ModelRisk example · General techniques
Forecast from a Leading Indicator
Can this year's building permits forecast next year's cement sales? A forecast from a leading indicator.
From the model’s saved run
The lead and the line
From the Data and Forecast sheets.
| Measure | Unit | Value |
|---|---|---|
| Lead with the highest R² | months | 11 |
| Lead used (Inputs sheet) | months | 11 |
| R² at the lead used | 0.971 | |
| Standard error of a forecast month | kt | 0.164 |
Line chart: 90th percentile, Median, Mean, 10th percentile.
The business question
A cement supplier wants to plan its production for the coming year. Construction starts a while after a building permit is issued, so permits ought to tell it something about future cement sales. It has 90 months of both.
Comparing sales with permits issued 0 to 20 months earlier shows one lead that fits far better than the others: sales follow permits by about eleven months. A straight line through those pairs explains most of the variation in sales, and because the permits for the next eleven months' sales have already been issued, they give a forecast with only the line's scatter as uncertainty.
- Who it is for
- Forecasters with an indicator that moves ahead of the quantity they need: orders, permits, enquiries, claims notified.
- Main outputs
- R² of the relationship for every lead from 0 to 20 months · the fitted line and its scatter · sales in each of the next eleven months at P10 / median / P90, and their total.
How the model works
Four sheets after this one, read from left to right. Each one feeds the next.
Inputs sheet
The lead in months, chosen from the table of R² on the Data sheet (11 for these data).
Data sheet
The history, and for every lead from 0 to 20 the R² between permits and the sales that many months later. INDEX picks the matching ranges, so the table needs no OFFSET.
Forecast sheet
SLOPE, INTERCEPT and STEYX of sales on permits at the chosen lead. Each forecast month's sales are VoseNormal(slope × the permits issued 'lead' months earlier + intercept, STEYX).
Results sheet
The best lead and its R², the fitted line, and the forecast's percentiles and band.
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The results in detail
Sales forecast
Sales in months 1, 6 and 11, and over all eleven.
| Measure | Unit | 10th pct | Median | 90th pct | Mean |
|---|---|---|---|---|---|
| Month 1 | kt | 5.03 | 5.24 | 5.46 | 5.24 |
| Month 6 | kt | 5.41 | 5.62 | 5.83 | 5.62 |
| Month 11 | kt | 6.27 | 6.48 | 6.69 | 6.48 |
| Eleven months | kt | 62.6 | 63.3 | 64.0 | 63.3 |
How to read these results
- R² rises to about 0.97 at a lead of eleven months and falls away on both sides: sales follow permits by about a year, and at the right lead the line explains almost all of their variation.
- Because the permits for the next eleven months' sales have already been issued, the forecast needs no forecast of the indicator: its only uncertainty is the scatter around the line, about 0.16 kt a month.
- Permits rose steeply over the last year, so the line forecasts sales rising from about 5.2 to about 6.5 kt a month: a jump from the 4.5 to 5 kt of recent months that the permits already issued make likely.
- Beyond eleven months the permits are not yet known; a longer forecast would need a forecast of permits, with its own uncertainty.
See it move. Open the workbook, change an input on the Inputs sheet and run the simulation: every table and chart on this page updates in Excel.
Inputs and assumptions
Every assumption in the model, with its uncertainty and where it comes from. The figures are illustrative.
The lead 1 input
How many months sales follow permits. Read it from the R² table on the Data sheet.
| Assumption | Unit | Value |
|---|---|---|
| Lead used for the forecastThe highest R² for these data. The forecast table needs a lead of at least 11. | months | 11 |
Units and conventions
- Permits
- Building permits issued per month.
- Sales
- Cement sales, thousand tonnes per month.
- Lead
- Sales in month t are compared with permits in month t − lead.
- Months
- Month 0 is the last month of data; months 1 to 11 are forecast.
Key assumptions and limitations
- Linear
- Sales are a straight-line function of permits issued 'lead' months earlier, plus Normal scatter.
- Stable
- The relationship and the lead stay as they were over the 90 months.
- Known parameters
- The line's slope and intercept are taken as known: with 79 pairs and R² near 0.97 their uncertainty is small next to the scatter.
- Data
- The 90 months of data are those of ModelRisk's earlier Leading Indicator example.
How to use it
- Replace the history on the Data sheet with your own indicator and quantity.
- Read the R² table, and set the lead with the highest R² on the Inputs sheet (11 or more for this layout).
- Run a simulation from the ModelRisk ribbon (10,000 samples with a fixed seed are set).
- Plan on the band, not the line: the scatter around the line is the forecast's uncertainty.
ModelRisk functions used
- RSQ, SLOPE, INTERCEPT, STEYX (Excel)
- The relationship's strength, its line and the scatter around it.
- VoseNormal
- Each forecast month's sales around the line.
- VoseOutput
- The eleven forecast months as an output range, and their total.
- VoseSimPercentile
- The forecast's percentiles and band.
Further reading
- Monte Carlo simulation explained (Vose guide)
- Vose, D. (2008). Risk Analysis: A Quantitative Guide, 3rd edition. Wiley: forecasting with leading indicators.
Download the workbook and run it yourself. It opens in Excel with ModelRisk. The free trial runs every example model.
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An illustrative example: the figures are invented for teaching and do not describe a real company, project or asset. Last updated 9 October 2026.