Self-assessment answers from Module 1
Before we start, here are the answers to the Module 1 self-assessment.
One. A forecast is the statistical prediction. A demand plan is the published, approved number the business plans around, after overrides and consensus.
Two. The four functions are sales (wants inventory available, optimistic), operations (wants stability), finance (wants accuracy and tracks bias), and supply chain (wants granularity per SKU per location per period).
Three. Bias is more actionable because it is systematic and can be corrected. Random error (captured by MAPE) cannot be corrected, only reduced through better methodology.
Four. Accuracy degrades with horizon because the signal-to-noise ratio decreases. Recent data is more predictive of next week than of next year. Long-horizon forecasts rely more on trend and seasonality assumptions, which are less stable than level.
Five. Published and locked means the demand plan is frozen after approval and not changed until the next cycle. It matters because post-publication edits make accuracy measurement impossible (you are measuring against a moving target) and destroy trust in the process.
If you got all five, continue. If you missed any, review Module 1 before proceeding.
What this module covers
This module covers the three statistical forecasting model families that every demand planner encounters: exponential smoothing (ETS), ARIMA, and seasonal decomposition. These are the workhorses of practical demand forecasting. They are not the most sophisticated methods available, but they are the methods that produce the majority of operational forecasts in manufacturing today, and they are the baseline against which more sophisticated methods (machine learning, ensembles) must be measured.
By the end of this module, you will know what each model does, what assumptions it makes, when it performs well, and when it fails. You will also know enough to evaluate whether your current forecasting tool is using the right model for your demand patterns, or whether it is applying one model blindly across all SKUs.
Exponential smoothing (ETS)
Exponential smoothing is the most widely used forecasting method in practice. The method was originally proposed by Robert Brown in 1956 for US Navy inventory forecasting, and the modern formulation (state space ETS) was developed by Hyndman, Koehler, Snyder, and Grose in a 2002 Journal of the American Statistical Association paper. The Hyndman et al. formulation is the basis for the ets() function in R's forecast package and for most modern ETS implementations.
The core idea is simple. The forecast for the next period is a weighted average of past observations, with weights that decay exponentially. Recent observations get more weight than older ones. The decay rate is a parameter (alpha) that controls how quickly the model adapts to changes. Alpha near 1 means the model reacts quickly to recent data. Alpha near 0 means the model is slow to react and more stable.
The ETS framework extends this to handle trend and seasonality. An ETS model has three components: Error (additive or multiplicative), Trend (none, additive, multiplicative, or damped), and Seasonal (none, additive, or multiplicative). The notation ETS(A,A,A) means additive error, additive trend, additive seasonal. ETS(M,N,M) means multiplicative error, no trend, multiplicative seasonal. There are 30 possible combinations, and modern implementations automatically select the best one per series using information criteria.
When ETS works well. ETS is excellent for SKU-location level forecasting of stable to moderately variable demand. It handles trend and seasonality well, it is fast to compute (which matters when you have 50,000 SKUs), and it produces prediction intervals that are useful for safety stock calculation. The Hyndman et al. automatic model selection is robust and rarely produces bad results, although it can be over-confident on short series.
When ETS fails. ETS struggles with intermittent demand (many zero periods), because the exponential weighting assumes continuous signal. It also struggles with sudden regime changes (a step change in demand level), because the exponential decay means the model takes several periods to adapt. For promotional demand, ETS will smooth the promotion into the baseline, which is usually not what you want.
ARIMA
ARIMA (AutoRegressive Integrated Moving Average) is the other major statistical forecasting family. The methodology was developed by Box and Jenkins in the 1970s, and the canonical reference is their 1976 book "Time Series Analysis: Forecasting and Control." ARIMA models are more flexible than ETS but also more complex to specify and tune.
An ARIMA model has three parameters: p (autoregressive order), d (differencing order), and q (moving average order). The autoregressive component means the forecast depends on past values. The differencing component makes the series stationary (constant mean and variance). The moving average component means the forecast depends on past forecast errors. Seasonal ARIMA (SARIMA) adds seasonal versions of the same parameters.
The practical difference from ETS is that ARIMA models the autocorrelation structure of the series explicitly, while ETS models the level, trend, and seasonal components. For some series, particularly those with complex autocorrelation patterns, ARIMA can outperform ETS. For most operational demand forecasting, the difference is small and ETS is preferred because it is easier to automate and explain.
When ARIMA works well. ARIMA excels on series with strong autocorrelation structure that ETS does not capture, particularly series where past forecast errors are predictive of future values. It is also the method of choice for economic and financial time series, where the autocorrelation structure is often the dominant signal.
When ARIMA fails. ARIMA requires more data than ETS to fit reliably (typically 50+ observations), which excludes new products and short-life SKUs. It is more sensitive to outliers. It is harder to automate, because model selection (choosing p, d, q) is more involved than ETS model selection. In practice, most demand planning tools that offer ARIMA use an automated variant (auto-ARIMA), which works but is slower than ETS auto-selection.
Seasonal decomposition
Seasonal decomposition is not a standalone forecasting method but a preprocessing step that underlies both ETS and ARIMA seasonal models. The idea is to decompose a time series into trend, seasonal, and residual components, forecast each separately, and recombine.
The classical decomposition (additive or multiplicative) is simple and still useful for understanding a series. The modern version is STL (Seasonal and Trend decomposition using Loess), developed by Cleveland and colleagues in 1990. STL is more robust to outliers and handles changing seasonality better than classical decomposition.
For demand planning, the practical use of decomposition is diagnostic. If you decompose a series and the seasonal component is unstable (the seasonal pattern changes over time), simple seasonal models (ETS with seasonal, SARIMA) will struggle. If the residual component is large relative to the trend and seasonal, the series is noisy and no model will forecast it accurately. Decomposition tells you, before you fit any model, how much signal there actually is.
How to choose
For a demand planner evaluating which model to use, the practical guidance is this.
Start with ETS. It is the most robust default. The automatic model selection in modern implementations (Hyndman's forecast package, statsforecast, most commercial tools) will pick a reasonable model per series without manual tuning. For 70-80% of SKUs at a typical manufacturer, ETS is sufficient.
Use ARIMA when ETS is underperforming on a specific series and you have enough data (50+ observations). Auto-ARIMA will explore the model space, but be prepared for longer compute times on large SKU counts.
Use decomposition as a diagnostic. When a forecast is suspicious, decompose the series and look at the components. The decomposition will usually tell you why the forecast is wrong (unstable seasonality, trend change, high noise) faster than tuning the model will.
For intermittent demand (more than 50% zero periods), none of these models are the right choice. Use a method designed for intermittent demand, covered in a dedicated article in this hub.
For ensemble forecasting (combining ETS, ARIMA, and machine learning), see the dedicated article on the M5 competition. Ensembles outperform single models on average, but they require more infrastructure and compute. If you are starting from scratch, get ETS working well first, then consider ensembles.
What to do next
This module covered the three statistical forecasting families. Module 3 covers accuracy metrics in depth: MAPE, WMAPE, bias, and forecast value added. Module 4 covers the S&OP process that wraps the forecast into a published demand plan.
Before moving to Module 3, do this exercise. Pull the demand history for 10 SKUs from your planning system. Plot each one. Classify each as continuous (demand every period), intermittent (many zero periods), or lumpy (variable but non-zero). For the continuous ones, note whether there is visible trend and seasonality. This exercise will tell you, before you fit any model, what kinds of models your SKU portfolio actually needs. If all 10 are continuous with trend and seasonality, ETS will handle most of them. If half are intermittent, you need a method designed for that, and no amount of ETS tuning will fix it.
Self-assessment
Question 1. What are the three components of an ETS model, and what does each capture?
Question 2. When does ARIMA outperform ETS, and when does ETS outperform ARIMA?
Question 3. Why is seasonal decomposition useful as a diagnostic even if you do not use it for forecasting?
Question 4. What is the minimum data length for reliable ARIMA fitting, and what does this exclude?
Question 5. For intermittent demand, which of the three methods (ETS, ARIMA, decomposition) should you use as the primary forecast method?
Answers are in Module 3's introduction.