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The original RBF, as presented in Collopy and Armstrong (1992), relied on 18 features of time series. Since then, the scope of RBF has expanded to now encompass 28 rules for RBF. The table below presents these features and their descriptions.

Feature Categories

RBF Features


Causal forces


The net directional effect of the principal factors acting on the series. Growthexerts an upward force. Decay exerts a downward force. Supporting forces push in direction of historical trend. Opposingforces work against the trend.Regressing forces work towards a mean. When uncertain, forces should be unknown.

Functional form

Multiplicative Additive

Expected pattern of the trend of the series.

Cycles expected

Cycles expected

Regular movement of the series about the basic trend.

Forecast horizon

Forecast horizon

Horizon for which forecasts are being made.

Subject to events

Subject to events


Start-up series

Start-up series

Series provides data for a start-up.

Related to other series

Related to other series


Types of data



Positive values

Only positive values in time series


Bounded values such as percentages and asymptotes

Missing observations

No missing observations in the series



Level is not biased by any other events.




Direction of basic trend

Direction of trend after fitting linear regression to past data.

Direction of recent trend

The direction of trend that results from fitting Holt’s to past data.

Significant basic trend (t>2)

The t-statistic for linear regression is greater than 2.

Length of series


Number of observations

Number of observations in the series.

Time interval (e.g. annual)

Time interval represented between the observations.



Whether seasonality is present in the series.



Coeff. of variation about trend >0.2

Standard deviation divided by the mean for the trend adjusted data.

Basic and recent trends differ

Basic and recent trends not in same direction










Irrelevant early data

Early portion of the series results from a substantially different underlying process.

Suspicious pattern

Series that show a substantial change in recent pattern.

Unstable recent trend

Series that show marked changes in recent trend pattern.

Outliers present

Isolated observation near a 2 std. deviation band of linear regress.

Recent run not long

The last six period-to-period movements are not in same direction.

Near a previous extreme

A last observation that is 90% more than the highest or 110% lower than lowest observation.

Changing basic trend

Underlying trend that is changing over the long run.

Level discontinuities

Changes in the level of the series (steps)

Last observation unusual

Last observation deviates substantially from previous data.

In the original paper by Collopy and Armstrong (1992), eight features were identified by analytical procedures coded in the expert system while the rest relied on the forecaster’s judgment and knowledge of the domain. The judgmental identification of these features, however, was time consuming and inconsistent, often taking over 5 minutes per series. In recent research, we have automated the feature identification process using simple statistical approaches. Consequently, time commitment to feature identification has dropped to under one minute per series without consequential decline in forecast accuracy.

Through extensive sensitivity analyses, we have found that causal forces are one of the key features of RBF. This feature represents the cumulative directional effect of the factors that influence the trends in a time series. As illustrated in the table above, causal forces can be classified in four ways based on their relation to historical trend. Several papers illustrate the use of causal forces in combining time series forecasts.