Developing Nonparametric Conditional Heteroscedastic Autoregressive Nonlinear Model by Using Maximum Likelihood Method (original) (raw)
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2019
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.
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The goal of this work is to develop a nonparametric regression model that not only account for possibly non-linear trend (i.e., conditional mean of the response variable) but also account for possibly non-linear conditional variance of response (i.e., heteroscedasticity) 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. The residuals are modeled as a long autoregressive process which can approximate almost any autoregressive moving average (ARMA) process by selecting an appropriate number of lag residuals. Both classical and Bayesian methodologies are developed to obtain the smooth estimates of the conditional mean and variance functions. The resulting estimated residuals are then used to fit a possibly long 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.
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