We consider temporal aggregation of stationary and nonstationary time series with short memory, long memory and antipersistence, within the framework of fractional autoregressive processes. Asymptotically, long memory and antipersistence are preserved whereas short memory components vanish. In...

In this paper data-driven algorithms for fitting SEMIFAR models (Beran, 1999) are proposed. The algorithms combine the data-driven estimation of the nonparametric trend and maximum likelihood estimation of the parameters. For selecting the bandwidth, the proposal of Beran and Feng (1999) based...

A market is described by two correlated asset prices. But only one of them is traded while the contingent claim is a function of both assets. We solve the mean-variance hedging prob- lem completely and prove that the optimal strategy consists of a modified pure hedge expressible in terms of the...

This paper analyzes optimal hedging of a tradable risk (e.g. price risk or exchange rate risk) with forward contracts in the presence of untradable inflation risk. Utility is defined over real wealth. Optimal forward positions are derived relative to a given initial exposure in the tradable...

In an arbitrage free incomplete market we consider the problem of maximizing terminal isoelastic utility. The relationship between the optimal portfolio, the optimal martingale measure in the dual problem and the optimal value function of the problem is described by an BSDE. For a totally...

Time series in many areas of application often display local or global trends. Typical models that provide statistical explanations of such trends are, for example, polynomial regression, smooth bounded trends that are estimated nonparametrically, and difference-stationary processes such as, for...

This paper puts focus on the hazard function of inter-trade durations to characterize the intraday trading process. It sheds light on the time varying trade intensity and, thus, on the liquidity of an asset and the informations channels which propagate price signals among asymmetrically informed...

In a continuous time, arbitrage free, non-complete market with a zero bond, we find the intertemporal price for risk to equal the standard deviation of the discounted variance opti- mal martingale measure divided by the zero bond price. We show the Hedging Numeraire to equal the Market Portfolio...

The procedures of estimating prediction intervals for ARMA processes can be divided into model based methods and empirical methods. Model based methods require knowledge of the model and the underlying innovation distribution. Empirical methods are based on the sample forecast errors. In this...

In this paper data-driven algorithms for fitting SEMIFAR models (Beran, 1999) are proposed. The algorithms combine the data-driven estimation of the nonparamet- ric trend and maximum likelihood estimation of the parameters. Convergence and asymptotic properties of the proposed algorithms are...