Two types of Brownian motion functionals, both time-homogeneous and time-inhomogeneous, are expanded in terms of orthonormal bases in respective Hilbert spaces. Meanwhile, different time horizons are treated from the applicability point of view. Moreover, the degrees of approximation of...

This paper establishes two simple and new specification tests based on the use of an orthogonal series. The paper then establishes an asymptotic theory for each of the proposed tests. The first test is initially proposed for the case where the regression function involved is integrable and the...

We reconsider the replication problem for contingent claims in a complete market under a general framework. Since there are various limitations in the Black-Scholes pricing formula, we propose a new method to obtain an explicit self-financing trading strategy expression for replications of...

In this paper, expansions of functionals of Lévy processes are established under some Hilbert spaces and their orthogonal bases. From practical standpoint, both time-homogeneous and time-inhomogeneous functionals of Lévy processes are considered. Several expansions and rates of convergence are...

This paper proposes two simple and new specification tests based on the use of an orthogonal series for a considerable class of cointegrated time series models with endogeneity and nonsta-tionarity. The paper then establishes an asymptotic theory for each of the proposed tests. The first test is...

In this paper, we consider a semiparametric single index panel data mode with cross-sectional dependence, high-dimensionality and stationarity. Meanwhile, we allow fixed effects to be correlated with the regressors to capture unobservable heterogeneity. Under a general spatial error dependence...

This paper considers a general model specification test for nonlinear multivariate cointegrating regressions where the regressor consists of a univariate integrated time series and a vector of stationary time series. The regressors and the errors are generated from the same innovations, so that...

Estimation in two classes of popular models, single-index models and partially linear single-index models, is studied in this paper. Such models feature nonstationarity. Orthogonal series expansion is used to approximate the unknown integrable link function in the models and a profile approach...

In this paper, we consider a partially linear panel data model with cross-sectional dependence and non-stationarity. Meanwhile, we allow fixed effects to be correlated with the regressors to capture unobservable heterogeneity. Under a general spatial error dependence structure, we then...

We reconsider the replication problem for contingent claims in a complete market under a general framework. Since there are various limitations in the Black–Scholes pricing formula, we propose a new method to obtain an explicit self-financing trading strategy expression for replications of...