SONGKLANAKARIN JOURNAL OF SCIENCE & TECHNOLOGY

Volume 41, No. 04, Month JULY, Year 2019, Pages 813 - 821

Estimating conditional heteroscedastic nonlinear autoregressive model by using smoothing spline and penalized spline methods

Autcha Araveeporn

Abstract Download PDF

We propose smoothing spline (SS) and penalized spline (PS) methods in a class of nonparametric regression methods for estimating the unknown functions in a conditional heteroscedastic nonlinear autoregressive (CHNLAR) model. The CHNLAR model consists of a trend and heteroscedastic functions in terms of past data at lag 1. The SS and PS methods were tested in estimating the unknown functions used to transform data so that it fits the trend and the heteroscedastic functions. In a simulation study, time series data were generated and hypothesis testing of the bias was used to check the accuracy. The SS and PS methods exhibit a good power estimation in most cases of generated data. As real data, gold price was modeled by using SS and PS methods in the CHNLAR model. The results show that the SS method performed better than the PS method.

Keywords

conditional heteroscedastic nonlinear autoregressive model, smoothing spline method, penalized spline method

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