Intermittent Demand Forecasting

Intermittent Demand Forecasting is the family of methods designed for time series with frequent zero values — the pattern that defies the standard forecasting toolkit. In workforce management, intermittent demand shows up at the skill level: low-volume specialty queues, off-hours support, niche worktypes, multi-skill data sliced finely enough that any individual cell has many zero intervals.

Standard methods (naive, ETS, ARIMA) fail on intermittent series in characteristic ways: they produce smooth forecasts that miss the discrete nature of arrivals, or they produce wildly unstable forecasts because percentage errors near zero blow up. The methods on this page are the WFM forecaster's toolkit when standard methods break down.

What "intermittent" means

A series is intermittent when many observations are zero and demand arrives sporadically. The Syntetos-Boylan demand classification is widely used:

Class	Average Demand Interval (ADI)	Coefficient of Variation² (CV²) of demand size
Smooth	≤ 1.32	≤ 0.49 (low variance)
Intermittent	> 1.32	≤ 0.49
Erratic	≤ 1.32	> 0.49 (high variance)
Lumpy	> 1.32	> 0.49

ADI is the average number of periods between non-zero observations; CV² is the squared coefficient of variation of the non-zero demand sizes. The threshold values (1.32 and 0.49) are empirically derived to predict which methods perform best.

In WFM, intermittent describes a low-volume queue with relatively consistent contact size when contacts arrive; lumpy describes a queue where both timing and size are unpredictable.

Why standard methods fail

Three failure modes:

1. ETS smoothing produces a flat forecast. Simple exponential smoothing on a series with mostly zeros and occasional spikes converges to a small positive number — the average demand per period, including the zero periods. The forecast is non-zero every period, never matching the actual pattern of zero-most-of-the-time, occasional spike.
2. ARIMA misses the discrete nature. ARIMA models assume continuous values; intermittent series violate the assumption. Differencing and AR/MA terms try to fit a pattern that isn't there in the standard sense.
3. MAPE explodes. MAPE is undefined when the actual is zero and unstable when actuals are near zero. The optimizer chases the explosions, biasing the method toward systematic under-prediction.

The fix: methods that explicitly model the two components of intermittent demand — when demand arrives and how much arrives when it does.

Croston's method

The original method (Croston, 1972). Decompose the series into two components estimated separately:

• Inter-demand interval $p_t$ — periods between non-zero observations
• Demand size $z_t$ — magnitude of non-zero observations

Each is smoothed via simple exponential smoothing:

${\hat{p}}_t=\alpha y_t^p+(1-\alpha ){\hat{p}}_{t-1}$

${\hat{z}}_t=\alpha y_t^z+(1-\alpha ){\hat{z}}_{t-1}$

(updating only when a non-zero observation occurs)

The forecast for the next period:

${\hat{y}}_{T+h|T}=\frac{{\hat{z}}_T}{{\hat{p}}_T}$

In plain language: forecast = average demand size, divided by average interval between demands. This is the per-period expected demand.

Strengths over ETS: Croston explicitly models the intermittent structure. The forecast captures the long-run rate without the smoothing artifacts of ETS.

Limitation: Croston's method is provably biased upward by a factor of approximately $\frac{1}{1-\alpha /2}$. The bias is small when $\alpha$ is small, but can produce systematically over-predicted forecasts.

Syntetos-Boylan Approximation (SBA)

The bias correction (Syntetos & Boylan, 2005). Same component decomposition as Croston, but the forecast applies a correction factor:

${\hat{y}}_{T+h|T}=(1-\frac{\alpha }{2})\frac{{\hat{z}}_T}{{\hat{p}}_T}$

For small $\alpha$ (typical in intermittent applications), the correction is small but consistent. SBA reduces the systematic upward bias of Croston while preserving the rest of the methodology.

When to use: SBA is the recommended default for intermittent series. It outperforms Croston on most benchmarks while being equally easy to implement.

Teunter-Syntetos-Babai (TSB) method

A different bias adjustment (Teunter, Syntetos, & Babai, 2011). TSB smooths the demand probability rather than the interval:

• Demand probability $p_t$ — probability of non-zero demand in any period (smoothed every period, not just on non-zero observations)
• Demand size $z_t$ — same as Croston (smoothed only on non-zero observations)

${\hat{y}}_{T+h|T}={\hat{p}}_T\cdot {\hat{z}}_T$

When to use: TSB has theoretical advantages when demand is genuinely sporadic (the demand probability is non-stationary). It also responds better to "obsolescence" — when a series stops generating demand entirely, TSB's probability decays toward zero, while Croston/SBA produce a constant forecast based on stale historical estimates.

For WFM contexts where demand can plausibly stop (a deprecated worktype, a discontinued product line), TSB is worth comparing against SBA.

ADIDA — Aggregate, Disaggregate, Intermittent Demand Approach

A different strategy: instead of forecasting at the original time granularity, aggregate to a longer time period (daily → weekly → monthly), forecast there, then disaggregate.

The intuition: temporal aggregation reduces intermittency. A skill that gets 0, 0, 0, 5, 0 calls on consecutive days has CV² around 5 and ADI around 5. Aggregated weekly, the same skill might get 5 calls per week — a non-intermittent series Croston/ETS handle normally.

Steps:

1. Aggregate the series to a longer period where intermittency is reduced
2. Forecast on the aggregated series with whatever method works (often ETS)
3. Disaggregate the forecast back to the original granularity using historical proportions

ADIDA pairs naturally with Hierarchical Forecasting — the temporal aggregation IS a hierarchy in time rather than in organization structure.

When to use which method

A practical decision matrix:

Series character	Recommended method
Smooth (low intermittency)	Standard ETS or ARIMA
Intermittent (consistent demand size when present)	SBA
Lumpy (variable demand size and interval)	SBA or TSB; consider ADIDA
Erratic (variable demand size, frequent observations)	Standard methods with robust loss; consider quantile regression
Demand may stop entirely (obsolescence likely)	TSB
Granular intervals (half-hour) with too many zeros to model directly	ADIDA — aggregate to hourly or daily first

Accuracy metrics for intermittent demand

The standard percentage-based metrics are unreliable on intermittent series. Practitioner alternatives:

• MASE — scaled by in-sample seasonal naive MAE; defined and stable on intermittent series
• Mean Absolute Scaled Error applied to the cumulative demand (the running sum) rather than per-period demand; reduces sensitivity to timing errors
• Mean Squared Rate Error (MSRE) — measures the error in the long-run rate forecast rather than per-period accuracy

Avoid MAPE entirely on intermittent data. The Forecast Accuracy Metrics page documents this; intermittent series is the canonical case where MAPE is misleading.

Common WFM pitfalls

• Using ETS or ARIMA on truly intermittent series. Symptoms: the forecast is a small positive number every period; actual demand pattern is mostly zeros with occasional spikes. The smooth forecast over-predicts in zero periods and under-predicts in spike periods.
• Choosing methods based on MAPE. Don't.
• Treating intermittent as a data-quality problem. It often is the actual data; the skill is genuinely low-volume. The methodological fix is to use intermittent-specific methods, not to "fix the data."
• Forgetting to test against ADIDA. Many series classified as intermittent at fine granularity become smooth at coarser granularity, where standard methods work well. Aggregate first, see what happens.
• Same method for every skill. A multi-skill operation has skills across the whole demand-character spectrum. Smooth high-volume skills get ETS; intermittent low-volume skills get SBA. One-size methods waste accuracy on both ends.

Connection to capacity planning

Intermittent demand affects capacity planning differently than smooth demand. Even if the forecast is correct on average, the realized period-to-period demand fluctuates wildly. Capacity plans built on point estimates of intermittent demand will systematically be wrong in any given period.

This is one of the situations where probabilistic forecasts and prediction intervals become essential — for an intermittent skill, planning to a point forecast guarantees over-staffing in zero periods and under-staffing in spike periods. Risk-aware capacity planning looks at the distribution of likely demand, not the mean.

Connection to hierarchical forecasting

Intermittent demand is the canonical case where Hierarchical Forecasting earns its complexity. Skill-level forecasts are often intermittent and unreliable; site-level or enterprise-level forecasts are smooth and accurate. Reconciling between the levels using MinT or top-down disaggregation produces better skill-level forecasts than forecasting each skill independently.

For multi-skill WFM operations, the combination of intermittent-specific methods at the skill level + hierarchical reconciliation across skills tends to dominate any single approach.

References

• Hyndman, R. J., & Athanasopoulos, G. Forecasting: Principles and Practice (Python edition). otexts.com/fpppy.
• Croston, J. D. "Forecasting and stock control for intermittent demands." Operational Research Quarterly 23(3), 1972.
• Syntetos, A. A., & Boylan, J. E. "The accuracy of intermittent demand estimates." International Journal of Forecasting 21(2), 2005. The SBA paper.
• Teunter, R. H., Syntetos, A. A., & Babai, M. Z. "Intermittent demand: linking forecasting to inventory obsolescence." European Journal of Operational Research 214(3), 2011. The TSB paper.
• Nikolopoulos, K., Syntetos, A. A., Boylan, J. E., Petropoulos, F., & Assimakopoulos, V. "An aggregate-disaggregate intermittent demand approach (ADIDA) to forecasting: an empirical proposition and analysis." Journal of the Operational Research Society 62(3), 2011.

See Also

• Forecasting Methods — overview where intermittent demand sits in the method-selection decision tree
• Forecast Accuracy Metrics — why MAPE fails on intermittent demand; what to use instead
• Naive and Seasonal Naive Forecasting — the baseline (which is often surprisingly competitive on intermittent data)
• Exponential Smoothing — the method Croston modifies for intermittent contexts
• Hierarchical Forecasting — pairs with intermittent demand at the skill level
• Probabilistic Forecasting — necessary for capacity planning on intermittent series
• Demand calculation — calculator that consumes forecasts including intermittent ones