# 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?

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Lottery sum of 6numbers frequency follows a normal distribution –  Shelagh Mar 16 '12 at 20:24
It would help if you give us more details. For example, how long is the series, what the frequency is, if there's any obvious seasonality/cyclicality, whether the volatility appears constant over time, and what the correlogram looks like. It would also help if you described what sort of software you are using. –  Dimitriy V. Masterov Mar 16 '12 at 20:51
Thanks for the response. I am using a free software called Zaitun. I have tried most of the forecast methods in it, including neural network sigmoid and bipolar sigmoid though I am not sure how to really use it efficiently for the time series given in the link below. Perhaps someone could give me some pointers on how to use Zaitun NN for my problem. –  Shelagh Mar 20 '12 at 21:04
zaitunsoftware.com –  Shelagh Mar 20 '12 at 21:35
@Shelagh, it seems to me that the root of your problem is that you lack a firm understanding of the basic concepts of time series analysis. Answering this question may help you temporarily, but you'll be better off in the long run if you study an introduction to time series. –  Firefeather Mar 22 '12 at 17:31

You might want to refer to this and the forecasted upper-lower limit plot in it. Problem in discrete valued time series forecasting

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The example actual/fit/forecast upperlower limit plot given in the 2nd answer looks similar to the discrete SUM time series I am looking for. How can I obtain it for a layman like myself? –  Shelagh Mar 21 '12 at 20:33

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.

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Thanks for the reply. The time series is trendless, range bounded and perhaps close to white noise. Maybe someone can identify if the SUM is forecastable or not .i.e.does not need to be an exact number but as a next period target range sg.myfreepost.com/… –  Shelagh Mar 20 '12 at 21:16
catchalotto.co.uk/post/sum-it-up –  Shelagh Mar 20 '12 at 21:33
@Shelagh Perhaps it is "trendless over all" but may contain local trends. Perhaps there are "level/step shifts" . Perhaps you could post an example time series. Often free software in the area of time series is not worth what you paid for it. –  IrishStat Mar 21 '12 at 13:15
The time series SUM is posted above in this link. Please check if it is forecastable?sg.myfreepost.com/… –  Shelagh Mar 21 '12 at 14:36

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.

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Can a discrete time series be projected/forecasted with continuous smooth cycles and moving averages models? Is Arima model more for series with trending & seasonal components? –  Shelagh Mar 22 '12 at 7:12
The SUM time series looks more like cyclical spikes similar to the example plot given above in the other post. –  Shelagh Mar 22 '12 at 7:21

Since each "sum" of the time series you have is Independent and Normally distributed, you need a different approach from autocorrelated time series models:

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.

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Is it implied that the time series is ergodic and not directly forecastable? How about Bayesian approach of credible interval? –  Shelagh Mar 22 '12 at 12:49