You can project your rainfall time series towards future time (forecast) using
Exponential smoothing. What particular technique of smoothing you use depends on your data, for instance, If you have a time series that can be described using an additive model with increasing or decreasing trend and no seasonality, you can
use Holt’s exponential smoothing.
In R you can use the function "forecast.HoltWinters()" of package “forecast”.
A brilliant book on time series forecast is:
Coghlan A. (2015). "A Little Book of R For Time Series", which can be found in the
Predicting any form of weather is always problematic. If the only inputs are previous rainfall values, I suggest you use a straightforward regression model. There is little point adding complexity to the model when it is not clear if the training data is adequate to predict the future. Ideally you would at least need to add some some attribute which increases rainfall based on say global warming predictions.