We consider asymptotic properties of the least squares estimator(LSE) in spatial regression with correlated errors. Firstly we derive sufficient conditions for the LSE to be strongly consistent and next necessary and/or sufficient conditions tor the LSE to be asymptotically efficient relative to...

The purpose of the paper is to propose a frequency domain approach for irregularly spaced data on "R"-super-"d". We extend the original definition of a periodogram for time series to that for irregularly spaced data and define non-parametric and parametric spectral density estimators in a way...

We propose a test for separability of the correlation structure of a multivariate time series. We construct test statistics based on a spectral density matrix estimated in a nonparametric way and derive their asymptotic properties. We use simulation to check the performance in finite samples....

We consider three estimators of the autocorrelation function for a stationary process with missing observations. The first estimator is linked with the Yule-Walker estimator, the second one the least squares estimator, and the third one the sample correlation coefficient. We clarify their...

This paper derives asymptotic expansion formulas for option prices and implied volatilities as well as the density of the underlying asset price in multi-dimensional stochastic volatility models. In particular, the integration-byparts formula in Malliavin calculus and the push-down of Malliavin...

The best linear unbiased predictor (BLUP) is called a kriging predictor and has been widely used to interpolate a spatially correlated random process in scientic areas such as geostatistics. The BLUP is identical with the conditional expectation if an underlying random eld is Gaussian and...

This paper develops methods of investigating the existence and extent of cointegration in fractionally integrated systems. We focus on stationary series, with some discussion of extension to nonstationarity. The setting is semiparametric, so that modelling is effectively confined to a...

We frequently observe that one of the aims of time series analysts is to predict future values of the data. For weakly dependent data, when the model is known up to a finite set of parameters, its statistical properties are well documented and exhaustively examined. However, if the model was...

This paper develops methods of investigating the existence and extent of cointegration in fractionally integrated systems. We focus on stationary series, with some discussion of extension to nonstationarity. The setting is semiparametric, so that modelling is effectively confined to a...