Everybody wants to see the future, but nobody does for sure. Reliably forecasting the solar activity in the near future looks like an easy task, but in fact still remains one of difficult problems in the solar-terrestrial research. We have sought for good univariate methods that can predict future smoothed sunspot numbers reasonably well based on past smoothed sunspot number data only. Here we consider a specific method we call principal component-and-autoregression (PCAR) method. The variation of sunspot number during a period of finite duration (past) before an epoch (present) is modeled by a linear combination of a small number of dominant principal components, and this model is extended to the period (future) beyond the epoch using the autoregressive model of finite order. From the application of this method, we find that the $24^{th}$ solar maximum is likely to occur near the end of the year 2013 (and there is a possibility that it occurs earlier near the start of 2013), and to have a peak sunspot number of about 86, indicating that the activity of the $24^{th}$ cycle will be weaker than the average. We will discuss how much this estimate is reliable.