Analysing the performance of bootstrap neural tests for conditional heteroskedasticity in ARCH-M models

The robustness against strongly non-linear forms for the conditional variance of tests for detecting conditional heteroskedasticity using both artificial neural network techniques and bootstrap methods combined, is analysed in the context of ARCH-M models. The size and the power properties in small samples of these tests are examined by using out Monte-Carlo experiments with various standard and non-standard models of conditional heteroskedasticity. The P value functions are explored in order to select particularly problematic cases. Graphical presentations, based on the principle of size correction, are used for presenting the true power of the tests, rather than a spurious nominal power as it is usually made in the literature. In addition, graphics linking the process dynamics with the heteroskedasticity forms are shown for analysing in which circumstances the neural networks are effective.

[1]  J. Moatti,et al.  [The handling of uncertainty in economic evaluations of health care strategies]. , 2003, Revue d'epidemiologie et de sante publique.

[2]  Neural Tests for Conditional Heteroskedasticity in ARCH-M Models , 2004 .

[3]  Craig S. Hakkio,et al.  Conditional variance and the risk premium in the foreign exchange market , 1985 .

[4]  Anil K. Bera,et al.  A test for the presence of conditional heteroskedasticity within ARCH-M framework , 1995 .

[5]  Jeremy Berkowitz,et al.  Recent developments in bootstrapping time series , 1996 .

[6]  Anders Milhøj,et al.  A Conditional Variance Model for Daily Deviations of an Exchange Rate , 1987 .

[7]  Kurt Hornik,et al.  Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks , 1990, Neural Networks.

[8]  Mark Kamstra.  A Neural Network Test for Heteroskedasticity , 1991 .

[9]  J. MacKinnon,et al.  The Size and Power of Bootstrap Tests , 1996 .

[10]  G. S. Hongyi Li,et al.  Bootstrapping time series models , 1996 .

[11]  E. Fama,et al.  Common risk factors in the returns on stocks and bonds , 1993 .

[12]  Kurt Hornik,et al.  Approximation capabilities of multilayer feedforward networks , 1991, Neural Networks.

[13]  J. Wooldridge,et al.  A Capital Asset Pricing Model with Time-Varying Covariances , 1988, Journal of Political Economy.

[14]  Anil K. Bera,et al.  A test for conditional heteroskedasticity in time series models , 1992 .

[15]  R. Davies.  Hypothesis testing when a nuisance parameter is present only under the alternative , 1977 .

[16]  C. Granger,et al.  Testing for neglected nonlinearity in time series models: A comparison of neural network methods and alternative tests , 1993 .

[17]  T. Bollerslev,et al.  ON THE CORRELATION STRUCTURE FOR THE GENERALIZED AUTOREGRESSIVE CONDITIONAL HETEROSKEDASTIC PROCESS , 1988 .

[18]  Ronald C. Davidson.  Comment on “recent developments in bootstrapping time series” , 2000 .

[19]  James G. MacKinnon,et al.  Graphical Methods for Investigating the Size and Power of Hypothesis Tests , 1998 .

[20]  Russell P. Robins,et al.  Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model , 1987 .

[21]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[22]  Anne Peguin-Feissolle.  A comparison of the power of some tests for conditional heteroscedasticity , 1999 .

[23]  Clive W. J. Granger,et al.  Testing for neglected nonlinearity in time series models: A comparison of neural network methods and alternative tests , 1993 .

[24]  James G. MacKinnon,et al.  The Power of Bootstrap Tests , 1996 .

[25]  J. MacKinnon,et al.  Estimation and inference in econometrics , 1994 .

[26]  Un test d'heteroscedasticite conditionnelle inspire de la modelisation en termes de reseaux neuronaux artificiels , 1999 .