The Probability of Information (PIN)-based trading introduced by Easley <italic>et al</italic>. (1996, 2002) has been adopted to address a variety of issues in empirical finance. To obtain PIN using numerical Maximum Likelihood Estimation (MLE) from transaction data, one may suffer from the numerical overflow or...

Nonparametric methods have been very popular in the last couple of decades in time series and regression, but no such development has taken place for spatial models. A rather obvious reason for this is the curse of dimensionality. For spatial data on a grid evaluating the conditional mean given...

This paper considers a nonparametric time series regression model with a nonstationary regressor. We construct a nonparametric test for whether the regression is of a known parametric form indexed by a vector of unknown parameters. We establish the asymptotic distribution of the proposed test...

In this paper, we introduce a kernel method to estimate a spatial conditional regression under mixing spatial processes. Some preliminary statistical properties including weak consistency and convergence rates are investigated. The sufficient conditions on mixing coefficients and the bandwidth...

For the pth-order linear ARCH model, , where [alpha]0 0, [alpha]i [greater-or-equal, slanted] 0, I = 1, 2, ..., p, {[var epsilon]t} is an i.i.d. normal white noise with E[var epsilon]t = 0, E[var epsilon]t2 = 1, and [var epsilon]t is independent of {Xs, s t}, Engle (1982) obtained the...

For spatio-temporal regression models with observations taken regularly in time but irregularly over space, we investigate the effect of spatial smoothing on the reduction of variance in estimating both parametric and nonparametric regression functions. The processes concerned are stationary in...