ARTICLE
ABSTRACT
Demand in the steel and iron industry is influenced by multiple factors. Not all of them can be identified and measured. The paper presents the results of the analysis of the levels of demand achieved by a selected enterprise from this sector in the years 2010–2014. The aim of the study is to build a hidden Markov model which would reflect the turning points of this demand, thus making it possible to forecast its future levels. The model’s forecasting properties and stability have been examined. A simulation has been carried out that involved generating a high number of series for selected model parameters and checking their properties. This demonstrated that a three-state second order hidden Markov model was most relevant to the purpose of the study. Thanks to the model’s application, it was possible to describe states which could potentially shape the demand. Moreover, taking the transition state into consideration allowed spotting the signal about the upcoming replacement of the growth phase with the decline phase, and vice versa. The presented second order hidden Markov model can serve as an alternative to the traditional methods of the analysis of time series. The forecast generated by the model informs about the shaping of a trend in demand and serves as an indication of the shifts in economic cycles.
KEYWORDS
forecasting, demand, latent variables, hidden Markov models
JEL
C15, C51
REFERENCES
Albert P. S., (1991), A Two-State Markov Mixture Model for a Time Series of Epileptic Seizure Counts, Biometrics, 47(4), 1371–1381. DOI: 10.2307/2532392.
Azzalini A., Bowman A. W., (1990), A Look at Some Data on the Old Faithful Geyser, Journal of the Royal Statistical Society. Series C (Applied Statistics), 39(3), 357–365. DOI: 10.2307/2347385.
Bartolucci F., Lupparelli M., Montanari G. E., (2009), Latent Markov Model for Longitudinal Binary Data: An Application to the Performance Evaluation of Nursing Homes, The Annals of Applied Statistics, 3(2), 611–636. DOI: 10.1214/08-AOAS230.
Baum L. E., Eagon J. A., (1967), An Inequality with Applications to Statistical Estimation for Probabilistic Functions of Markov Processes and to a Model of Ecology, Bulletin of the American Mathematicians Society, 73(3), 360–363. DOI: 10.1090/S0002-9904-1967-11751-8.
Baum L. E., Petrie T., (1966), Statistical Interference for Probabilistic Functions of Finite State Markov Chains, The Annals of Mathematical Statistics, 37(6), 1554–1563. DOI: 10.1214/aoms/1177699147.
Bernardelli M., (2013), Nieklasyczne modele Markowa w analizie cykli koniunktury gospodarczej w Polsce, Roczniki Kolegium Analiz Ekonomicznych, 30, 59–74.
Briffaut J. P., Lallement P., (2010), Volatility Forecasting of Market Demand as Aids for Planning Manufacturing Activities, Service Science & Management, 3, 383–389. DOI: 10.1109/ICCIE.2009. 5223926.
Cappé O., Moulines E., Rydén T., (2005), Inference in Hidden Markov Models, Springer.
Crowder M., Davis M., Giampieri G., (2005), Analysis of Default Data Using Hidden Markov Model of Default Interaction, Quantitative Finance, 5(1), 27–34. DOI: 10.1080/14697680500039951.
Figielska E., (2011), Ewolucyjne metody uczenia ukrytych modeli Markowa, Zeszyty Naukowe Warszawskiej Wyższej Szkoły Informatyki, 5, 63–74.
Hamilton J. D., (1990), Analysis of Time Series Subject to Changes in Regime, Journal of Econometrics, 45(1–2), 39–70. DOI: 10.1016/0304-4076(90)90093-9.
Hidalgo Gonzalez I., Kamiński J., (2011), The Iron and Steel Industry: A Global Market Perspective, Gospodarka Surowcami Mineralnymi, 27(3), 5–28.
Hutnicza Izba Przemysłowo-Handlowa, (2017), Polski przemysł stalowy 2017. Pobrane z: http://www.hiph.org//ANALIZY_RAPORTY/pliki/PPS-2017.pdf.
http://www.hiph.org//ANALIZY_RAPORTY/pliki/PPS-2017.pdf.
Instytut Studiów Wschodnich, (2008), Polski przemysł stoczniowy – stan obecny, perspektywy, zagrożenia, Forum Ekonomiczne, Warszawa.
Jelinek F. (1976), Continuous Speech Recognition by Statistical Methods, Proceedings of the IEEE, 64(4), 532–556. DOI: 10.1109/PROC.1976.10159.
Jurafsky D., Martin J. H., (2008), Speech and Language Recognition, Prentice Hall.
Klug F., (2011), Automotive Supply Chain Logistics: Container Demand Planning using Monte Carlo Simulation, International Journal of Automotive Technology and Management, 11(3), 254–268. DOI: 10.1504/IJATM.2011.040871.
Kwilinski A., (2018), Mechanism of formation of industrial enterprise development strategy in the information economy, Virtual Economics, 1(1), 7–25. DOI: 10.34021/ve.2018.01.01(1).
Le N.D., Leroux B. G., Puterman M. L., (1992), Reading Reaction: Exact Likelihood Evaluation in a Markov Mixture Model for Time Series of Seizure Counts, Biometrics, 48(1), 317–323. DOI: 10.2307/2532758.
Mitchell T. M., (1997), Machine Learning, McGraw-Hill Corporation, New York.
Nguyen N., Nguyen D., (2015), Hidden Markov Model for Stock Selection, Risks, 3(4), 455–473. DOI: 10.3390/risks3040455.
Nowara W., Szarzec K., (2004), Skutki procesów upadłościowych i układowych przedsiębiorstw w Polsce w latach 1990–2002, w: A. Manikowski, A. Psyk (red.), Unifikacja gospodarek europejskich: szanse i zagrożenia, Wydawnictwo Naukowe Wydziału Zarządzania Uniwersytetu Warszawskiego, Warszawa.
Pietrzykowski M., Sałabun W., (2014), Applications of Hidden Markov Model: State-of-the-Art, International Journal of Computer Technology and Applications, 5(4), 1384–1391.
Rabiner L. R., (1989), Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition, Proceedings of the IEEE, 77(2), 257–286. DOI: 10.1109/5.18626.
Rabiner L. R., Juang B. H., (1991), Hidden Markov Models for Speech Recognition, Technometrics, 33(3), 251–272. DOI: 10.2307/1268779.
Rachwał T., (2008), Problematyka badawcza funkcjonowania przedsiębiorstw przemysłowych, w: Z. Zioło, M. Rachwał (red.), Problematyka badawcza geografii przemysłu, 11, 53–85. Wydawnictwo Naukowe AP, Kraków.
Rippe R., Wilkinson W., Morrison D., (1976), Industrial Market Forecasting with Anticipations Data, Management Science, 22(6), 639–651. DOI: 10.1287/mnsc.22.6.639.
Schrodt P. A., (2006), Forecasting Conflict in the Balkans using Hidden Markov Models, w: R. Trapple (ed.), Programming for Peace: Computer-Aided Methods for International Conflict Resolution and Prevention, Springer, 161–184.
Skrondal A., Rabe-Hesketh S., (2004), Generalized Latent Variable Modeling: Multilevel, Longitudinal, and Structural Equation Models, Chapman and Hall/CRC, Boca Raton.
Tirole J., (1988), The Theory of Industrial Organization, MIT Press, Cambridge.
Urbaniak M., (1999), Marketing przemysłowy, Wydawnictwo Infor, Warszawa.
Zucchini W., Guttorp P., (1991), A Hidden Markov Model for Spacetime Precipitation, Water Resources Research, 27(28), 1917–1923. DOI: 10.1029/91WR01403.
Zwiernik P. W., (2005), Wstęp do ukrytych modeli Markowa i metody Bauma-Welcha. Pobrane z: http://www.mimuw.edu.pl/~pzwiernik/docs/hmm.pdf.
