Sunspot activity is highly variable and challenging to forecast. Yet forecasts are important, since peak activity has profound effects on major geophysical phenomena including space weather (satellite drag, telecommunications outages) and has even been correlated speculatively with changes in global weather patterns. This paper investigates trends in sunspot activity, using new techniques for decadal-scale prediction of the present solar cycle (cycle 24). First, Hurst exponent H analysis is used to investigate the autocorrelation structure of the putative dynamics; then the Sugihara-May algorithm is used to predict the ascension time and the maximum intensity of the current sunspot cycle. Here we report H = 0.86 for the complete sunspot number data set (1700-2007) and H = 0.88 for the reliable sunspot data set (1848-2007). Using the Sugihara-May algorithm analysis, we forecast that cycle 24 will reach its maximum in 2012 December at approximately 87 sunspot units.