Nonlinear Volatility Models in Economics: Smooth Transition and Neural Network Augmented GARCH, APGARCH, FI-GARCH and FIAGARCH Models

36 Pages Posted: 29 Jul 2012 Last revised: 9 Aug 2012

See all articles by Melike Bildirici

Melike Bildirici

Yildiz Technical University

Ozgur Omer Ersin

Istanbul Ticaret University

Date Written: July 27, 2012


Recently, Donaldson and Kamstra (1997) proposed a class of NN-GARCH models which are extended to a class of NN-GARCH family by Bildirici and Ersin (2009). The study aims to analyze the nonlinear behavior and leptokurtic distribution in petrol prices by utilizing a newly developed family of econometric models that deal with these concepts by benefiting from both LSTAR type and ANN based nonlinearity. With this purpose, the study proposed several LSTAR-GARCH-NN family models. It is noted that the multilayer perceptron (MLP) neural network and LSTAR models have significant architectural similarities. Accordingly, linear GARCH, fractionally integrated FI-GARCH, asymmetric power APGARCH and fractionally integrated asymmetric power APGARCH models are augmented with a family of Neural Network models. The study has following contributions: i. STAR-GARCH and LSTAR-GARCH are extended to their fractionally integrated asymmetric power versions and STAR-ST-FIGARCH and STAR-ST-APGARCH, STAR-ST-FIAPGARCH models are developed and evaluated. ii. By extending these models with neural networks, LSTAR-LST-GARCH-MLP family models are developed and investigated. These models benefit from LSTAR type nonlinearity and NN based nonlinear NN-GARCH models to capture time varying volatility and nonlinearity in petrol prices. ANN augmented versions of LSTAR-LST-GARCH models are as follows: LSTAR-LST-GARCH-MLP, LSTAR-LST-FIGARCH-MLP, LSTAR-LST-APGARCH-MLP and LSTAR-LST-FIAPGARCH-MLP. Empirical findings are collected as follows. i. To model petrol prices, fractionally integrated and asymmetric power versions provided improvements among the GARCH family models in terms of forecasting. ii. LSTAR-LST-GARCH model family is promising and show significant gains in out-of-sample forecasting. iii. MLP-GARCH family provided similar results with the LSTAR-LST-GARCH family models, except for the MLP-FIGARCH and MLP-FIAPGARCH models. iv. Volatility clustering, asymmetry and nonlinearity characteristics of petrol prices are captured most efficiently with the LSTAR-LST-GARCH-MLP models benefiting from forecasting capabilities of neural network techniques, whereas, among the newly developed models, LSTAR-LST-APGARCH-MLP model provided the best performance overall.

Keywords: Volatility, Stock Returns, ARCH, Fractional Integration, MLP

JEL Classification: G12, C32, C52, C53

Suggested Citation

Bildirici, Melike and Ersin, Ozgur Omer, Nonlinear Volatility Models in Economics: Smooth Transition and Neural Network Augmented GARCH, APGARCH, FI-GARCH and FIAGARCH Models (July 27, 2012). Available at SSRN: or

Melike Bildirici (Contact Author)

Yildiz Technical University ( email )

Davutpasa Mh., Esenler
Besiktas, Istanbul 80750

Ozgur Omer Ersin

Istanbul Ticaret University ( email )

Imrahor caddesi, Sutluce

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