When designing renewable energy systems it is common practice to use a short period of historical weather data or Typical Meteorological Year (TMY) data to evaluate the performance of a renewable energy system for a particular location. However, short periods of historical data or TMY data do not capture enough of the variation required to design a reliable renewable energy system. Longer data sequences are necessary to include a greater variety of sequences; synthetic sequences are useful because they can include sequences that have not occurred in the recorded data but are nonetheless as likely to occur as the observed data. We propose a method to generate synthetic sequences of daily and hourly global horizontal irradiation (GHI) by developing a model to deal with the deterministic component of GHI, and then adding a stochastic component using a nonparametric bootstrapping technique. We use our synthetic daily and hourly models separately and reconcile them to match afterwards, unlike other studies that generate synthetic GHI data downscaled/interpolated from observed data. This is a fundamental difference to the literature. The synthetic daily and hourly GHI sequences can be used, for example, as input for testing the performance and operation of a solar energy system for a wider range of scenarios than previously observed data. Further, one could incorporate synthetic GHI with other synthetic renewable energy data, such as synthetic wind farm electricity output. Both of these approaches would be useful when designing a reliable renewable energy system. The synthetic sequences of daily and hourly GHI exhibit the same statistical properties as the real data. The two-sample Kolmogorov-Smirnov (KS) test shows that the distribution of the synthetic sequences of daily and hourly GHI match the distribution of the observed daily and hourly GHI respectively. The synthetic sequences of daily GHI have the same serial correlation structure as the observed data, an autoregressive model of order 1, AR (1), with similar AR(1) coefficients. Also, the synthetic sequences of hourly GHI have the same serial correlation structure as the observed data, an autoregressive model of order 3, AR(3), with similar AR(3) coefficients.