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Developing nonparametric conditional heteroscedastic autoregressive nonlinear model by using maximum likelihood method
Author(s)
Date Issued
January 1, 2011
Type
Article
Abstract
The goal of this work is to develop a nonparametric conditional heteroscedastic autoregressive nonlinear (NCHARN) model by using maximum likelihood method that not only account for possibly non-linear trend but also account for possibly non-linear conditional variance of response as a function of predictor variables in the presence of auto-correlated errors. The trend and the heteroscedasticity are modeled using a class of penalized spline and the residuals are modeled as a autoregressive process (AR) by selecting an appropriate number of lag residuals. Both classical penalized spline and AR process of penalized spline under NCHARN model are developed to obtain the smooth estimates of the conditional mean and variance functions. The resulting estimated values are then used the maximum likelihood method to fi t a trend, volatility, and a coeffi cient of AR process by suitably choosing the order of AR using the Akaike Information Criteria (AIC). The forecasting performance of the proposed methods is then applied to the series of monthly observations of the Stock Exchange Rate of Thailand (SERT) to illustrate the methodology. The forecasts these methods are compared with those obtained based on future six months of withheld observations.
Citation
Chiang Mai Journal of Science, 38(3), 331-345, 2011