We propose a flexible GARCH-type model for the prediction of volatility in financial time series. The approach relies on the idea of using multivariate B-splines of lagged observations and volatilities. Estimation of such a B-spline basis expansion is constructed within the likelihood framework...

In this paper I propose a novel optimal linear filter for smoothing, trend and signal extraction for time series with a unit root. The filter is based on the Singular Spectrum Analysis (SSA) methodology, takes the form of a particular moving average and is different from other linear filters...

We introduce a new hybrid approach to joint estimation of Value at Risk (VaR) and Expected Shortfall (ES) for high quantiles of return distributions. We investigate the relative performance of VaR and ES models using daily returns for sixteen stock market indices (eight from developed and eight...

This paper develops the asymptotic theory of the threshold pre-averaged multi-power variation estimation in the simultaneous presence of jumps and market microstructure noise and then proposes an improved estimator for integrated volatility of an Itô semi-martingale based on the obtained...

Empirical risk minimization is a standard principle for choosing algorithms in learning theory. In this paper we study the properties of empirical risk minimization for time series. The analysis is carried out in a general framework that covers different types of forecasting applications...

We introduce a new hybrid approach to joint estimation of Value at Risk (VaR) and Expected Shortfall (ES) for high quantiles of return distributions. We investigate the relative performance of VaR and ES models using daily returns for sixteen stock market indices (eight from developed and eight...

We propose a multiplicative component model for intraday volatility. The model consists of a seasonality factor, as well as a semiparametric and parametric component. The former captures the well-documented intraday seasonality of volatility, while the latter two account for the impact of the...

In statistical modeling contexts, the use of one-step-ahead prediction errors for testing hypotheses on the forecasting ability of an assumed model has been widely considered (see, e.g., Xekalaki et al. (2003, in Stochastic Musings, J.Panaretos (ed.), Laurence Erlbaum), Degiannakis and Xekalaki...

The main objective of this paper is to propose a feasible, model free estimator of the predictive density of integrated volatility. In this sense, we extend recent papers by Andersen, Bollerslev, Diebold and Labys (2003), and by Andersen, Bollerslev and Meddahi (2004, 2005), who address the...

Weekly, quarterly and yearly risk measures are crucial for risk reporting according to Basel III and Solvency II. For the respective data frequencies, the authors show in a simulation and back-test study that available data series are not sufficient in order to estimate Value at Risk and...