The problem of determining confidence intervals for climatic signals using data sets with spatial and temporal sampling inhomogeneities is solved by a four-step process. First, the actual data set is analysed to determine autoregressive models which are consistent with the actual data at daily, monthly and annual time scales. Second, these models are used to generate artificial, but realistic, data sets which reproduce selected statistical properties of the actual data. Third, these artificial data sets are sampled by Monte Carlo techniques to determine certain confidence interval coefficients appropriate to different fields, geographical regions, and averaging periods. Fourth, these confidence interval coefficients are used to place error bars on climatic signals derived from the actual data set. The technique is illustrated by the analysis of historical sea surface temperature and sea level pressure data in the eastern tropical Pacific Ocean.