It is well known that atmospheric data is autocorrelated. Techniques for fitting a model to autocorrelated data without data gaps are well known. However in cases where large data gaps exist the analysis ins more challenging. By large data gaps we mean 16-24% of the possible data present. This paper explores the challenges of estimating the correlation coefficient in an autocorrelated data set containing large data gaps and suggests ways to accurately estimate the autocorrelation and linear trend in a signal when such cases arise.