We construct an orthonormal basis for the family of bi-variate α-modulation spaces. The construction is based on local trigonometric bases, and the basis elements are closely related to so-called brushlets. As an application, we show that m-term nonlinear approximationwith the system in an α-modulation space can be completely characterized.

The augmented GARCH model is a unification of numerous extensions of the popular and widely used ARCH process. It was introduced by Duan and besides ordinary (linear) GARCH processes, it contains exponential GARCH, power GARCH, threshold GARCH, asymmetric GARCH, etc. In this paper, we study the probabilistic structure of augmented GARCH(1,1) sequences and the asymptotic distribution of various ...

The classical method of quantitative structure-activity relationships (QSAR) is enriched using non-linear models, as Thom's polynomials allow either uni- or bi-variate structural parameters. In this context, catastrophe QSAR algorithms are applied to the anti-HIV-1 activity of pyridinone derivatives. This requires calculation of the so-called relative statistical power and of its minimum princi...

This paper used different copula-based GARCH models (Copula-GARCH model and Copula-GJR-GARCH model) to analyze the dependence structure among gold price, stock price index of gold mining companies and Shanghai Composite Index in China. The empirical results found that the suitable margins were skew-t distribution, and the GJR-GARCH marginal distribution had better explanatory ability than the G...

This paper proposes a hybrid multi-step-ahead forecasting model based on two stages to improve monthly pelagic fish-catch time-series modeling. In the first stage, the stationary wavelet transform is used to separate the raw time series into a high frequency (HF) component and a low frequency (LF) component, whereas the periodicities of each time series is obtained by using the Fourier power sp...

As extensions to the Black-Scholes model with constant volatility, option pricing models with time-varying volatility have been suggested within the framework of generalized autoregressive conditional heteroskedasticity (GARCH). However, application of the GARCH option pricing model has been hampered by the lack of simulation techniques able to incorporate early exercise features. In the presen...

Many researchers use GARCH models to generate volatility forecasts. We show, however, that such forecasts are too variable. To correct for this, we extend the GARCH model by distinguishing two regimes with different volatility levels. GARCH effects are allowed within each regime, so that our model generalizes existing regime-switching models that allow for ARCH terms only. The empirical applica...

This paper considers the pricing of options when there are jumps in the pricing kernel and correlated jumps in asset returns and volatilities. Our model nests Duan’s GARCH option models where conditional returns are constrained to being normal, as well as extends Merton’s jump-diffusion model by allowing return volatility to exhibit GARCH-like behavior. Empirical analysis on the S&P 500 index r...