This study presents a method for using copulas to model the temporal variability of the clear-sky index, which in turn can be used to produce realistic time-series of photovoltaic power generation. The method utilizes the autocorrelation function of a clear-sky index time-series, and based on that a correlation matrix is set up for the dependency between clear-sky indices at N time-steps. With the use of this correlation matrix an N-dimensional copula function is configured so that correlated samples for these N time-steps can be obtained. Results from the copula model are compared with the original data set and an uncorrelated model based on zero correlated clear sky index data in terms of distribution, autocorrelation, step changes and distribution. The copula model is shown to be superior to the uncorrelated model in these aspects. As a validation the model is tested with solar irradiance for two different geographical regions: Norrkoping, Sweden and Hawaii, USA. The copula model is also applied to a set of bins of daily mean clear-sky index and the use of bins is shown to improve the results.