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Example of hierarchical forecasts for a store from the M5 competition

Source: R/data.R
M5_CA1_basefc.Rd

This dataset contains forecasts for the hierarchy of time series related to the store CA_1 from the M5 competition.

Usage

M5_CA1_basefc

Format

A list containing:

  • upper: a list of 11 elements each representing an aggregation level. Each element contains: mu, sigma the mean and standard deviation of the Gaussian forecast, actual the actual value, residuals the residuals of the model used to estimate forecasts covariance.

  • lower: a list of 3049 elements each representing a forecast for each item. Each element contains pmf the probability mass function of the item level forecast, actual the actual value.

  • A: the aggregation matrix for A.

  • S: the S matrix for the hierarchy.

  • Q_u: scaling factors for computing MASE on the upper forecasts.

  • Q_b: scaling factors for computing MASE on the bottom forecasts.

Source

Makridakis, Spyros & Spiliotis, Evangelos & Assimakopoulos, Vassilis. (2020). The M5 Accuracy competition: Results, findings and conclusions. International Journal of Forecasting 38(4) 1346-1364. doi:10.1016/j.ijforecast.2021.10.009

Details

The store CA_1 contains 3049 item level time series and 11 aggregate time series:

  • Store level aggregation (CA_1)

  • Category level aggregations (HOBBIES, HOUSEHOLD, FOODS)

  • Department level aggregations (HOBBIES_1, HOBBIES_2, HOUSEHOLD_1, HOUSEHOLD_2, FOODS_1, FOODS_2, FOODS_3)

Forecasts are generated with the function forecast and the model adam from the package smooth.

  • The models for the bottom time series are selected with multiplicative Gamma error term (MNN);

  • The models for the upper time series (AXZ) is selected with Gaussian additive error term, seasonality selected based on information criterion.

The raw data was downloaded with the package m5.

References

Joachimiak K (2022). m5: 'M5 Forecasting' Challenges Data. R package version 0.1.1, https://CRAN.R-project.org/package=m5.

Makridakis, Spyros & Spiliotis, Evangelos & Assimakopoulos, Vassilis. (2020). The M5 Accuracy competition: Results, findings and conclusions. International Journal of Forecasting 38(4) 1346-1364. doi:10.1016/j.ijforecast.2021.10.009

Svetunkov I (2023). smooth: Forecasting Using State Space Models. R package version 4.0.0, https://CRAN.R-project.org/package=smooth.