The problem of predicting 0-1-events is considered under general conditions, including stationary processes with short and long memory as well as processes with changing distribution patterns. Nonparametric estimates of the probability function and prediction intervals are obtained.

In this paper, we estimate the Shannon entropy S(f)=-E[log(f(x))] of a one-sided linear process with probability density function f(x). We employ the integral estimator Sn(f), which utilizes the standard kernel density estimator fn(x) of f(x). We show that Sn(f) converges to S(f) almost surely...

A limit theory is developed for the least squares estimator for mildly and purely explosive autoregressions under drifting sequences of parameters with autoregressive roots ρn satisfying ρn → ρ ∈ (-∞, -1] ∪ [1, ∞) and n (|ρn| -1) → ∞. Drifting sequences of innovations and...

Standard approaches to constructing nonparametric confidence bands for functions are frustrated by the impact of bias, which generally is not estimated consistently when using the bootstrap and conventionally smoothed function estimators. To overcome this problem it is common practice to either...