Neural Tests for Conditional Heteroskedasticity in ARCH-M Models

This paper deals with tests for detecting conditional heteroskedasticity in ARCH-M models using three kinds of methods: neural networks techniques, bootstrap methods and both combined.As regards the ARCH models, Péguin-Feissolle (2000) developed tests based on the modelling techniques with neural network. However, as regards the ARCH-M models, a nuisance parameter is not identified and the tests are not applicable. To solve this problem, we propose to adapt these neural tests to Davies procedure (1987) leading to new tests. The performance of these latter tests are compared with those of Bera and Ra test (1995).However, Bera and Ra test has not really satisfactory performance and suffer from serious size distortion. Our neural test will have the same problem. To solve this second problem, without loss of power, we apply parametric and nonparametric bootstrap methods on the underlying test statistics.Lastly, to examine the size and the power properties of the tests in small samples, Monte Carlo simulations are carried out with various standard and non-standard models for conditional heteroskedasticity as to illustrate a variety of situations. In addition, the graphical presentation of Davidson and MacKinnon (1998a) is used to show the "true" power of the tests and not only the (nominal) power, as it is often the case, that can be meaningless.