Abstract: | Let X1 be a strictly stationary multiple time series with values in Rd and with a common density f. Let X1,.,.,Xn, be n consecutive observations of X1. Let k = kn, be a sequence of positive integers, and let Hni be the distance from Xi to its kth nearest neighbour among Xj, j i. The multivariate variable-kernel estimate fn, of f is defined by where K is a given density. The complete convergence of fn, to f on compact sets is established for time series satisfying a dependence condition (referred to as the strong mixing condition in the locally transitive sense) weaker than the strong mixing condition. Appropriate choices of k are explicitly given. The results apply to autoregressive processes and bilinear time-series models. |