Cumulative and Lag-1 Forecasts are the Most Important
Most supply chain leaders analyze forecasting accuracy over a single (or just a few) lags. This article explains why cumulative forecasting accuracy is more important than period accuracy and why Lag 1 is the most important forecasting horizon — even if short-term decisions are already finalized. We conclude by advising supply chain leaders to start measuring cumulative accuracy.
I have been advising S&OP leaders to focus on short-term forecasting for quite some time (or at least not to forget to forecast short-term demand). When advocating for lag-1, or short-term forecasts, here are the most common arguments I hear,
“The real value sits where the forecast can still influence production, purchasing, or allocation.”
“By Lag 1, the big decisions are already locked in: POs placed months ago, production scheduled, containers already on the water.”
“Lag 0 mostly tells you what’s happening rather than letting you change it.”
“How does it help with our 3-month lead time suppliers?”
In this article, I will address and debunk these statements by showing why and how cumulative forecasts are key, and that, mechanically, lag-1 is the most important lag.
This article is 100% human-written thanks to numerous reviewers. You can find their names in the acknowledgment section at the end of the article.
Terminology: Lag 0 or Lag 1?
Let’s first align terminology. We call lag 1 forecasts made at the start of a period (week, month) for that same period. For example, for forecasts published on the first of January (or early January), Lag 1 would be the January forecast. Many supply chain practitioners call this lag 0, but we prefer to start counting as of 1; nevertheless, feel free to use any notation you prefer.
In this article, I will also use M+1 (or M1) to denote Month+1, that is, lag 1 in a monthly-bucket demand planning process.
Finally, I call period forecasts forecasts made for a single period, and cumulative forecasts forecasts made over a horizon of multiple periods (in other words, the aggregation of multiple period forecasts into a cumulative horizon — for example, you could forecast January, February, and March separately and also look at the overall Q1 forecast and accuracy).
Forecasting Horizon and Inventory Decisions
Let’s imagine the following supply process: at the start of each month, you can make an order that your supplier will deliver in 3 months.
With this simple setup, which forecast lag(s) (M+1, M+2, M+3, etc.) do you think are the most important?
I routinely ask this question to the demand and supply planners joining SupChains’ training courses, and usually get very different answers. See below an example of answers received in one of the latest sessions we delivered.
Many planners think that M+4 and M+5 are the most important because they are the months during which your order will be consumed. Some also think that M+1 to M+3, the months leading to the reception, are key.
As detailed in my book Demand Forecasting Best Practices and in this article, when you make an inventory decision, you must be able to project your inventory levels into the future. In our example setup, you want to know what your inventory situation will look like at the end of M4, so you can place an order today to bring this projected level to the desired level (usually called your safety stock target — but feel free to call it any which way you want).
To place an order today, you need to project your inventory at the end of M4 and match it against your desired inventory level. To do so,
- You need to track how many units you will receive from your suppliers at the start of M2 and M3 (you have yet to make the order to be received at the start of M4).
That’s easy, you just have to look at how much you ordered in the past - You need to forecast demand for M1, M2, M3, and M4.
- Assess how much (safety) stock you want to have at the end of M4.
It’s likely to correlate with future demand (M5 onwards). Either because you express stock targets directly as a forecast-coverage (“I need to have 2 weeks of safety stock”) or because you use M5 onwards to simulate how the remaining stock at the end of M4 is likely to be consumed in the future using probabilistic forecasts (to put it differently, as your stock at the end of M4 is likely to be consumed in M5 onward, you want to simulate how long it’ll take for this stock to be consumed even if you do not make any order in M5 — that’s what one of the winners of the VN2 inventory competition did).
We can translate the previous figure into a table (where 📦 is the amount we should order now)
If your M4 stock target is 30, you need to order 20 pieces.
“The real value sits where the forecast can still influence production, purchasing, or allocation.”
“By Lag 1, the big decisions are already locked in: POs placed months ago, production scheduled, containers already on the water.”
I often hear these kinds of arguments from supply chain planners when I advise them to pay attention to short-term forecasts. But, as illustrated, because short-term forecasts help you to project your mid-term inventory, short-term forecasts are as important as any other forecasts to place mid-term orders — even if you can’t change short-term orders.
Supply planning is a continuous chain of dependencies, not a series of isolated months. In the example, we already confirmed the amounts to be received at the start of M2 and M3; yet, M1, M2, and M3 forecasts are as important as the M4 forecast for projecting our inventory in M4. We also need a clear view of M5 to determine the optimal stock target and the end of M4. To put it differently, you cannot make an accurate decision for M4 if your starting position is a guess.
Most supply chain leaders dismiss short-term forecasting accuracy as irrelevant once near-term orders are locked. That instinct is understandable but wrong. We need accurate forecasts over the whole risk-horizon[1] plus the safety-stock-coverage-period. Forecasts beyond this horizon are still useful: they can provide your suppliers with a future order plan, simulate how your inventory levels will behave, or support capacity planning.[2] But long-term forecasts at product level become less and less important as they are not used to drive inventory replenishment decisions.
[1] I coined the term risk-horizon in my books, Inventory Optimization: Models and Simulations, and Demand Forecasting Best Practices, to denote the lead time plus the review period, as both are equally important when it comes to (safety) stock setting. Unfortunately, most practitioners (software vendors and consultants alike) often forget to account for the review period.
[2] Capacity planning can be piloted using higher aggregation levels (usually per product group) than inventory decisions (usually per product-market). So, accurate forecasts per product-market are less important over a longer horizon, whereas accuracy per product group might become more relevant.
Cumulative Forecasts (mostly) Drive Inventory Decisions
Lost Sales or Backorders?
Supply chains in general, and each product-market combination specifically, can be put along a lost-sales-backorders spectrum with two extreme cases:
- Backorders. When you run out of stock, customers wait for you to replenish your inventory before they can get their orders. Extra demand that can’t be fulfilled immediately stacks up in a backlog.
Many manufacturers and distributors (to some extent) track backorders when orders from their B2B customers aren’t fulfilled immediately. Make-to-Order (MTO) businesses and the pharma industry, for example, are usually inclined towards pure backorder systems.
- Lost-sales. When you run out of stock, customers cancel their orders. Any extra demand that can’t be fulfilled immediately is lost.
Typically, retailers and FMCG are lost-sales businesses: if you miss demand in Week 1, that revenue is gone forever.
In practice, every supply chain sits somewhere along this spectrum. Within the same supply chain, specific products or markets can also face different customer behaviors. Finally, the duration of the shortage might also affect customers’ reactions.
Let’s see how these two customer behaviors (backorders and lost sales) impact our inventory projection.
Backorders
Let’s first imagine a pure backorder situation where your customers’ orders sit in a backlog until you can fulfill them. In such a case, period forecasts are not so important; only the cumulative forecast over the horizon does. In other words, as long as you get the total demand right over the next x months, you don’t have to worry about when customers will order your products.
Let’s illustrate this using our previous example by moving all the forecasts to M1. We should still order 20 pieces to reach our stock target of 30 pieces.
With this setup, we should still order 20 pieces to reach our M4 stock target of 30 pieces. (This example is also a good case to illustrate the difference between demand and sales forecasts.)
Now, an extreme focus on cumulative forecasts comes with two limitations,
- Forecasts over the safety coverage period still need to be accurate per period.
Let’s illustrate this with our example: If we want to somehow link M4 safety stocks to future expected demand, we need an accurate M5 forecast (whether we use forecast coverage as safety stock or probabilistic forecasts to simulate how the order will be consumed). - You will struggle to properly simulate inventory levels, plan production and capacity, and forecast sales period by period if you only have a good cumulative forecast.
Lost Sales
Let’s imagine a second pure lost-sales scenario, where any shortage would result in lost sales for all extra demand. In this case, you need to account for shortages to project your inventory. As an illustration, let’s again consider an extreme case in which we expect a surge in demand in M1, followed by a drop to zero.
Based on this projection, we should not order anything as we project to finish M4 with an inventory of 70 pieces. This is because we expect to lose 60 units of sales in M1 due to a massive shortage.
The higher the fill rate, the more a lost-sales scenario resembles a backorder scenario, where cumulative forecasts are more important than period forecasts. But with low fill rates (and especially with high seasonality or promotions), period forecasts become more important for assessing how much and when sales will be lost.
Lag 1 Forecasts
“Lag 1 mostly tells you what’s happening rather than letting you change it.”
As we see in all our examples, accurate Lag 1 forecasts won’t help you change short-term orders, but they will help you make the best possible mid-term decisions. In other words, Lag 1 forecasts are as important as any other forecast within the risk horizon (plus some coverage) for making the best possible mid-term ordering decisions to help reach inventory targets.
VN2, the inventory competition I hosted in 2025, simulated a lost-sales supply chain. All top participants forecasted lag 1 demand and used it to project their inventories. See this article to read more about how top competitors dealt with it.
Measuring Cumulative Forecast Accuracy
In the previous Section, we recognized that cumulative accuracy matters often more than period accuracy (which is still important, just less so). Let’s discuss further how to track it (using dummy data) and illustrate how it behaves based on two case studies.
How to Compute Cumulative Forecast Accuracy
Let’s use a simple example to illustrate cumulative forecasting accuracy.[1] You are responsible for forecasting the demand for one of your products. On the first of January 2026, you generated the 3 forecasts below using 3 different techniques. On the 1st of May 2026, you looked back at these figures to assess the quality of the forecasts. (You can reproduce the results using the source data here.
To perform an extensive analysis of forecasting quality, we advise tracking accuracy on all products and for multiple forecasting cycles. This example contains only dummy data for a single fictitious product over one forecast cycle (2026–01).
Here are the period metrics,
Based on this analysis, Forecast 1 should be considered the best as it displays the lowest score. Let’s now look at the cumulative demand and forecast,
The Score, computed as MAE + abs(Bias), is a metric I like to use to evaluate forecasting quality because it captures both accuracy and bias. See my book Demand Forecasting Best Practices for more details.
We see the following absolute errors,
As you can see,
- 🟧Forecast 1. Cumulative error worsens over time because it is inherently biased (i.e., it suffers from systematic errors), despite its excellent period accuracy.
- 🟩Forecast 2. Jack-of-all-trades, displaying an overall naturally decreasing cumulative forecast error.
- 🟥Forecast 3. Perfect 4-month cumulative forecast error, but the timing of the period demand was always wrong.
Lag 1 and Cumulative Accuracy
Measuring cumulative accuracy sounds straightforward until you have to track it at scale. The right horizon isn’t universal. It shifts by product, by lead time, review cycle, and by how your supply chain evolves over time. A single three-month window applied across your entire portfolio will be relevant for some SKUs and meaningless for others. Too long for products replenished in two weeks, too short for those tied to five-month overseas lead times.
So, which horizon(s) should you track to evaluate cumulative forecasting accuracy?
This is still a debate at SupChains, but, for now, we decided to track cumulative forecast error for all horizons. And, as we work with cumulative accuracy across various horizons, we must acknowledge that, mechanically, lag-1 forecasts are the most important because they are included in all horizons.
Let’s illustrate this with two case studies.
Case Studies
Danfoss
SupChains recently delivered a forecasting POC for a business unit of Danfoss (we will publish a full case study later in 2026). This business unit has an interesting supply chain with weekly replenishment and short lead times between its factories and distribution centers, and longer lead times towards its raw-material suppliers.
During the POC, we showcased the following results per forecasting horizon.
As you can see, SupChains’ engine delivers better forecasts until around week 10, then reverts to the mean (with an exception during weeks 28–30 due to a seasonal event). With these results, we got the following question from Danfoss leadership,
“How does it help with our 3-month lead time suppliers?”
If we look at the cumulative error over various horizons, we get the following picture. SupChains’ engine gains an edge from its short-term forecasts and then maintains it over mid- and long-term horizons (with a 28% reduction in forecast error after 30+ weeks).
We also observe a reversal between their Current Software versus the 6-month moving average. One is better for the short term, whereas the other is better for longer horizons.
Animalcare
SupChains is currently implementing an inventory optimization engine (similar to the one taught in my Udemy course) for Animalcare. This inventory engine simulates forecast-coverage-based policies throughout 2024 and 2025 using historical demand and forecasts (as they were available at the time) while accounting for lead time variability, MOQ, production schedules, and maximum shelf life. We will publish a detailed case study later in 2026. In the meantime, we analyzed forecasting accuracy (period and cumulative) for different models.
Comparing Forecasts
Let’s first compare the Animalcare consensus forecast with the SupChains forecast engine and a statistical baseline. If we look at period-forecasts, we obtain the following results,
Find more information about the metrics we use in our latest case studies. For more information, we extensively discuss forecasting variability in this article.
MAE% (lower is better) is the Mean Absolute Error expressed as a percentage of total demand.
Score (lower is better) combines MAE% and absolute Bias% into a single metric to measure forecasting quality. It is SupChains’ favorite KPI.
Variability (lower is better) measures how much a forecast from the same model varies from one cycle to the next. You can find more details about variability in this article.
Note that these results are based on a recent back-testing of SupChains’ current engine using up-to-date (corrected) demand data. Whereas consensus forecasts the actual numbers as they were published at the time (enriched with product transitions). This gives the SupChains’ engine an edge as some market-allocation rules changed over time, and we can’t re-populate historical consensus forecasts. So, these results shouldn’t be used to draw any conclusions regarding Forecast Value Added (FVA); instead, we just want to use these two sets of forecasts as Guinea pigs to learn more about how period-forecast accuracy translates into cumulative forecasting accuracy.
Looking at period-forecasts absolute errors, SupChains’ engine seems to always have a small advantage (that is growing with the horizon).
But this added value for period-forecasts doesn’t translate into a clear advantage in terms of cumulative errors (except in the long term, where the added value at 12 months is around 4%). This may be because SupChains’ engine errors tend not to offset each other much from one period to another
Conclusion
We conclude our analysis with four main points,
- Short-term forecasts are key even if they can’t impact short-term decisions.
- Cumulative accuracy is more important than period accuracy — especially if you have a supply chain with little lost sales (either because of high service level, or because of back orders).
- Period-forecast accuracy and cumulative accuracy do not always correlate as some models (or people) make systemic errors when forecasting demand.
- Lag 1 is the most important lag because it is included in the risk-horizons of all your product-market combinations.
We conclude that supply chain S&OP leaders should measure forecast accuracy and FVA for both cumulative horizons and lag 1. This is a major shift from the current practice of mostly measuring accuracy and added value for a single lag (usually lag 3).
Acknowledgments
Justin Matthews, Stephan Kolassa, Agustin Peña Camprubí, Konrad Grondek, Prince Boadu, Siddharth Sharma.
