Bernhard Schipp

Extreme value models in a conditional duration intensity framework

The analysis of return series from financial markets is often based on the Peaks-over-threshold (POT) model. This model assumes independent and identically distributed observations and therefore a Poisson process is used to characterize the occurrence of extreme events. However, stylized facts such as clustered extremes and serial dependence typically violate the assumption of independence. In this paper we concentrate on an alternative approach to overcome these difficulties. We consider the stochastic intensity of the point process of exceedances over a threshold in the framework of irregularly spaced data. The main idea is to model the time between exceedances through an Autoregressive Conditional Duration (ACD) model, while the marks are still being modelled by generalized Pareto distributions. The main advantage of this approach is its capability to capture the short-term behaviour of extremes without involving an arbitrary stochastic volatility model or a prefiltration of the data, which certainly impacts the estimation. We make use of the proposed model to obtain an improved estimate for the Value at Risk. The model is then applied and illustrated to transactions data from Bayer AG, a blue chip stock from the German stock market index DAX.

The bias of OLS, GLS and ZEF estimators in dynamic seemingly unrelated regression models

Abstract Asymptotic expansions are employed to derive and compare O ( T −1 ) approximations to the biases of the OLS, systems GLS, and Zellners efficient estimators for a system of seemingly unrelated dynamic regression equations. The bias approximations are used to construct estimators which are unbiased to O ( T −1 ) and the performance of these bias corrected estimators is examined and compared through Monte Carlo simulation of a two equation model.

Self-exciting Extreme Value Models for Stock Market Crashes

We demonstrate the usefulness of Extreme value Theory (EVT) to evaluate magnitudes of stock market crashes and provide some extensions. A common practice in EVT is to compute either unconditional quantiles of the loss distribution or conditional methods linking GARCH models to EVT. Our approach combines self-exciting models for exceedances over a given threshold with a marked dependent process for estimating the tail of loss distributions. The corresponding models allow to adopt ex-ante estimation of two risk measures in different quantiles to assess the expected frequency of different crashes of important stock market indices. The paper concludes with a backtesting estimation of the magnitude of major stock market crashes in financial history from one day before an important crash until one year later. The results show that this approach provides better estimates of risk measures than the classical methods and is moreover able to use available data in a more efficient way.

Alternative bias approximations in first order dynamic reduced form models

Abstract The small sample bias of the least squares estimator is examined in the context of a first-order dynamic reduced form model with normally distributed white noise disturbances and an arbitrary number of exogenous regressors. Bias approximations are derived based on small disturbance ( σ →0) and large sample ( T →∞) asymptotics which are both used to construct bias corrected estimators. The performance of the two bias corrected estimators is compared in a number of Monte Carlo experiments which show that, whereas both estimators are often approximately unbiased, the small disturbance procedure may sometimes yield poor results. However, this does not occur with the large sample procedure which yields almost unbiased estimators in a variety of experimental situations with a mean square error comparable to (though slightly larger than) that of the least squares estimator.

Minimax estimation with additional linear restrictions - a simulation study

Let the parameter vector of the ordinary regression model be constrained by linear equations and in addition known to lie in a given ellipsoid. Provided the weight matrix A of the risk function has rank one, a restricted minimax estimator exists which combines both types of prior information. For general n.n.d. A two estimators as alternatives to the unfeasible exact minimax estimator are developed by minimizing an upper and a lower bound of the maximal risk instead. The simulation study compares the proposed estimators with competing least-squares estimators where remaining unknown parameters are replaced by suitable estimates.

Quasi-Minimax Estimation, Prior Information and Money Demand in Germany

We illustrate the application of various quasi minimax estimators in a linear regression model in which money demand in Germany is related to real GNP, inflation- and nominal interest rate. Initial interval constraints on the coefficients are transformed into ellipsoidal restrictions. The resulting quasi minimax estimators are shown to outperform ordinary least squares according to a minimax risk criterion.

Feasible minimax estimators in the simultaneous equations model under partial restrictions

Approximate minimax estimators based on partial constraints on the structural parameters are derived in a single equation of a simultaneous equations model. The feasible versions of these estimators are shown to be biased but consistent.

Minimax estimation with random coefficients: Theory and application to stock returns

Testing the reliability of the capital asset pricing model (CAPM) for various stock market returns is an important task in capital market research. In all previous studies, a common feature consists in the application of ordinary least squares or Bayesian methods when it comes to estimation of parameters. The Bayesian approach seems to be fairly intractable by practitioners whereas the OLS approach often yields imprecise and thus doubtful results. In this paper, the CAPM is estimated by approximate minimax techniques extended to a random coefficient regression model (RCR). The method turns out to be efficient from both the economical and computational point of view.

Assessing coverage-probabilities for approximate minimax estimators with respect to interval restrictions

If a priori information given by interval or ellipsoidal constraints on the unknown coefficients is used by (approximate) Minimax estimators, it is not ensured, that the estimates lie within the restricted set. In the present paper, the probability of such events is investigated on the basis of multivariate two-sided normal probability integrals.

Approximate minimax estimators in the simultaneous equations model

Abstract Approximate and exact minimax estimators are derived for the structural and reduced form parameters in the simultaneous equations model. A priori knowledge about the coefficients given by ellipsoidal restrictions and additional equality constraints may be incorporated easily. Asymptotic properties of the estimators are established in case of structural parameter estimation, whereas some finite sample properties are derived for the parameters of the reduced form. The estimators are compared to a variety of traditional estimators by means of a simulation study.