Informatics and Applications

2015, Volume 9, Issue 2, pp 75-87

FORECASTS RECONCILIATION FOR HIERARCHICAL TIME SERIES FORECASTING PROBLEM

M. M. Stenina
V. V. Strijov

Abstract

The hierarchical time series forecasting problem is researched. Time series forecasts must satisfy the physical constraints and the hierarchical structure. In this paper, a new algorithm for hierarchical time series forecasts reconciliation is proposed. The algorithm is called GTOp (Game-theoretically optimal reconciliation).
It guarantees that the quality of reconciled forecasts is not worse than the quality of self-dependent forecasts. This approach is based on Nash equilibrium search for the antagonistic game and turns the forecasts reconciliation problem into the optimization problem with equality and inequality constraints. It is proved that the Nash equilibrium in pure strategies exists in the game if some assumptions about the hierarchical structure, the physical constraints, and the loss function are satisfied. The algorithm performance is demonstrated for different types of hierarchical structures of time series.

[+] References (22)

Tokmakova, A. A., and V.V. Strizhov. 2012. Otsenivanie giperparametrov lineynykh i regressionnykh modeley pri otbore shumovykh i korreliruyushchikh priznakov [Estimation of linear model hyperparameters for noise or correlated feature selection problem]. Informatika i ee Primeneniya - Inform. Appl. 6(4):66-75.
Vasil'ev, N. S. 2014. Ispol'zovanie printsipa ravnovesiya dlya upravleniya marshrutizatsiey v transportnykh setyakh [Equilibrium principle application to routing control in packet data transmission networks]. Informatika i ee Primeneniya - Inform. Appl. 8(1):28-35.
Hong, T, P. Pinson, and S. Fan. 2014. Global energy forecasting competition 2012. Int. J. Forecasting 30(2):357- 363.
Kaggle. Available at: https://www.kaggle.com (accessed May 20, 2015).
Hyndman, R. J., R. A. Ahmed, G. Athanasopoulos, and H.L. Shang. 2011. Optimal combination forecasts for hierarchical time series. Comput. Stat. Data Anal. 55(9):2579-2589.
Kuznetsov, M.P, A. A. Mafusalov, N. K. Zhivotovskiy, E.Yu. Zaytsev, and D. S. Sungurov. 2011. Sglazhivayushchie algoritmy prognozirovaniya [Smoothing forecast algorithms]. Mashinnoe obuchenie i analiz dannykh [J. Machine Learning Data Anal.] 1(1):104-112.
Stenina, M. M., and V.V. Strizhov. 2014. Soglasovanie agregirovannykh i detalizirovannykh prognozov pri reshe- nii zadach neparametricheskogo prognozirovaniya [Rec-onciliation of aggregated and disaggregated time series forecasts in nonparametric forecasting problem]. Sistemy i Sredstva Informatiki - Systems and Means of Informatics 24(2):21-34.
Grunfeld, Y., andZ. Griliches. 1960. Is aggregation nec-essarily bad? Rev. Econ. Stat. 42(1):1-13.
Orcutt, G.H., H.W. Watts, and J. B. Edwards. 1968. Data aggregation and information loss. Am. Econ. Rev. 58(4):773-787.
Edwards, J. B., and G. H. Orcutt. 1969. Should aggregation prior to estimation be the rule? Rev. Econ. Stat. 51(4):409-420.
Shlifer, E., and R. W. Wolff. 1979. Aggregation and prora-tion in forecasting. Manage. Sci. 25(6):594-603.
Fogarty, D. W., J. H. Blackstone, andT. R. Hoffman. 1990. Production and inventory management. 2nded. Cincinnati, OH: South-Western Publication Co. 880 p.
Narasimhan, S. L., D. W McLeavey, and P J. Billington. 1995. Production planning and inventory control. 2nd ed. Englewood Cliffs, NJ: Prentice Hall. 716 p.
Schwarzkopf, A. B., R. J. Tersine, and J. S. Morris. 1998. Top-down versus bottom-up forecasting strategies. Int. J. Prod. Res. 26(11):1833-1843.
Fliedner, G. 1999. An investigation of aggregate variable time series forecast strategies with specifc subaggregate time series statistical correlation. Comput. Oper. Res. 26(10-11):1133-1149.
Van Erven, T, and J. Cugliari. 2013. Game-theoretically optimal reconciliation of contemporaneous hierarchical time series forecasts. Available at: https://hal.inria.fr/hal- 00920559 (accessed May 20, 2015).
Petrosyan, L. A., N.A. Zenkevich, and E.A. Semina. 1998. Teoriya igr [Games theory]. Moscow: Knizhnyy Dom Universitet. 301 p.
Men'shikov, I. S. 2010. Lektsii po teorii igr i ekonomi- cheskomu modelirovaniyu [Games theory and economics modeling lectures]. 2nd ed. Moscow: OOO Kontakt Plyus. 336 p.
Cesa-Bianchi, N., and G. Lugosi. 2006. Prediction, learn-ing, and games. Cambridge: Cambridge University Press. Vol. 1. 403 p.
Boyd, S., and L. Vandenberghe. 2009. Convex optimization. Cambridge: Cambridge University Press. 732 p.
Bregman, L. M. 1967. The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming. USSR Comput. Math. Math. Phys. 7(3):200-217.
Val'kov, A. S., E. M. Kozhanov, M. M. Medvednikova, and F. I. Khusainov. 2012. Neparametricheskoe prog- nozirovanie zagruzhennosti sistemy zheleznodorozhnykh uzlov po istoricheskim dannym [Nonparametric forecasting of railroad stations occupancy according to historical data]. Mashinnoe Obuchenie i Analiz Dannykh [J. Machine Learning Data Anal.] 1(4):448-465.

[+] About this article