Satellite observation is one of the most useful methods for monitoring the power generated by photovoltaic systems. We propose a method for predicting time series of the surface solar irradiance (SSI) from one-granule cloud properties data obtained by satellite observation. This method has two parts. One is prediction of time series features from cloud properties, which is based on a previous study. The other is prediction of a time series from time series features, which is developed in this work. Seven time series features are used: mean, standard deviation, skewness, kurtosis, linear regression coefficient, autocorrelation coefficient with lag-1, and sample entropy. The prediction skill is characterized in two ways: by the distance between the predicted and observed time series (metric D), and by the similarity of the spectrum between the two time series (metric S). Verifying the time series prediction method from time series features shows that the mean and linear regression coefficient are the first and second most influential factors for metric D, and standard deviation and autocorrelation coefficient with lag-1 are those for metric S. The prediction skill of the prediction method for the time series features from cloud properties is also verified, indicating that predictors for the mean, standard deviation lag-1 autocorrelation coefficient, and sample entropy have sufficient prediction skill, measured by the standardized root mean square error. Finally, the two methods are integrated to construct the prediction system using four time series features. The overall skill of the prediction system for the time series is evaluated. The proposed system provides information about the strength of the SSI time series and its variation for several hours over the satellite observation area.