We present a robust Generalized Empirical Likelihood estimator and confidence region for the parameters of an autoregression that may have a heavy tailed error, and the error may be conditionally heteroscedastic of unknown form. The estimator exploits two transformations for heavy tail...

This paper offers a new method for estimation and forecasting of the linear and nonlinear time series when the stationarity assumption is violated. Our general local parametric approach particularly applies to general varying-coefficient parametric models, such as AR or GARCH, whose coefficients...

An intensive and still growing body of research focuses on estimating a portfolio’s Value-at-Risk.Depending on both the degree of non-linearity of the instruments comprised in the portfolio and thewillingness to make restrictive assumptions on the underlying statistical distributions, a...

We investigate a model in which we connect slowly time varying unconditional long-run volatility with short-run conditional volatility whose representation is given as a semi-strong GARCH (1,1) process with heavy tailed errors. We focus on robust estimation of both long-run and short-run...

Local linear fitting is a popular nonparametric method in nonlinear statistical and econometric modelling. Lu and Linton (2007) established the point wise asymptotic distribution (central limit theorem) for the local linear estimator of nonparametric regression function under the condition of...

We propose a new methodology based on Fourier analysis to estimate the fourth power of the volatility function (spot quarticity) and, as a byproduct, the integrated function. We prove the consistency of the proposed estimator of the integrated quarticity. Further, we analyse its efficiency in...

Leverage effect has become an extensively studied phenomenon which describes the negative relation between the stock return and its volatility. Although this characteristic of stock returns is well acknowledged, most studies about it are based on cross-sectional calibration with parametric...

For a class of parametric ARCH models, Whittle estimation based on squared observations is shown to be inconsistent and asymptotically normal. Our conditions require the squares to have short memory autocorrelation, by comparison with the work of Zaffaroni (1999), who established the same...

Sufficient conditions for strict stationarity of ARCH(8) are established, without imposing covariance stationarity and for any specification of the conditional second moment coefficients. GARCH(p,q) as well as the case of hyperbolically decaying coefficients are included, such as the...

Semi-parametric estimators for non-Gaussian GARCH processes based on Feasible Weighted Least Squares (FWLS) are proposed. The estimators are consistent and do not require the specification of the innovations distribution family. The FWLS estimators incorporate information related to the skewness...