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...

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...

We propose an adaptive varying-coefficient spatiotemporal model for data that are observed irregularly over space and regularly in time. The model is capable of catching possible non-linearity (both in space and in time) and non-stationarity (in space) by allowing the auto-regressive...

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...

In this note, the condition to ensure the L1 geometric ergodicity of a multivariate nonlinear AR model mixed with an ARCH term (also called conditional heteroscedastic autoregressive nonlinear model) is investigated. Under some mild conditions on the white noise process with first absolute...

This paper establishes a general moment inequality for spatial processes satisfying the [alpha]-mixing condition [cf., Tran, 1990. Kernel density estimation on random fields. J. Multivariate Analy. 34, 37-53]. Such a general moment inequality is a nontrivial extension of the corresponding result...

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...

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...