Department of Banking and Financial Management

The problem of inference in autoregressions around polynomial trends, under nonstationary, possibly explosive, volatility is investigated. It is shown that the well-known t-statistics that incorporate the Eicker-White covariance matrix estimator are asymptotically standard normal. Simulation results show that the application of a residual-based recursive-design wild bootstrap reduces significantly the size distortions in small samples.

In this paper, we study second order differential inclusions in R N with a maximal monotone term and generalized boundary conditions. The nonlinear differential operator need not be necessary homogeneous and incorporates as a special case the one-dimensional p-Laplacian. The generalized boundary conditions incorporate as special cases well-known problems such as the Dirichlet (Picard), Neumann and periodic problems. As application to the proven results we obtain existence theorems for both "convex" and "nonconvex" problems when the maximal monotone term A is defined everywhere and when not (case of variational inequalities).

In this paper we take issue with the applicability of the central limit theorem (CLT) on aggregate crop yields. We argue that even after correcting for the e¤ects of spatial dependence, systemic heterogeneities and risk factors, aggregation does not necessarily lead to normality. We show that aggregation is also likely to lead to nonnormal distributions, which exhibit both skewness and excess kurtosis. In particular, we consider the case in which the number of summands is not constant but varies with time, which corresponds to the empirically relevant situation where the number of acres used for cultivation of a particular crop exhibits substantial variation over time. In this case, the CLT is not applicable while the limit theorems for random sums of random variables, which apply, predict that the limiting distribution of the sum is not normal and depends on the postulated distribution of the number of summands. Using data from aggregate US states crop yields, we provide empirical support regarding the deviation of aggregate crops yields from normality.

The problem of inference in autoregressions around polynomial trends, under nonstationary, possibly explosive, volatility is investigated. It is shown that the well-known t-statistics that incorporate the Eicker-White covariance matrix estimator are asymptotically standard normal. Simulation results show that the application of a residual-based recursive-design wild bootstrap reduces significantly the size distortions in small samples.

We consider quasilinear strongly resonant problems with discontinuous right-hand side. To develop an existence theory we pass to a multivalued problem by, roughly speaking, filling in the gaps at the discontinuity points. We prove the existence of at least three nontrivial solutions. Our approach uses the nonsmooth critical point theory for locally Lipschitz functionals due to Chang (1981) and a generalized version of the Ekeland variational principle. At the end of the paper we show that the nonsmooth Palais-Smale (PS)-condition implies the coercivity of the functional, extending this way a well-known result of the “smooth” case.

We study quasilinear hemivariational inequalities involving thep-Laplacian. We prove two existence theorems. In the first, we allow “crossing” of the principal eigenvalue by the generalized potential, while in the second, we incorporate problems at resonance. Our approach is based on the nonsmooth critical point theory for locally Lipschitz energy functionals.

In this paper we study quasilinear second order boundary value problems with multivalued right hand side and Dirichlet boundary conditions. We prove three existence theorems. The ®rst two deal with the``convex'' and``nonconvex'' problems respectively, while the third establishes the existence of extremal solutions. For the ®rst two the proof is based on the theory of nonlinear operators of monotone type, while the proof of the third uses a ®xed point argument.

In this paper we study the existence of solution for two different eigenvalue problems. The first is nonlinear and the second is semilinear. Our approach is based on results from the nonsmooth critical point theory. In the first theorem we prove the existence of at least two nontrivial solutions when is in a half-axis. In Ž the second theorem based on a nonsmooth variant of the generalized mountain. pass theorem , we prove the existence of at least one nontrivial solution for every g ‫.ޒ‬

We study a quasilinear elliptic equation at resonance with discontinuous right hand side. To have an existence theory, we pass to a multivalued version of the problem by filling in the gaps at the discontinuity points. Using the nonsmooth critical point theory of Chang for locally Lipschitz functionals and the Ekeland variational principle, we show that the resulting elliptic inclusion has three distinct nontrivial solutions.

In this paper we complete two tasks. First we extend the nonsmooth critical point theory of Chang to the case where the energy functional satisfies only the weaker nonsmooth Cerami condition and we also relax the boundary conditions. Then we study semilinear and quasilinear equations (involving the p-Laplacian). Using a variational approach we establish the existence of one and of multiple solutions. In simple existence theorems, we allow the right hand side to be discontinuous. In that case in order to have an existence theory, we pass to a multivalued approximation of the original problem by, roughly speaking, filling in the gaps at the discontinuity points.

In this paper we examine nonlinear elliptic equations driven by the p-Laplacian and with a discontinuous forcing term. To develop an existence theory we pass to an elliptic inclusion by filling in the gaps at the discontinuity points of the forcing term. We prove three existence theorems. The first is a multiplicity result and proves the existence of two bounded solutions one strictly positive and the other strictly negative. The other two theorems deal with problems at resonance and prove the existence of solutions using Landesman-Lazer type conditions.

In this paper, we consider a quasilinear ordinary differential equation with Neumann boundary conditions. Our formulation is general and incorporates the case of the one-dimensional Laplacian. Using an abstract result on the range of the sum of certain monotone operators, we prove the existence of a solution. Our approach is based on the theory of monotone operators and does not use degree theoretic arguments, which is usually the case in the literature for such problems.

In this paper we examine a nonlinear hemivariational inequality of second order. The differential operator is set-valued, nonlinear and depends on both x and its gradient Dx. The same is true for the zero order term f , while the right-hand side nonlinearity satisfies a one-sided Lipschitz condition. We use the method of upper and lower solutions, coupled with truncation and penalization techniques and the fixed point theory for multifunctions in an ordered Banach space.

While the …nancial world is experiencing a crisis, the prices of most agricultural commodities have remained high, although exhibiting extreme volatilidy. Motivated by evidence showing that volatility trends are present in agricultural commodity prices, we analyze stochastic processes whose unconditional variance changes with time. This analysis suggests a semi-parametric model for capturing the trending behavior of second moments, in which these moments are polynomial-like functions of time. Based on this model, we formulate the portfolio problem faced by an investor when the variances and the covariances of the returns of the available assets are trending. Then, we obtain an approximate solution of the problem, which is based on the consistent estimation of the order of variance-covariance growth and apply it for the construction of an optimal portfolio of agricultural commodities. It is shown that the performance of this portfolio is superior to those of alternative portfolios which are formed by employing methods not accounting for the presence of volatility trends in commodity returns.

This paper investigates the performance of the OLS estimator in the context of a cointegrating system, which exhibits a single variance shift. It is shown that the limiting distribution of OLS and that of the associated t-statistic depend on the time, the size and the direction of the break.

This paper aims at reconciling two apparently contradictory empirical regularities of financial returns, namely the fact that the empirical distribution of returns tends to normality as the frequency of observation decreases (aggregational Gaussianity) combined with the fact that the conditional variance of high frequency returns seems to have a unit root, in which case the unconditional variance is infinite. We show that aggregational Gaussianity and infinite variance can coexist, provided that all the moments of the unconditional distribution whose order is less than two exist. The latter characterises the case of Integrated GARCH (IGARCH) processes. Finally, we discuss testing for aggregational Gaussianity under barely infinite variance.

In this paper we investigate whether the empirical regularities of stock returns are independent of each other or whether any one of them implies all the others. If such a regularity exists, it is called "fundamental" and is usually thought of as a "deductive explanation" of the others. We demonstrate that such a fundamental regularity of stock returns is the one represented by the single factor model with a stochastically persistent beta coe¢ cient (SFM-AR). Indeed, this regularity alone entails all the usual regularities of stock returns, including conditional heteroskedasticity, leptokurtosis aggregational Gaussianity and aggregational Independence. Hence, SFM-AR may be thought of as an "explanatory uni…er" of the empirical regularities of stock returns. However, since the theoretical origins of SFM-AR are weak, its explanatory status falls short of meeting the standards of the "ideal explanatory text".

The purpose of this paper is twofold: first, to survey the statistical models of stock returns that have been suggested in the finance literature since the middle of the twentieth century; second, to examine under the prism of the contemporary philosophy of science, which of the aforementioned models can be classified as explanatory and which as descriptive. Special emphasis is paid on tracing the interactions between the motivation for the birth of statistical models of stock returns in any given historical period and the concurrent changes of the theoretical paradigm in financial economics, as well as those of probability theory.