What method is suitable for short-term forecast for a trendless, oscillatory, bounded time series? I am new to time series analysis and I would appreciate if anyone could provide me some insight on it.
I am trying to analyse a past series of numbers that fluctuates between 107 & 210 with a normal frequency bell curve distribution of mean 162.
What is a suitable approach to forecast short-term future range for a trendless but oscillatory, range bound type of time series?
 A: When you say normal , I assume you don't mean independent and identically distributed observations. If you do then proceed with the standard prediction of the mean. If each observation in the set is not independent from every other observation then one studies the auto-regressive structure and forms an ARIMA Model. After forming such a model you need to verify that there are no level shifts ( i.e. different means ) over time and that there are no trends in the residuals and the parameters of your ARIMA Model are constant over time and the variance of the residuals is homogeneous and here are no outliers/inliers biasing estimated parameters. If the variance of the residuals is not homogeneous you might have to perform Weighted Least Squares or transform your data via a power transform e.g. logs/reciprocals etc or actually identify an ARIMA model for the squared residuals aka a Garch Model. Now if you have some idea as to possible right-hand side/supporting/auxiliary/helping Exoneous Series you would have to seamlessly incorporate these variables into the above and culminate in a Transfer Function. Your question is simple but with most things the answer is complex due to the sample space of opportunities.
A: You might want to refer to this and the forecasted upper-lower limit plot in it.
Problem in discrete valued time series forecasting
A: If your series oscillates with smooth cycles you may use a spectral approach to forecasting. If you are interested in one step ahead forecasts, use an adaptive model such as an ARIMA(0,1,1) model or exponential smoothing model which models the change from period to period.
A: Since each "sum" of the time series you have is Independent and Normally distributed, you need a different approach from autocorrelated time series models:
(1) http://en.wikipedia.org/wiki/Prediction_interval 
(2) How to calculate the confidence interval for time-series prediction?
I leave it for the experts here to illustrate how to go about with methodology(1) as I have no idea of the detailed steps to construct Prediction Intervals for your discrete time series.
