Analysis of Time Series from Mixed Distributions

Abstract

Some stationary and non-stationary time series arise from mixed distributions, the probabilities attached to the occurrence of certain values being positive, while a continuum of possible values is also involved. Such series are modeled in terms of a stationary Gaussian process $X_t$, which is censored when it crosses certain thresholds. Procedures are proposed for estimating the autocorrelation function of $X_t$. Their strong consistency and asymptotic normality are established. We suggest tests of the hypothesis that $X_t$ is white noise.