Last update: March 10th, 1998
| 10. | Name: | PEGUIN-FEISSOLLE Anne | |
| Organiz.: | GREQAM | ||
| Co-Authors: | Anne PEGUIN-FEISSOLLE and Renaud CAULET | ||
| JELC: | C12 C22 | ||
| Keys: | conditional heteroscedasticity, artificial neural networks | ||
| Title: | A test for conditional heteroscedasticity based on artificial neural networks | ||
| The conditional heteroscedasticity disturbance modeling has became particularly popular since Engle (1982) introduced the autoregressive conditional heteroscedastic (ARCH) models; various derivatives of this modeling have been proposed and applied in the financial literature. We know that tests for heteroscedasticity are important because, in the presence of heteroscedasticity of error variances, least squares method gives inefficient parameter estimates and biased variance estimates. The aim of this article is to introduce a test for conditional heteroscedastic regression disturbances; it is based on the neural network modeling techniques developed by cognitive scientists. Recently, Lee, White and Granger (1993) proposed a neural network test for neglected nonlinearity in conditional mean. Following this seminal paper, the test we introduce here is based on the approximating ability by the neural function of an arbitrary nonlinear specification of the conditional variance. More precisely, this test does not require the exact specification of the functional form of the conditional variance under the alternative hypothesis. The performance of this test for conditional heteroscedasticity is compared with three other tests; one of them is a variant of the Kamstra test (Kamstra (1993)); this last test is a neural network test for heteroscedasticity but with a different test statistics. Monte Carlo methods are used to examine these different test procedures for some conditional heteroscedastic variance structures. The article is organized as follows. The test for conditional heteroscedasticity is described in section 2. In a conditional heteroscedastic context, we are going to include past squared disturbance terms as explanatory variables (or input variables) in the network to capture dynamics. The neural network we consider is the single hidden layer feedforward network : input units send signals, amplified or attenuated by weighting factors, to hidden units (or hidden nodes). We develop the test by using a Lagrange multiplier procedure; the test statistics is computed and can be based on an auxiliary regression. Section 3 deals with experimental design and discusses the results. To investigate the small-sample size and power properties of the neural network test, we compare them with those of three other tests for conditional heteroscedasticity: the Engle test, a variant of the Engle test and a variant of the Kamstra test. We will present the results concerning the size and the power of all these tests by using the graphical presentation of Davidson and MacKinnon (1993 and 1994). It yields graphs that are easier to interpret than the conventional tabular form used generally to report this kind of result. We present the results concerning the size of the different tests in the case where the data are generated from a normal homoscedastic model. Then, in order to compare the power of the tests for conditional heteroscedasticity, we generate the size-power curves: the alternative hypothesis is represented by different conditional heteroscedastic models, chosen to represent a variety of conditional heteroscedastic situations. On the whole, experimental results show that the neural test and the Engle test strongly dominate the other two test procedures; the neural test has power qualitatively similar or sometimes superior to the power of the Engle test. We explain this phenomena by using a Taylor expansion: it shows that the space spanned by the test regressors for the neural network alternative is almost identical, for a first set of regressors, to the space spanned by the test regressors for the Engle test. This explains why the neural test and the Engle test give, in some cases, similar results and shows that the neural test can be considered as a generalization of the Engle test on the whole. In section 4, we expound some empirical applications of the different tests. To illustrate the behavior of the different tests for conditional heteroscedasticity for economic time series, we report in this section the application of these tests to some empirical examples. We focus on daily observations on stock price indexes (CAC40, DAX, NIKEI, FTSE and SP500) and on exchange rates (DM/FF, US$/DM and US$/FF). Some concluding remarks are made in section 5. | |||