, Mile End Road, London E1 4NS, UK; e-mail:
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H.J. Bierens (1984) Model specification testing of time series regression. Journal of Econometrics 26, 323353.

H.J. Bierens (1990) A consistent conditional moment test of functional form. Econometrica 58, 14431458.

H.J. Bierens & W. Ploberger (1997) Asymptotic theory of integrated conditional moment tests. Econometrica 65, 11291151.

A.P. Blake & G. Kapetanios (2000) A radial basis function artificial neural network test for ARCH. Economics Letters 69, 1523.

A.P. Blake & G. Kapetanios (2003a) Pure significance tests of the unit root hypothesis against nonlinear alternatives. Journal of Time Series Analysis 24(3), 253267.

A.P. Blake & G. Kapetanios (2003b) A radial basis function artificial neural network test for neglected nonlinearity. The Econometrics Journal 6(2), 357373.

A.P. Blake & G. Kapetanios (2007) Testing for ARCH in the presence of nonlinearity of unknown form in the conditional mean. Journal of Econometrics 137(2), 472488.

P. Buhlmann (2006) Boosting for high-dimensional linear models. Annals of Statistics 34, 559583.

J. Davidson (1994) Stochastic Limit Theory. Oxford University Press.

R.M. de Jong (1996) The Bierens tests under data dependence. Journal of Econometrics 72, 132.

R.S. Deo (2000) Spectral tests of the martingale hypothesis under conditional heteroskedasticity. Journal of Econometrics 99, 291315.

M. Dominguez & I.N. Lobato (2003) A consistent test for the martingale difference hypothesis. Econometric Reviews 22, 351377.

J.C. Escanciano & C. Velasco (2006a) Generalised spectral tests for the martingale difference hypothesis. Journal of Econometrics 134(1), 151185.

J.C. Escanciano & C. Velasco (2006b) Testing the martingale difference hypothesis using integrated regression functions. Computational Statistics and Data Analysis 51(1), 22782294.

J. Friedman (2001) Greedy function approximation: A gradient boosting machine. Annals of Statistics 29, 11891232.

J. Friedman , T. Hastie , & R. Tibshirani (2000) Additive logistic regression: A statistical view of boosting. Annals of Statistics 28, 337374.

K. Hornik , M. Stinchcombe , & H. White (1989) Multi-layer feedforward networks and universal approximators. Neural Network 2, 359366.

T.H. Lee , H. White , & C.W.J. Granger (1993) Testing for neglected nonlinearity in time series models: A comparison of neural network methods and alternative tests. Journal of Econometrics 56, 269290.

M. Lettau & S. Ludvigson (2001) Consumption, aggregate wealth and expected stock returns. Journal of Finance 56, 815849.

J. Moody & C. Darken (1989) Fast learning in networks of locally-tuned processing units. Neural Computation 1(2), 289303.

M.J. Orr (1995) Regularisation in the selection of radial basis function centers. Neural Computation 7(3), 606623.

J. Park & I.W. Sandberg (1991) Universal approximation using radial-basis-function networks. Neural Computation 3(4), 246257.

M.B. Stinchcombe & H. White (1998) Consistent specification testing with nuisance parameters present only under the alternative. Econometric Theory 14, 295325.

V.N. Temlyakov (2000) Weak greedy algorithms. Advances in Computational Mathematics 12, 213227.

T. Teräsvirta , C.F. Lin , & C.W.J. Granger (1993) Power of the neural network linearity test. Journal of Time Series Analysis 14, 209220.

Y.J. Whang (2000) Consistent bootstrap tests of parametric regression functions. Journal of Econometrics 98, 2746.

H. White (2006) Approximate nonlinear forecasting methods. In G. Elliott , C.W.J. Granger , & A. Timmermann (eds.), Handbook of Economics Forecasting. Elsevier.

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Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
  • URL: /core/journals/econometric-theory
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