Purpose – Financial returns are often modeled as stationary time series with innovations having heteroscedastic conditional variances. This paper seeks to derive the kurtosis of stationary processes with GARCH errors. The problem of hypothesis testing for stationary ARMA(p, q) processes with...

This paper studies the problem of volatility forecasting for some financial time series models. We consider several stochastic volatility models including GARCH, Power GARCH and non-stationary GARCH for illustration. In particular, a martingale representation is used to obtain the l-steps-ahead...

This note considers a new class of nonparametric estimators for nonlinear time-series models based on kernel smoothers. Various new results are given for two popular nonlinear time-series models and compared with the results of Thavaneswaran and Peiris (Statist. Probab. Lett. 28 (1996) 227).

Godambe's (1985) theorem on optimal estimating equations for stochastic processes is applied to nonparametric estimation problems for nonlinear time-series models with time-varying parameter [alpha](t). Examples are considered from the usual classes of nonlinear time-series models. The goal of...

In financial modeling, the moments of the observed process, the kurtosis and the moments of the conditional volatility play important roles. They are very important in model identification and in forecasting the volatility (see Thavaneswaran et al. [(2005b). Forecasting volatility. Statist....

This paper is concerned with filtering for various types of time series models including the class of generalized ARCH models and stochastic volatility models. We extend the results of Thavaneswaran and Abraham (1988) for some time series models using martingale estimating functions. Nonlinear...

Following the general approach for constructing test statistics for stochastic models based on optimal estimating functions by Thavaneswaran (1991), a new test statistic via martingale estimating function is proposed. Applications to some time-series models such as random coefficient...

Purpose – Option pricing based on Black-Scholes model is typically obtained under the assumption that the volatility of the return is a constant. The purpose of this paper is to develop a new method for pricing derivatives under the jump diffusion model with random volatility by viewing the...

Recently there has been a growing interest in the problems of inference for stochastic processes when the underlying distribution is not specified in terms of a parametric family. Godambe's (1985) approach is here employed to obtain estimates for random signals for a continuous semimartingale...

The kernel function and convolution-smoothing methods developed to estimate a probability density function and distribution are essentially a way of smoothing the empirical distribution function. This paper shows now one can generalize these methods to estimate signals for a semimartingale...