Calculation Setup for Forecast Methods

Formula	Description
Adaptive exponential smoothing	In Adaptive Exponential Smoothing, the smoothing constant is calculated every time a new forecast is made. To control and follow up forecast precision, two types of measurements are used: Mean Absolute Deviation (MAD) and Mean Error (Forecast error, AVER). These measurements measure the deviation between forecast and actual demand.
Adaptive-response-rate single exponential smoothing	In Adaptive-response-rate single exponential smoothing (also known as Trigg and Leach's method), the calculation for alpha (α) uses the smoothed forecast error. The calculation also uses the smoothed absolute forecast error. The beta parameter is the smoothing constant applied to the trend in forecast versus demand. Alpha is adaptive and calculated automatically. Only Beta needs to be defined. The Calculation Initialization Point defined on Data Set Properties is where the adoption starts. This point gives the formula a chance to get a better starting estimate for Alpha. Applying an additional trend is not common because this method already uses the Beta trend smoothing constant to estimate adaptivity. You can apply seasonality when appropriate.
Auto ARIMA	The Autoregressive Integrated Moving Average (ARIMA) forecast method delivers a robust, production-ready time series solution for DMP by combining classic ARIMA modeling with full automation and resilience. It automatically selects optimal ARIMA parameters (P, D, Q), detects and handles seasonality using centered moving-average decomposition, and applies validation and cross-validation to ensure forecast quality. The solution is designed to always produce a forecast through built-in fallback mechanisms, even in edge cases or limited data scenarios. Seasonality detection is data-driven, configurable, and based on detrended autocorrelation analysis, with clear requirements to ensure statistical reliability. Overall, the approach balances methodological rigor with operational reliability, providing accurate, automated, and scalable forecasting.
Auto BATS	Box-Cox transformation, Trend, and Seasonal components (BATS) method automatically supports multiplicative patterns where seasonal variation increases with the level, complex seasonality using flexible Fourier-based seasonal modeling, and applies transformations to handle non-normal or skewed data. Use BATS when forecasting data with exponential or multiplicative growth, complex or changing seasonal patterns, declining markets with seasonal effects, or seasonal amplitude that varies over time. This option uses optimized defaults to ensure performance and stability for MRP scenarios. It supports a single seasonality optimized for MRP, generates point forecasts only by skipping prediction intervals, and uses fixed Fourier terms per period based on M3 and MRP industry optimization. MA error modeling is not included because it provides minimal additional benefit and reduces robustness.
Auto ETS	The Exponential Smoothing State Space (ETS) model provides model selection, data cleaning, and fallback strategies. The model fits ETS models that use error types {A, M}, trend types {N, A, Ad}, and season types {N, A, M}. This results in 18 possible model combinations. The model evaluates all valid models and selects the best model based on the minimum AIC. Model selection uses an analytical heuristic for non-seasonal models. For seasonal models, the model uses a grid search as a fallback. Known limitations include a tendency to prefer simpler models (for example, A,A,N over A,Ad,N) and reliance on AIC rather than BIC or AICc. The model handles missing data. The model replaces missing values by using linear interpolation between valid neighbors. For edge cases, the model uses forward fill or backward fill. Outlier detection is based on the IQR method, where Q1 is the 25th percentile, Q3 is the 75th percentile, and IQR = Q3 − Q1. The model treats values outside the range y_t < Q1 - 1.5·IQR or y_t > Q3 + 1.5·IQR as outliers. The model replaces these values by using interpolation from neighboring values.
Auto PROPHET	PROPHET enables an optimized implementation of the Prophet forecasting algorithm designed for ERP and MRP use in M3 industries. This forecast method uses Fourier-based seasonality with supported periods of 4, 7, 12, and 52. It provides robust data handling through built-in outlier detection and interpolation of missing values, ensuring reliable results even when source data is incomplete or irregular. The method is designed for fast execution and supports optional holiday and event effects with industry-specific presets. A linear trend is supported without changepoint detection, resulting in stable and predictable forecasts. Use PROPHET when holiday or event effects have a significant impact on demand, when it is necessary to separate holiday spikes from the underlying trend, and when long-term forecasting beyond one seasonal cycle is required. You can use PROPHET on its own or in combination with BATS for scenarios that involve complex multiple seasonalities, require smooth trends without breaks, or focus on short- to medium-term forecasting. For short-term forecasting of less than two seasons, particularly when the data is stationary or near-stationary with seasonality, we recommend the ARIMA method. This forecasting approach is optimized for speed, stability, and predictability. Bayesian inference and changepoint detection are not supported to ensure deterministic results and faster execution. The method focuses on linear growth and a single dominant additive seasonal pattern, which are both common and sufficient for demand forecasting. Auto-tuning, external regressors, and built-in cross-validation are not included to keep configuration simple and performance consistent, with holiday effects capturing most external demand influences
Auto TSB Intermittent	Teunter–Syntetos–Babai (TSB) is a forecasting method designed specifically for intermittent demand - items with sporadic, irregular demand patterns that include many periods with zero demand. This method has automatic fitting. When you use TSB, you can extrapolate forecasts using either the Standard Forecast (default), which provides the expected average demand per period, or the Intermittent Pattern Forecast, which predicts full demand at expected intervals and zero demand elsewhere. TSB uses exponential smoothing so that recent demand has greater influence on the forecast, separates demand size from demand timing, adapts automatically to changes in demand patterns, and does not require knowledge of data frequency (weekly, monthly, quarterly, or otherwise). It is best suited for spare and service parts, slow-moving inventory items, products with infrequent, unpredictable orders, and items with several zero-demand periods. Use this option only when demand history is sporadic or intermittent, as TSB is not intended for regular, consistent demand patterns, trending, or seasonal demand. For those patterns, use Prophet or ARIMA instead.
Centered Moving Average	Centered Moving Average is a specific form of Centered Weighted Moving Average. The smoothing constants are the same, except for the start and end when the length is an even number. The weight function for Centered Moving Average uses the number of calculation periods (>=2).
Constant	Constant is used for forecasts as a fixed value or per record using a numerical key as input.
Exponential smoothing	Exponential Smoothing calculates the forecast based on the demand and forecast for the previous periods by setting Offset periods to 1. To use different Offset periods, select Smoothing constant Alpha (α) with a value between zero (0) and one (1). The higher the value for α, the faster the method reacts to changes in demand. This model is good for non-seasonal data that is fairly level (that is, without a trend).
Exponential smoothing of two periods	Exponential smoothing uses two period values. The formula combines the average demand for the last 25 percent of the calculation periods and the average demand for n periods. The smoothing constant α controls how strongly the forecast responds to changes in demand. Smoothing constants of 0.2 and 0.3 are typical. These values adjust the current forecast by 20 to 30 percent of the error in the prior forecast.
Forecast as demand from preceding period	In the Forecast as demand from preceding period formula, the forecast for the next period is equal to the actual demand n periods back in time. You can use Offset Periods, Offset Years, or a combination of the two. For example, if Offset Periods is equal to zero (0), the forecast for the preceding period is equal to the demand for the previous period. If Offset Periods is equal to eleven (11), the forecast for the preceding period is equal to the demand for the same period last year. In the last example, you can also set Offset Years to 1 and Offset Periods to 0.
Holt's linear method	Holt's linear method is an extension of exponential smoothing to take into account a possible linear trend. This model is good for non-seasonal data with a trend.
Holt-Winter's Additive method	The method takes both trend and seasonality into consideration.
Holt-Winter's Multiplicative method	This method takes both trend and seasonality into consideration. A seasonal index is included in the equation.
Intermittent - Croston	Exponential smoothing is often used to forecast demand for inventory in stock management. However, if demand is sporadic or intermittent, the exponent smoothing often produce stock level that are too low. The Intermittent Croston Method improves the exponential smoothing by estimating the average size of demand (Z) first and then in a second step (X), the average interval between demands. This formula is very useful when forecasting spare parts or equipment when the demand appears random or with irregular patterns and when there are in many periods with zero demand.
Intermittent - Croston Modified	Sometimes, the forecast can be estimated more accurately by using the Croston Modified method. This method considers the effects of the last two periods of demand, especially if the interval between demands is changing.
Moving Average	The Forecast Calculation with the Moving Average Formula projects values for the forecast period. This calculation is based on the average demand (sales) over a specific number of preceding periods. These periods are weeks or months. The number of preceding periods used in the forecast calculation is referred to as n. The number of periods used determines how quickly the forecast reacts to changes in actual trends and how sensitive the forecast is to random variations. Using more periods results in a more stable forecast for random variations, but the forecast reacts more slowly to real trends. In M3 BE, several moving average hybrids exist. In M3 DMP, one formula replaces these hybrids because the setup is more dynamic and flexible. The concepts of 'offset periods' and 'offset years' enable you to determine the first historical period that is used in the forecast calculation. You use this historical period when you calculate the moving average based on n calculation periods.
Period Relation	The Period Relation forecast formula calculates the forecast equal to the relation between previous x number of periods and the same x number of periods last year multiplied with the average demand for y number of periods last starting with the current period previous year.
Weighted Moving Average	Weighted Moving Average are averages that have multiplying factors to give different weights to data points. M3 DMP uses a table of pre-defined smoothing constants that depend on the selected Weight Function. M3 DMP includes the most used variations including Spencer’s and Henderson’s weight functions.

Adaptive exponential smoothing

In Adaptive Exponential Smoothing, the smoothing constant is calculated every time a new forecast is made. To control and follow up forecast precision, two types of measurements are used: Mean Absolute Deviation (MAD) and Mean Error (Forecast error, AVER). These measurements measure the deviation between forecast and actual demand.

Adaptive-response-rate single exponential smoothing

In Adaptive-response-rate single exponential smoothing (also known as Trigg and Leach's method), the calculation for alpha (α) uses the smoothed forecast error. The calculation also uses the smoothed absolute forecast error. The beta parameter is the smoothing constant applied to the trend in forecast versus demand.

Alpha is adaptive and calculated automatically. Only Beta needs to be defined.

The Calculation Initialization Point defined on Data Set Properties is where the adoption starts. This point gives the formula a chance to get a better starting estimate for Alpha.

Applying an additional trend is not common because this method already uses the Beta trend smoothing constant to estimate adaptivity. You can apply seasonality when appropriate.

Auto ARIMA

The Autoregressive Integrated Moving Average (ARIMA) forecast method delivers a robust, production-ready time series solution for DMP by combining classic ARIMA modeling with full automation and resilience. It automatically selects optimal ARIMA parameters (P, D, Q), detects and handles seasonality using centered moving-average decomposition, and applies validation and cross-validation to ensure forecast quality. The solution is designed to always produce a forecast through built-in fallback mechanisms, even in edge cases or limited data scenarios. Seasonality detection is data-driven, configurable, and based on detrended autocorrelation analysis, with clear requirements to ensure statistical reliability. Overall, the approach balances methodological rigor with operational reliability, providing accurate, automated, and scalable forecasting.

Auto BATS

Box-Cox transformation, Trend, and Seasonal components (BATS) method automatically supports multiplicative patterns where seasonal variation increases with the level, complex seasonality using flexible Fourier-based seasonal modeling, and applies transformations to handle non-normal or skewed data. Use BATS when forecasting data with exponential or multiplicative growth, complex or changing seasonal patterns, declining markets with seasonal effects, or seasonal amplitude that varies over time.

This option uses optimized defaults to ensure performance and stability for MRP scenarios. It supports a single seasonality optimized for MRP, generates point forecasts only by skipping prediction intervals, and uses fixed Fourier terms per period based on M3 and MRP industry optimization. MA error modeling is not included because it provides minimal additional benefit and reduces robustness.

Auto ETS

The Exponential Smoothing State Space (ETS) model provides model selection, data cleaning, and fallback strategies. The model fits ETS models that use error types {A, M}, trend types {N, A, Ad}, and season types {N, A, M}. This results in 18 possible model combinations.

The model evaluates all valid models and selects the best model based on the minimum AIC. Model selection uses an analytical heuristic for non-seasonal models. For seasonal models, the model uses a grid search as a fallback. Known limitations include a tendency to prefer simpler models (for example, A,A,N over A,Ad,N) and reliance on AIC rather than BIC or AICc. The model handles missing data. The model replaces missing values by using linear interpolation between valid neighbors. For edge cases, the model uses forward fill or backward fill. Outlier detection is based on the IQR method, where Q1 is the 25th percentile, Q3 is the 75th percentile, and IQR = Q3 − Q1. The model treats values outside the range y_t < Q1 - 1.5·IQR or y_t > Q3 + 1.5·IQR as outliers. The model replaces these values by using interpolation from neighboring values.

Auto PROPHET

PROPHET enables an optimized implementation of the Prophet forecasting algorithm designed for ERP and MRP use in M3 industries. This forecast method uses Fourier-based seasonality with supported periods of 4, 7, 12, and 52. It provides robust data handling through built-in outlier detection and interpolation of missing values, ensuring reliable results even when source data is incomplete or irregular. The method is designed for fast execution and supports optional holiday and event effects with industry-specific presets. A linear trend is supported without changepoint detection, resulting in stable and predictable forecasts.

Use PROPHET when holiday or event effects have a significant impact on demand, when it is necessary to separate holiday spikes from the underlying trend, and when long-term forecasting beyond one seasonal cycle is required. You can use PROPHET on its own or in combination with BATS for scenarios that involve complex multiple seasonalities, require smooth trends without breaks, or focus on short- to medium-term forecasting. For short-term forecasting of less than two seasons, particularly when the data is stationary or near-stationary with seasonality, we recommend the ARIMA method.

This forecasting approach is optimized for speed, stability, and predictability. Bayesian inference and changepoint detection are not supported to ensure deterministic results and faster execution. The method focuses on linear growth and a single dominant additive seasonal pattern, which are both common and sufficient for demand forecasting. Auto-tuning, external regressors, and built-in cross-validation are not included to keep configuration simple and performance consistent, with holiday effects capturing most external demand influences

Auto TSB Intermittent

Teunter–Syntetos–Babai (TSB) is a forecasting method designed specifically for intermittent demand - items with sporadic, irregular demand patterns that include many periods with zero demand. This method has automatic fitting. When you use TSB, you can extrapolate forecasts using either the Standard Forecast (default), which provides the expected average demand per period, or the Intermittent Pattern Forecast, which predicts full demand at expected intervals and zero demand elsewhere.

TSB uses exponential smoothing so that recent demand has greater influence on the forecast, separates demand size from demand timing, adapts automatically to changes in demand patterns, and does not require knowledge of data frequency (weekly, monthly, quarterly, or otherwise). It is best suited for spare and service parts, slow-moving inventory items, products with infrequent, unpredictable orders, and items with several zero-demand periods. Use this option only when demand history is sporadic or intermittent, as TSB is not intended for regular, consistent demand patterns, trending, or seasonal demand. For those patterns, use Prophet or ARIMA instead.

Centered Moving Average

Centered Moving Average is a specific form of Centered Weighted Moving Average. The smoothing constants are the same, except for the start and end when the length is an even number.

The weight function for Centered Moving Average uses the number of calculation periods (>=2).

Constant

Constant is used for forecasts as a fixed value or per record using a numerical key as input.

Exponential smoothing

Exponential Smoothing calculates the forecast based on the demand and forecast for the previous periods by setting Offset periods to 1. To use different Offset periods, select Smoothing constant Alpha (α) with a value between zero (0) and one (1). The higher the value for α, the faster the method reacts to changes in demand.

This model is good for non-seasonal data that is fairly level (that is, without a trend).

Exponential smoothing of two periods

Exponential smoothing uses two period values. The formula combines the average demand for the last 25 percent of the calculation periods and the average demand for n periods. The smoothing constant α controls how strongly the forecast responds to changes in demand. Smoothing constants of 0.2 and 0.3 are typical. These values adjust the current forecast by 20 to 30 percent of the error in the prior forecast.

Forecast as demand from preceding period

In the Forecast as demand from preceding period formula, the forecast for the next period is equal to the actual demand n periods back in time. You can use Offset Periods, Offset Years, or a combination of the two.

For example, if Offset Periods is equal to zero (0), the forecast for the preceding period is equal to the demand for the previous period. If Offset Periods is equal to eleven (11), the forecast for the preceding period is equal to the demand for the same period last year. In the last example, you can also set Offset Years to 1 and Offset Periods to 0.

Holt's linear method

Holt's linear method is an extension of exponential smoothing to take into account a possible linear trend. This model is good for non-seasonal data with a trend.

Holt-Winter's Additive method

The method takes both trend and seasonality into consideration.

Holt-Winter's Multiplicative method

This method takes both trend and seasonality into consideration. A seasonal index is included in the equation.

Intermittent - Croston

Exponential smoothing is often used to forecast demand for inventory in stock management. However, if demand is sporadic or intermittent, the exponent smoothing often produce stock level that are too low. The Intermittent Croston Method improves the exponential smoothing by estimating the average size of demand (Z) first and then in a second step (X), the average interval between demands. This formula is very useful when forecasting spare parts or equipment when the demand appears random or with irregular patterns and when there are in many periods with zero demand.

Intermittent - Croston Modified

Sometimes, the forecast can be estimated more accurately by using the Croston Modified method. This method considers the effects of the last two periods of demand, especially if the interval between demands is changing.

Moving Average

The Forecast Calculation with the Moving Average Formula projects values for the forecast period. This calculation is based on the average demand (sales) over a specific number of preceding periods. These periods are weeks or months. The number of preceding periods used in the forecast calculation is referred to as n. The number of periods used determines how quickly the forecast reacts to changes in actual trends and how sensitive the forecast is to random variations. Using more periods results in a more stable forecast for random variations, but the forecast reacts more slowly to real trends. In M3 BE, several moving average hybrids exist. In M3 DMP, one formula replaces these hybrids because the setup is more dynamic and flexible. The concepts of 'offset periods' and 'offset years' enable you to determine the first historical period that is used in the forecast calculation. You use this historical period when you calculate the moving average based on n calculation periods.

Period Relation

The Period Relation forecast formula calculates the forecast equal to the relation between previous x number of periods and the same x number of periods last year multiplied with the average demand for y number of periods last starting with the current period previous year.

Weighted Moving Average

Weighted Moving Average are averages that have multiplying factors to give different weights to data points.

M3 DMP uses a table of pre-defined smoothing constants that depend on the selected Weight Function. M3 DMP includes the most used variations including Spencer’s and Henderson’s weight functions.