VRCPI Forecast Model Consultations - Model Testing Results
On this page
Introduction
As part of its commitment to greater transparency and predictability, including as it relates to the Maximum Revenue Entitlement Program, the Agency is implementing an annual, regularized and cyclical consultation process related to the Volume-Related Composite Price Index (VRCPI). The Agency intends to consult on specific components of the VRCPI following a schedule whereby in:
- Year 1, the forecasting models for the labour, fuel and material components of the VRCPI will be examined;
- Year 2, comments on the development of the historical (actual) price indices will be sought; and
- Year 3, the investment index components of the VRCPI will be examined.
Background
The Agency recently held its first consultation on the effectiveness of the models used to predict future price changes for the labour, fuel and material components of the VRCPI. Interested stakeholders were given an opportunity to respond to various questions posed in the consultation document over the period from July 10, 2025, to October 31, 2025. The Agency received a wide range of responses and has identified and evaluated a number of suggestions for improvement which are discussed further below.
On April 17, 2026, the Agency issued LET-R-18-2026, in which it committed to extending the consultation on the VRCPI forecasting models to allow industry participants an opportunity to comment on the results of the Agency’s testing of various suggested alternative approaches.
Ongoing VRCPI model consultation
Model selection
Over the course of the consultative process, the Agency received many comments and suggestions for improvements to its forecasting models ranging from modifications to the existing forecast approaches to entirely new approaches. Keeping within the boundaries of the existing legislation and with the goal of finding a balanced approach that is as accurate and reliable as possible, but that remains relatively easy to understand, the Agency selected six approaches for testing which are described in Appendix A of this document.
Model testing
Following the closure of the initial consultative process on October 31, 2025, the Agency began testing various alternative forecasting approaches proposed by participants to determine the effectiveness of each approach.
Beginning with the status quo, and for each of the remaining five alternative approaches, the Agency generated historical forecasts for the last ten crop years and compared them to known, actual price changes. This technique is commonly referred to as “back-casting”. Each method was then analysed and ranked using various forecast error metrics including:
- mean error, cumulative error, absolute mean error, root mean squared error;
- standard deviation S; and
- coefficient of variance.
Appendix B provides a description of what each of these metrics measure.
Preliminary results
While the back-casting exercise has proven to be an effective analytic tool, it has not resulted in the identification of an alternative approach that produced results that are sufficiently consistent, either across railways or across various components. In some instances, one model may work well for one railway but not for the other.
For example, one of the more intuitively preferable approaches for the labour component involves a modification of the method used to calculate forecasts for the wage-related items Stock Based Compensation and Bonuses. Rather than using five-year averages of actual rates per hour, five-year averages of growth rates were analyzed. The error levels were not consistent across railways in this instance.
Also, while three and five-year averaging of historical railway price indices tested relatively well for the labour and material components, it did not test well for the fuel index, where the error levels were extremely high.
Appendix C to this document provides a summary of the test results of the various proposed methods.
Consultation final question
The Agency is of the opinion that sharing the analysis of the test results (attached as Appendix C) for all of the alternative suggestions with the industry, including with the railways, would be helpful in enhancing its understanding and help it to ultimately choose the most appropriate forecasting approaches to be used in next year’s determination of the VRCPI.
To that end, having seen the test results for the various approaches, do you have any comments on which of the potential approaches would be the most appropriate for the Agency to adopt?
Appendices
Appendix A
Labour
| Approach | Description |
|---|---|
| Method 1
Status Quo |
The labour price index is comprised of three main components: wages; wage-related; and fringe benefits. Forecasts for wages is based largely on annual negotiated wage contracts, while wage-related1 and fringe benefit2 forecasts are based on 5- and 10-year moving averages of historical rates per hour, respectively. Forecasts for the wage-related components are calculated as follows: 3, 4 The 2024 value [A] = Average [2020-2024] Further details of the status quo labour forecast model is found on pages three and four and in Annex A of the Agency’s Consultation Document. |
| Method 2
Modified Status Quo |
Same general approach as method 1 with the following modifications:
The 2024 value [A] = Single year preliminary actual value |
| Methods 3 & 4
Three or five year moving average growth rates Proposed by CPKC (CN – 3-year avg) |
Bases the forecasts on three- or five-year moving averages of the historical labour price index (LPI) where5: The 2024 value [A] = single year preliminary actual LPI value |
| Method 5
Modified application of three or five year moving average growth rates Proposed by CPKC |
This is the same approach as Methods 3 and 4 described above but calculated slightly differently. Here the same initial three- or five-year average (i.e., the “average growth rate [2020-2024]” in the example above is used in both years): The 2024 value [A] = single year preliminary actual LPI value |
| Method 6
Historical growth rates of Stats Can indicators Proposed by CN |
This approach uses the historical single year growth rate for a given publicly available price index as the forecast for the crop year. For the Labour price index forecasts – the Statistics Canada Industrial Aggregate Index of hourly Earnings is used (Table 14-10-0213-01). 2025-2026 LPI = [A] × StatsCan [2024/2023] where A equals 2024-2025 LPI index |
Notes
- Bonuses, stock-based compensation, etc. Return to note 1 reference↩
- Government and company pensions health and welfare plans, etc. Return to note 2 reference↩
- Example shown is for the 2025-2026 crop year where 2024 is the preliminary actual and 2025 and 2026 are the two forecasted amounts. Return to note 3 reference↩
- For all approaches, crop year forecasts are calculated as 5/12 of year one forecast value plus 7/12 of year two forecast value. Return to note 4 reference↩
- Illustrates the five-year moving average approach. Return to note 5 reference↩
Fuel
| Approach | Description |
|---|---|
| Method 1
Status Quo |
The Agency forecasts the price of fuel using a simple linear regression model that tracks the relationship between the railway fuel price index and global crude oil prices as represented by West Texas Intermediate at Cushing OK (WTI). The model includes an additional compounding adjustment for refiner’s margins and is based on a monthly time series dating back to 1988. Further details of the Agency’s approach are found on pages five and six and in Annex B of the Agency’s Consultation Document. |
| Method 2
Modified Status Quo |
Same approach as method 1 with the following modifications: The compounding adjustment for refiner’s margins is removed and the time series is annual rather than monthly dating back to 1988. |
| Methods 3 & 4
Three or five year moving average growth rates Proposed by CPKC and CN |
Bases the forecasts solely on three- or five-year moving averages of the historical fuel price index (FPI) where: The 2024 value [A] = single year preliminary actual FPI value |
| Method 5
Modified application of three or five year moving average growth rates Proposed by CPKC |
This is the same approach as Methods 3 and 4 described above but calculated slightly differently. Here the same initial three- or five-year average (i.e., the “average growth rate [2020-2024]” in the example above is used in both years): The 2024 value [A] = single year preliminary actual FPI value |
| Method 6
Historical growth rates of Stats Can indicators Proposed by CN |
This approach uses the historical single year growth rate for a given publicly available price index as the forecast for the crop year. For the Fuel price index forecasts – the Statistics Canada Industrial Product Price Index (IPPI) – Diesel Fuel is used (Table 18-10-0272-01). 2025-2026 FPI = [A] × StatsCan [2024/2023] where A equals 2024-2025 FPI index |
Material
| Approach | Description |
|---|---|
| Method 1
Status Quo |
The Agency’s material forecast models measure the relationship between the railway material price index and selected sub-components of the Industrial Product Price Index (IPPI). The Agency’s material forecast model comprises of four regression equations that measure the effect of material price changes on a railways' MPI. The models rely heavily on fabricated metals and steel and include separate adjustments to better reflect the impact of petroleum products and the Canadian dollar/American dollar exchange rate. Further details of the Agency’s approach are found on pages six -eight and in Annex C of the Agency’s Consultation Document. Please note that while the current (status quo) material model remains an option, the Agency did not use it to determine the latest 2026-2027 VRCPI for the reasons summarized in paragraph 11 of R-2026-78, the 2026-2027 VRCPI Determination. |
| Method 2
Simple Regression using MPI and Statistics Canada Fabricated metals index |
This model forecasts the railway MPI using a simple linear regression model that tracks the relationship between the railway material price index and the Statistics Canada Industrial Product Price Index (IPPI) – Fabricated Metals Products and Construction Materials Index. Table 18-10-0265-01 (NAPCS code P63) |
| Methods 3 & 4
Three or five year moving average growth rates Proposed by CPKC (CN – 3-year avg) |
Bases the forecasts solely on three- or five-year moving averages of the historical material price index (MPI) where: The 2024 value [A] = single year preliminary actual MPI value |
| Method 5
Modified application of three or five year moving average growth rates Proposed by CPKC |
This is the same approach as Methods 3 and 4 described above but calculated slightly differently. Here the same initial three- or five-year average (i.e., the “average growth rate [2020-2024]” in the example above is used in both years): The 2024 value [A] = single year preliminary actual MPI value |
| Method 6
Historical growth rates of Stats Can indicators Proposed by CN |
This approach uses the historical single year growth rate for a given publicly available price index as the forecast for the crop year. For the material price index forecasts – Statistics Canada Industrial Product Price Index (IPPI) – Fabricated Metals Products and Construction Materials Index. Table 18-10-0265-01 (NAPCS code P63) 2025-2026 MPI = [A] × StatsCan [2024/2023] where A equals 2024-2025 MPI index |
Appendix B
| Error metric | What does this measure |
|---|---|
| Cumulative Error | Cumulative error is defined as the total accumulation of individual errors in a series of computations. The total value indicates overall model bias. |
| Mean Error | Mean error calculates the average of forecast errors in a data set. An error is the difference between estimated and actual values. Positive values indicate the model is over-forecasting and negative values signify under-forecasting. |
| Mean Absolute Error | MAE is defined as the average sum of absolute deviations between predicted and actual values. It serves as a robust indicator of model fit and overall predictive accuracy. |
| Root Mean Square Error | RMSE measures the average difference between a model's predicted and actual values. A low RMSE means the model’s predictions are very close to the actual data. A high RMSE indicates larger prediction errors. |
| Standard Deviation of Error | A high standard deviation means the error is highly volatile across different years. |
| Coefficient of Variation | The coefficient of variation, calculated as the standard deviation divided by the mean, is a relative measure of variability that shows the extent of dispersion in the data relative to the average. A value above 1.0 implies a high degree of variability relative to the mean. |
Appendix C
Labour
| Metrics | Method 1: Status Quo | Method 2: Modified Status Quo | Method 3: 3-year growth rate moving average | Method 4: 5-year growth rate moving average | Method 5: CPKC's 5-year growth rate | Method 6: CN's Index of Hourly Earnings | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CN | CPKC | CN | CPKC | CN | CPKC | CN | CPKC | CN | CPKC | CN | CPKC | |
| Cumulative Error | -2.3% | -5.97% | 14.7% | 49.2% | 0.30% | -3.6% | 3.6% | -0.04% | 4.1% | 2.0% | 11.4% | 21.27% |
| Mean Error | -0.23% | -0.60% | 1.5% | 4.9% | 0.03% | -0.36% | 0.36% | -0.004% | 0.41% | 0.20% | 1.1% | 2.1% |
| Mean Absolute Error | 3.1% | 3.2% | 3.0% | 6.9% | 4.6% | 2.3% | 4.6% | 2.3% | 4.7% | 2.3% | 1.9% | 2.1% |
| Root Mean Squared Error (RMSE) | 3.6% | 3.8% | 3.7% | 9.2% | 5.2% | 2.6% | 5.3% | 2.8% | 5.4% | 2.6% | 2.4% | 2.4% |
| Standard Deviation of Error (STDEV) | 3.8% | 3.9% | 3.6% | 8.2% | 5.5% | 2.7% | 5.5% | 2.9% | 5.7% | 2.8% | 2.2% | 1.1% |
| Coefficient of Variance (CV) | 1.23 | 1.24 | 1.20 | 1.19 | 1.20 | 1.19 | 1.21 | 1.28 | 1.21 | 1.22 | 1.21 | 0.53 |
Fuel
| Metrics | Method 1: Status Quo | Method 2: Modified Status Quo | Method 3: 3-year growth rate moving average | Method 4: 5-year growth rate moving average | Method 5: CPKC's 5-year growth rate | Method 6: CN's IPPI's Diesel Fuel | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CN | CPKC | CN | CPKC | CN | CPKC | CN | CPKC | CN | CPKC | CN | CPKC | |
| Cumulative Error | -13.6% | -10.8% | -7.5% | -2.5% | 135% | 121% | 76% | 67% | 85% | 77% | 67.0% | 63.6% |
| Mean Error | -1.36% | -1.08% | -0.75% | -0.25% | 13.5% | 12.1% | 7.6% | 6.7% | 8.5% | 7.7% | 6.70% | 6.36% |
| Mean Absolute Error | 11.5% | 10.7% | 12.2% | 11.6% | 43% | 41% | 32% | 29% | 33% | 30% | 32.9% | 32.5% |
| Root Mean Squared Error (RMSE) | 14.6% | 13.6% | 15.0% | 13.8% | 49% | 45% | 37% | 34% | 39% | 35% | 41.1% | 40.0% |
| Standard Deviation of Error (STDEV) | 15.3% | 14.3% | 15.8% | 14.5% | 50% | 46% | 39% | 35% | 40% | 36% | 43% | 42% |
| Coefficient of Variance (CV) | 1.33 | 1.33 | 1.30 | 1.25 | 1.16 | 1.11 | 1.21 | 1.18 | 1.23 | 1.20 | 1.30 | 1.28 |
Material
| Metrics | Method 1: Status Quo | Method 2: Modified Status Quo | Method 3: 3-year growth rate moving average | Method 4: 5-year growth rate moving average | Method 5: CPKC's 5-year growth rate | Method 6: IPPI's Fabricated Metal Index | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| CN | CPKC | CN | CPKC | CN | CPKC | CN | CPKC | CN | CPKC | CN | CPKC | |
| Cumulative Error | -44.6% | -41.6% | -87.4% | -70.6% | 8.7% | -1.8% | -7.9% | -14.6% | -7.7% | -14.1% | 17.5% | 17.3% |
| Mean Error | -4.5% | -4.2% | -8.7% | -7.1% | 0.87% | -0.18% | -0.79% | -1.46% | -0.77% | -1.41% | 1.75% | 1.73% |
| Mean Absolute Error | 7.4% | 5.3% | 9.0% | 7.3% | 8.8% | 5.39% | 8.5% | 5.2% | 8.4% | 5.0% | 5.8% | 5.2% |
| Root Mean Squared Error (RMSE) | 9.2% | 6.8% | 10.4% | 8.2% | 10.9% | 7.06% | 10.1% | 6.9% | 10.1% | 6.8% | 8.0% | 6.9% |
| Standard Deviation of Error (STDEV) | 8.4% | 5.6% | 5.9% | 4.3% | 11.5% | 7.44% | 10.6% | 7.1% | 10.6% | 7.0% | 8.21% | 7.0% |
| Coefficient of Variance (CV) | 1.15 | 1.06 | 0.66 | 0.60 | 1.30 | 1.38 | 1.26 | 1.35 | 1.26 | 1.38 | 1.42 | 1.36 |
Milestones
| Date | Status |
|---|---|
Tuesday, September 22, 2026 | Last day to submit your input on the test results |
Wednesday, October 7, 2026 | Public submissions posted online |
- Date modified: