Does Absolute-Loss Fitting Travel Across Forecast Horizons? Evidence from a Public Smart-Home Recording

Authors

  • Charles Russell Author
  • Owen Allen Author
  • Paul Lewis Author

Abstract

In a smart-home recording, an estimator that improves the next quarter-hour forecast need not show equally clear gains an hour ahead. We fitted ordinary least squares and median regression to an earlier SML2010 recording and evaluated both on a later recording from the same house. Daily mean absolute error favored median regression by 0.00035 degrees Celsius at fifteen minutes. At sixty minutes the point difference was larger, 0.00453 degrees, but its dependence-adjusted interval crossed zero. Both models used the same available predictors and evaluation rows within each horizon. The evidence supports a small short-horizon advantage under absolute error, while leaving the longer-horizon comparison uncertain over only fifteen evaluation days.

Chronological temperature-forecast reanalysis. The household recording is real; no new sensor experiment was conducted.

Original publication: October 28, 2026.

References

  1. Roberts, David R., et al. “Cross-validation strategies for data with temporal, spatial, hierarchical, or phylogenetic structure.” Ecography, vol. 40, no. 8, 2017, pp. 913-929. https://doi.org/10.1111/ecog.02881.
  2. Foucquier, Aurélie; Robert, Sylvain; Suard, Frédéric; Stéphan, Louis; Jay, Arnaud. (2013). State of the art in building modelling and energy performances prediction: A review. Renewable and Sustainable Energy Reviews. https://doi.org/10.1016/j.rser.2013.03.004.
  3. Yan, Yi; Adel, Radwa; Kuruoglu, Ercan E.. (2021). Adaptive Normalized LMP Estimation for Graph Signal Processing. 2021 IEEE 31st International Workshop on Machine Learning for Signal Processing (MLSP), 1-6. https://doi.org/10.1109/mlsp52302.2021.9596181.
  4. Ioannidis, John P. A.. (2005). Why Most Published Research Findings Are False. PLoS Medicine. https://doi.org/10.1371/journal.pmed.0020124.
  5. Gebru, Timnit, et al. "Datasheets for datasets" Communications of the ACM, 2021. https://doi.org/10.1145/3458723.
  6. Candanedo, Luis M.; Feldheim, Véronique; Deramaix, Dominique. (2017). Data driven prediction models of energy use of appliances in a low-energy house. Energy and Buildings. https://doi.org/10.1016/j.enbuild.2017.01.083.
  7. Wasserstein, Ronald L.; Lazar, Nicole A.. (2016). The ASA Statement on p -Values: Context, Process, and Purpose. The American Statistician. https://doi.org/10.1080/00031305.2016.1154108.
  8. Hampel, Frank R.. (1974). The Influence Curve and its Role in Robust Estimation. Journal of the American Statistical Association. https://doi.org/10.1080/01621459.1974.10482962.
  9. West, Kenneth D.. (1996). Asymptotic Inference about Predictive Ability. Econometrica. https://doi.org/10.2307/2171956.
  10. Firth, S.; Lomas, K.; Wright, A.; Wall, R.. (2008). Identifying trends in the use of domestic appliances from household electricity consumption measurements. Energy and Buildings. https://doi.org/10.1016/j.enbuild.2007.07.005.
  11. Little, Roderick J. A., and Donald B. Rubin. Statistical Analysis with Missing Data. Wiley, 2002. https://doi.org/10.1002/9781119013563.
  12. Rousseeuw, Peter J.. (1984). Least Median of Squares Regression. Journal of the American Statistical Association. https://doi.org/10.1080/01621459.1984.10477105.
  13. Jones, Rory V.; Lomas, Kevin J.. (2016). Determinants of high electrical energy demand in UK homes: Appliance ownership and use. Energy and Buildings. https://doi.org/10.1016/j.enbuild.2016.02.020.
  14. Newey, Whitney K., and Kenneth D. West. “A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica, vol. 55, no. 3, 1987, pp. 703-708. https://doi.org/10.2307/1913610.
  15. Amasyali, Kadir; El-Gohary, Nora M.. (2018). A review of data-driven building energy consumption prediction studies. Renewable and Sustainable Energy Reviews. https://doi.org/10.1016/j.rser.2017.04.095.
  16. Ruellan, Marie; Park, Herie; Bennacer, Rachid. (2016). Residential building energy demand and thermal comfort: Thermal dynamics of electrical appliances and their impact. Energy and Buildings. https://doi.org/10.1016/j.enbuild.2016.07.029.
  17. Diebold, Francis X.; Mariano, Roberto S.. (1995). Comparing Predictive Accuracy. Journal of Business & Economic Statistics. https://doi.org/10.1080/07350015.1995.10524599.
  18. Koenker, Roger; Bassett, Gilbert. (1978). Regression Quantiles. Econometrica. https://doi.org/10.2307/1913643.
  19. Bergmeir, Christoph; Hyndman, Rob J.; Koo, Bonsoo. (2018). A note on the validity of cross-validation for evaluating autoregressive time series prediction. Computational Statistics & Data Analysis. https://doi.org/10.1016/j.csda.2017.11.003.
  20. Varma, Sudhir and Richard Simon. “Bias in error estimation when using cross-validation for model selection.” BMC Bioinformatics, vol. 7, no. 1, 2006. https://doi.org/10.1186/1471-2105-7-91.
  21. Hong, Tianzhen; Yan, Da; D’Oca, Simona; Chen, Chien-fei. (2017). Ten questions concerning occupant behavior in buildings: The big picture. Building and Environment 114, 518-530. https://doi.org/10.1016/j.buildenv.2016.12.006.
  22. Wilkinson, Mark D.; Dumontier, Michel; Aalbersberg, IJsbrand Jan; Appleton, Gabrielle; Axton, Myles; Baak, Arie; Blomberg, Niklas; Boiten, Jan-Willem; da Silva Santos, Luiz Bonino; Bourne, Philip E.; Bouwman, Jildau; Brookes, Anthony J.; Clark, Tim; Crosas, Mercè; Dillo, Ingrid; Dumon, Olivier; Edmunds, Scott; Evelo, Chris T.; Finkers, Richard; Gonzalez-Beltran, Alejandra; Gray, Alasdair J.G.; Groth, Paul; Goble, Carole; Grethe, Jeffrey S.; Heringa, Jaap; ’t Hoen, Peter A.C; Hooft, Rob; Kuhn, Tobias; Kok, Ruben; Kok, Joost; Lusher, Scott J.; Martone, Maryann E.; Mons, Albert; Packer, Abel L.; Persson, Bengt; Rocca-Serra, Philippe; Roos, Marco; van Schaik, Rene; Sansone, Susanna-Assunta; Schultes, Erik; Sengstag, Thierry; Slater, Ted; Strawn, George; Swertz, Morris A.; Thompson, Mark; van der Lei, Johan; van Mulligen, Erik; Velterop, Jan; Waagmeester, Andra; Wittenburg, Peter; Wolstencroft, Katherine; Zhao, Jun; Mons, Barend. (2016). The FAIR Guiding Principles for scientific data management and stewardship. Scientific Data. https://doi.org/10.1038/sdata.2016.18.
  23. Hyndman, Rob J. and Anne B. Koehler. “Another look at measures of forecast accuracy.” International Journal of Forecasting, vol. 22, no. 4, 2006, pp. 679-688. https://doi.org/10.1016/j.ijforecast.2006.03.001.
  24. White, Halbert. “A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity.” Econometrica, vol. 48, no. 4, 1980, pp. 817-838. https://doi.org/10.2307/1912934.
  25. Romeu-Guallart, Pablo; Zamora-Martinez, Francisco. (2014). SML2010 [Dataset]. UCI Machine Learning Repository. https://doi.org/10.24432/C5RS3S.
  26. Carroll, Raymond J., David Ruppert, Leonard A. Stefanski, and Ciprian M. Crainiceanu. “Measurement Error in Nonlinear Models.” 2006. https://doi.org/10.1201/9781420010138.
  27. Huber, Peter J.. (1964). Robust Estimation of a Location Parameter. The Annals of Mathematical Statistics. https://doi.org/10.1214/aoms/1177703732.
  28. Gneiting, Tilmann; Raftery, Adrian E. (2007). Strictly Proper Scoring Rules, Prediction, and Estimation. Journal of the American Statistical Association. https://doi.org/10.1198/016214506000001437.
  29. Cook, R. Dennis. (1977). Detection of Influential Observation in Linear Regression. Technometrics. https://doi.org/10.1080/00401706.1977.10489493.
  30. Candanedo, Luis. (2017). Appliances Energy Prediction [Dataset]. UCI Machine Learning Repository. https://doi.org/10.24432/C5VC8G.

Downloads

Published

2026-10-28

Issue

Vol. 1 No. 1 (2026): Inaugural Issue

Section

Articles

License

Copyright (c) 2026 Charles Russell, Owen Allen, Paul Lewis

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.