We consider the parameter restrictions that need to be imposed to ensure that the conditional variance process of a GARCH(<italic>p</italic>,<italic>q</italic>) model remains nonnegative. Previously, Nelson and Cao (1992, <italic>Journal of Business ’ Economic Statistics</italic> 10, 229–235) provided a set of necessary and sufficient...

This paper presents a set of rate of uniform consistency results for kernel estimators of density functions and regressions functions. We generalize the existing literature by allowing for stationary strong mixing multivariate data with infinite support, kernels with unbounded support, and...

In the context of testing for a unit root in a univariate time series, the convention is to ignore information in related time series. This paper shows that this convention is quite costly, as large power gains can be achieved by including correlated stationary covariates in the regression equation.

This paper presents maximal inequalities and strong law of large numbers for weakly dependent heterogeneous random variables. Specifically considered are <italic>L</italic>^r mixingales for <italic>r</italic> 1, strong mixing sequences, and near epoch dependent (NED) sequences. We provide the first strong law for <italic>L</italic>^r-bounded <italic>L</italic>^r...