On the basis of a model of a given time series, future values of a series may be generated as a forecast over a chosen time horizon. The researcher first graphs the data and then divides it into initial and validation datasets. After formulating a model on the basis of the initial dataset, he compares its predicted values to the actual values of the validation dataset. The forecast is fit to the validation data, and residuals of different models are compared to determine the best-fitting model. The researcher can then use this model to forecast later developments in the time series.
Extrapolative methods consist of a variety of exponential smoothing techniques.
There is also stepwise autoregressive exponential smoothing for more short-run fluctuations. Exponential smoothing methods are typically cheaper, easier to use, and need less data than the fifty or more equally spaced values over time required by the Box-Jenkins techniques. Dynamic regression may not be as easy to develop and apply as the more mechanical exponential-smoothing methods. Exponential smoothing is based on the concept of moving average. Exponential smoothing represents an improvement on moving-average smoothing.