We develop a stochastic model of nonsynchronous asset prices based on sampling with random censoring. In addition to generalizing existing models of non-trading our framework allows the explicit calculation of the effects of infrequent trading on the time series properties of asset returns. These are empirically testable implications for the variances, autocorrelations, and cross-autocorrelations of returns to individual stocks as well as to portfolios. We construct estimators to quantify the magnitude of non-trading effects in commonly used stock returns data bases and show the extent to which this phenomenon is responsible for the recent rejections of the random walk hypothesis.