We develop methods of non-parametric estimation for the Expected Shortfall of possibly heavy tailed asset returns that leads to asymptotically standard inference. We use a tail-trimming indicator to dampen extremes negligibly, ensuring standard Gaussian inference, and a higher rate of...

In this paper we analyze the convergence of interest rates in the European MonetarySystem (EMS) in a framework of changing persistence. This allows us to estimate the exact date of full convergence from the data. A change in persistence means that a time series switches from stationarity to...

This article proposes an interest rate model ruled by mean reverting Lévy processes with a sub-exponential memory of their sample path. This feature is achieved by considering an Ornstein-Uhlenbeck process in which the exponential decaying kernel is replaced by a Mittag-Leffler function. Based...

This paper studies large and moderate deviation properties of a realized volatility statistic of high frequency financial data. We establish a large deviation principle for the realized volatility when the number of high frequency observations in a fixed time interval increases to infinity. Our...

This chapter provides an overview over the recently developed so called multifractal (MF) approach for modeling and forecasting volatility. We outline the genesis of this approach from similar models of turbulent flows in statistical physics and provide details on different specifications of...

Nonlinear, non-Gaussian state space models have found wide applications in many areas. Since such models usually do not allow for an analytical representation of their likelihood function, sequential Monte Carlo or particle filter methods are mostly applied to estimate their parameters. Since...

We study optimality properties in finite samples for time-varying volatility models driven by the score of the predictive likelihood function. Available optimality results for this class of models suffer from two drawbacks. First, they are only asymptotically valid when evaluated at the...