The following sections contain the corrected version of the rule-base contained in Rule-Based Forecasting as proposed by Collopy and Armstrong (1992). The major changes to these rules have been as follows:
Short Range Model: Selecting Smoothing Factors for Level (Brown's Alpha)
Rule 11: Base Value
Set alpha for the short-range model to 0.7.
Rule 12: Variation
Multiply alpha for the short range model by the variation about the trend.
Rule 13: Last Observation Unusual
IF the last observation is unusual, THEN subtract 0.2 from alpha for the short-range model.
Rule 14: Discontinuities in Level
IF there are level discontinuities, AND the variation about the trend is greater than 0.9 THEN add 0.1 to alpha for the short-range period.
Rule 15: Causal Force
IF the direction implied by the causal force is the same as the direction of the recent trend AND the variation about the trend is greater than 0.9 THEN add 0.1 to alpha for the short-range period.
Rule 16: Unstable Recent Trend
IF there is an unstable recent trend THEN add 0.1 to alpha for the short-range period.
Rule 17: Maximum Value
IF alpha for the short range model is calculated to be greater than 0.7 THEN use 0.7.
Rule 18: Minimum Value
IF alpha for the short range model is less than 0.2 THEN use 0.2.
Short Range Model: Selecting Smoothing Factors for Recent Trend (Brown's Beta)
Rule 19: Base Value
Set beta for the short-range model to 0.7
Rule 20: Variation
Multiply beta for the short-range model by the variation about the trend.
Rule 21: Last Observation Unusual
IF the last observation is unusual THEN subtract 0.4 from the beta for the short-range model.
Rule 22: Discontinuities in Level
IF there are level discontinuities, AND the variation about the trend is greater than 0.9 THEN subtract 0.1 from beta for the short-range period.
Rule 23: Causal Force
IF the direction implied by the causal force is the same as the direction of the recent trend AND the variation about the trend is greater than 0.9 THEN add 0.1 to beta for the short-range period.
Rule 24: Unstable Recent Trend
IF there is an unstable recent trend THEN subtract 0.2 from beta for the short-range period.
Rule 25: Changing Basic Trend
IF the basic trend has been changing THEN add 0.3 to beta for the short-range period.
Rule 26: Maximum Value
IF beta for the short range model is calculated to be greater than 0.7 THEN use 0.7.
Rule 27: Minimum Value
IF beta for the short range model is less than 0.2 THEN use 0.2.
Short Range Model: Estimating Levels
Rule 28: Benchmark Weights
Use 20%, 0%, 40%, and 40% to weight the estimates of the level from the random walk, linear regression, Holt's, and Brown's respectively.
Rule 29: Level Discontinuities
IF there are level discontinuities THEN add 10% to the weight on the random walk and subtract it from that on Brown's and Holt's.
Rule 30: Near Extreme
IF the last observation is near a previous extreme AND the series has cycles present, THEN subtract 10% from the weight on random walk and add it to that on regression and Brown's.
Rule 31: Suspicious Pattern
IF there is a suspicious pattern THEN add 10% to the weight on the random walk and subtract it from that on the other three methods.
Rule 32: Unstable Recent Trends
IF there is an unstable recent trend THEN add 45% to the weight on random walk and subtract it from that on the other three methods.
Rule 33: Changing Basic Trends
IF there is a changing basic trend THEN add 15% to the weight on the random walk and subtract it from that on the other three methods.
Rule 34: Last Observation Consistent with Causal Forces
IF the difference between the last observation and the current level is in the same direction as the causal forces THEN replace the level by L' = L + ((0.3{abs(x-L)/S})(x-L)) where x is the last observation, L is the level as determined from the application of the preceeding rules, and S is the standard deviation of the trend-adjusted series.
Rule 35: Last Observation Inconsistent with Causal Forces
IF the difference between the last observation and the current level is in the same direction as the causal forces THEN replace the level by L' = L - ((0.3{abs(x-L)/S})(x-L)) where x is the last observation, L is the level as determined from the application of the preceeding rules, and S is the standard deviation of the trend-adjusted series.
Rule 36: Mechanical Adjustment - Causal Forces Unknown
IF NOT last observation unusual AND the direction of the causal forces is unknown, THEN add 12.5% of the difference between the last observation and the one-ahead rule-based forecast made at t-1.
Rule 37: Mechanical Adjustment - Causal Forces Agree with the Forecast Error for the Last Observation
IF NOT last observation unusual AND the direction of the causal forces is the same as the last observation minus the one-ahead rule-based forecast made at t-1, THEN add 15% of the difference between the last observation and the corresponding rule-based forecast.
Rule 38: Mechanical Adjustment - Causal Forces Oppose Direction of Forecast Error for the Last Observation
IF NOT last point unusual AND the direction of the causal forces is opposite to the last observation minus the one-ahead rule-based forecast made at t-1, THEN add 10% of the difference between the last observation and the the corresponding rule-based forecast.
Short Range Model: Estimating Trends
Rule 39: Benchmark Weights
Use 0%, 20%, 40%, and 40% to weight the estimates of the level from the random walk, linear regression, Holt's, and Brown's respectively.
Rule 40: Causal Forces Unknown
IF the causal forces are unknown, THEN add 5% to the weight on the random walk and subtract it from that on the regression trend estimate.
Rule 41: Dissonance
IF the direction of the basic trend and the direction of the recent trend are not the same, THEN add 15% to the weight on the random walk and subtract it from the other three trend methods.
Rule 42: Inconsistent Trends
IF the directoin of the basic trend and the direction of the recent trend are not the same, THEN add 20% to the weight on the regression trend and subtract it from Brown's and Holt's.
Rule 43: Incoherent Long Series
IF the causal forces are not in the same direction as the basic trend, THEN subtract 30% from the weight on the regression and add it to that on Brown's and Holt's.
Rule 44: Recent Run
IF the recent run is long, THEN subtract 10% from the weight on regression and add it to that on Brown's and Holt's.
Rule 45: Unstable Recent Trend
IF there is an unstable recent trend, THEN add 20% to the weight on the random walk and subtract it from that on Brown's and Holt's.
Rule 46: Suspicious Pattern
IF there is a suspicious pattern, THEN add 10% to the weight on random walk and subtract it from that on the other three methods.
Rule 47: Insignificant Basic Trend
IF NOT a significant basic trend, THEN add 5% to the weight on random walk and subtract it from that on the regression.
Rule 48: Last Observation Unusual
IF the last observation is unusual, THEN add 10% to the weight on regression and subtract it from that on Brown's and Holt's.
Long Range Model: Selecting Smoothing Factors for Level (Brown's Alpha)
Rule 49: Base Value
Set alpha for the long-range model to 0.6.
Rule 50 through 54:
Same as rules 12 through 16.
Rule 55: Maximum Value
IF alpha for the long range model is calculated to be greater than 0.6 THEN use 0.6.
Rule 56: Minimum Value
IF alpha for the long range model is less than 0.1 THEN use 0.1.
Long Range Model: Selecting Smoothing Factors for Trend (Brown's Beta)
Rule 57: Base Value
Set beta for the long-range model to 0.6.
Rule 58 through 63:
Same as rules 20 through 25.
Rule 64: Maximum Value
IF beta for the long range model is calculated to be greater than 0.6 THEN use 0.6.
Rule 65: Minimum Value
IF beta for the long range model is less than 0.1 THEN use 0.1.
Long Range Model: Estimating Levels
Rules 66-68: Same as rules 28-30
Rule 69: Stable Basic Trend
IF NOT a changing basic trend, THEN add 5% to the weight on regression and subtract it from that on the random walk.
Rules 70-74: Same as rules 31-35
Long Range Model: Estimating Trend
Rules 75-84: Same as rules 39-48
Rule 85: Stable Basic Trend
IF NOT a changing basic trend, THEN add 15% to the weight on regression and subtract it from that on Holt's and Brown's.
Rule 86: Inconsistent Trends
IF the directions of the recent and basic trends are not the same, THEN subtract 10% from the weight on regression and add it to that on the other three methods.
Rule 87: Changing Basic Trend
IF there is a changing basic trend, THEN add 20% to the random walk and 5% to Brown's and subtract 25% from regression.
Rule 88: Regression to Mean
IF the causal forces is regressing, THEN set the trend for the long-range model equal to T' = 0.2 * T + 0.8(M - L)/(P - R), subject to R > 0.5P, where T is the trend for the long-range model as estimated from the preceding rules, M is the long range mean to which the series trends, L is the level as determined by rules, P is the number of preiods it takes to go from an extreme to the long range level, and R is the number of periods during which the series has been moving toward the long-range level.
Long Range Model: Damping Trend
Rule 89: Unknown Causality
IF the causal forces are unknown THEN damp the long-range model trend estimate by 5%.
Rule 90: Inconsistent Model Trends
IF the directions of the basic and recent trends are different THEN damp the long-range model trend estimate by 5%.
Rule 91: Incoherent Forces
IF the directions of the basic and recent trends are contrary to the causal forces, THEN damp the trend by 5% for each contrary trend.
Rule 92: Uncertainty
IF the direction of the causal forces is the same as the direction of the trend from the long range model THEN add (1-R2)/B to the damping factor ELSE add 2(1-R2)/B to the damping factor. B is the number of periods before the long range model reaches 100% of the forecast, and R2 from the linear regression is expressed in decimal form.
Rule 93: Suspicious Pattern
IF there is a suspicious pattern THEN damp the trend by 5%.
Rule 94: Unstable Recent Trend
IF there is an unstable recent trend THEN damp the trend by 10%.
Rule 95: Horizon
Multiply the trend for the long range model by (1-D)h-1, where D is the damping factor and h is the forecast horizon.
Blending the Forecasts from the Short-Range and Long-Range Models
Rule 96: Blend Period
IF the data are annual, THEN the blend period is 6.
Rule 97: Blend Period
IF the trends from the short-range model and the long-range models are in the same direction OR if the causal forces are known THEN Lh = 1 - {(100/B) * [(1 + B - h)/100]}, where Lh is the percentage of the long -range model used in the forecsating horizon h, and B is the blend period, the number of preiods over the forecast horizon until the long-range model equals 100%.
Rule 97: Standard Blend
IF the trends from the short-range model and the long-range models are in the same direction OR if the causal forces are known THEN Lh = 1 - {(100/B) * [(1 + B - h)/100]}, where Lh is the percentage of the long -range model used in the forecsating horizon h, and B is the blend period, the number of preiods over the forecast horizon until the long-range model equals 100%.
Rule 98: Quick Blend
IF the short range model direction conflicts with the long range model direction AND the causal force direction is the same as the long-range model THEN set the share of the long range model to …h1 (x) / …B1 (y) where h is the horizon and B is the blend period.
Rule 98: Slow Blend
IF the short range model direction conflicts with the long range model direction AND the causal force directionis the same as the short-range model THEN set the share of the long range model to …1+B+h1 (x) / …B1 (y) where h is the horizon and B is the blend period.
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