Milk is a product of strategic importance for countries due to its nutritional value and its status as a priority
foodstuff. Feed raw materials represent a critical input item within the dairy cattle sector. It is of great importance
for producers to maintain their activities and profitability so that they ensure the balance of milk/feed parity. In
countries such as Turkey, where inflationary effects are observed, the prices of feed raw materials are not stable. In
an environment characterized by high price volatility, the ability to forecast feed raw material prices is of paramount
importance for producers engaged in future planning. In this study, the price forecasting of 43 feed raw materials,
which are extensively utilized in the ration preparation process within the dairy cattle sector, was conducted. The
efficacy of 11 methods based on time series, statistics and grey system theory was evaluated. Following the assessment
of model success criteria, it was determined that the DGM (1,1) method exhibited superior forecasting capabilities
compared to exponential smoothing and regression models, as well as other grey forecasting models. Based on MAD, MSE and
MAPE values, it can be posited that grey forecasting methods may serve as a viable alternative for price forecasting of
feed ingredients.
Ahumada, H., & Cornejo, M. (2016). Forecasting food prices: The case of corn, soybeans and wheat. International Journal of Forecasting, 32(3), 838–848. https://doi.org/10.1016/j.ijforecast.2016.01.002
Akan, B., & Baylan, E. B. (2022). Box-Jenkins yöntemiyle çilek satış fiyatları için tahmin modelikurulması ve tahmin sonuçlarının değerlendirilmesi. İstanbul Ticaret Üniversitesi Fen Bilimleri Dergisi, 21(42), 211–234. https://doi.org/10.55071/ticaretfbd.1092970
Akdemir, H. A., & Çebi, Y. (2023). Tarımsal Ürünlerin İhracat Fiyatlarının Tahminlenmesinde Yapay Sinir Ağlarının Kullanım. 15. Ulusal Tarım Ekonomisi Kongresi, 306–309.
Aksoy, E., & Gençtürk, M. (2024). COVID-19 Döneminde Banka Kredi Risk Bilgileri Üzerine Bir Analiz. Afyon Kocatepe Üniversitesi Sosyal Bilimler Dergisi, 26(1), 194–206. https://doi.org/10.32709/akusosbil.1109545
Anggraeni, W., Andri, K. B., Sumaryanto, & Mahananto, F. (2017). The Performance of ARIMAX Model and Vector Autoregressive (VAR) Model in Forecasting Strategic Commodity Price in Indonesia. Procedia Computer Science, 124, 189–196. https://doi.org/10.1016/j.procs.2017.12.146
Arsy, F. A. (2021). Demand Forecasting of Toyota Avanza Cars in Indonesia: Grey Systems Approach. International Journal of Grey Systems, 1(1), 38–47. https://doi.org/10.52812/ijgs.24
Atıcı, E., & Elen, A. (2024). Optimization of Feed Ration Cost in Dairy Cattle by Genetic Algorithm. Mühendislik Bilimleri Ve Araştırmaları Dergisi, 6(1), 65–76. https://doi.org/10.46387/bjesr.1435749
Aydemir, E., & Turhan, T. (2022). Comparison of Grey Incidence Degrees of Selected Stock Indices According to BIST100 Index in the Covid19 Pandemic Process. 1st International Conference on Engineering and Applied Natural Sciences, 10–13.
Aydın, S., Çetinkaya, A., & Bayrakçı, E. (2010, ). Kars İlinde Üretilen İnek Sütlerinin Bazı Kimyasal Özellikleri. Ulusal Meslek Yüksekokulları Öğrenci Sempozyumu.
Bas, E., Egrioglu, E., & Yolcu, U. (2021). Bootstrapped Holt Method with Autoregressive Coefficients Based on Harmony Search Algorithm. Forecasting, 3(4), 839–849. https://doi.org/10.3390/forecast3040050
Bessler, D. A., Yang, J., & Wongcharupan, M. (2003). Price Dynamics in the International Wheat Market: Modeling with Error Correction and Directed Acyclic Graphs. Journal of Regional Science, 43(1), 1–33. https://doi.org/10.1111/1467-9787.00287
Beşel, C., & Kayıkçı, E. T. (2016). Interpretation of meteorological data with time series and descriptive statistics; Black Sea Region example. TÜCAUM Uluslararası Coğrafya Sempozyumu, 13–14.
Bocsi, V., Hajnalka, F., & Pusztai, G. (2022). First-generation Students at Universities from the Aspect of Achievement, Motivation and Integration. Revija Za Sociologiju, 52(1), 61–85. https://doi.org/10.5613/rzs.52.1.3
Brandt, J. A., & Bessler, D. A. (1984). Forecasting with Vector Autoregressions versus a Univariate ARIMA Process: An Empirical Example with U.S. Hog Prices. North Central Journal of Agricultural Economics, 6(2), 29. https://doi.org/10.2307/1349248
Cahyo, P. W., Aesyi, U. S., & Santosa, B. D. (2024). Topic Sentiment Using Logistic Regression and Latent Dirichlet Allocation as a Customer Satisfaction Analysis Model. JURNAL INFOTEL, 16(1). https://doi.org/10.20895/infotel.v16i1.1081
Can, Ş., & Gerşil, M. (2018). Manisa Pamuk Fiyatlarının Zaman Serisi Analizi ve Yapay Sinir Ağı Teknikleri İle Tahminlenmesi Ve Tahmin Performanslarının Karşılaştırılması. Yönetim Ve Ekonomi, 25(3), 1017–1031.
Chen, J., Chen, C., Lin, Y., Su, Y., Yu, X., Jiang, Y., Chen, Z., Ke, S., Lin, S., Chen, L., Zhang, Z., & Zhang, T. (2021). Downregulation of SUMO2 inhibits hepatocellular carcinoma cell proliferation, migration and invasion. FEBS Open Bio, 11(6), 1771–1784. https://doi.org/10.1002/2211-5463.13173
Dang, H.-S., Huang, Y.-F., Wang, C.-N., & Nguyen, T.-M.-T. (2016). An Application of the Short-Term Forecasting with Limited Data in the Healthcare Traveling Industry. Sustainability, 8(10), 1037. https://doi.org/10.3390/su8101037
Dong, Z., & Sun, F. (2011). A novel DGM (1, 1) model for consumer price index forecasting. Proceedings of 2011 IEEE International Conference on Grey Systems and Intelligent Services, 303–307. https://doi.org/10.1109/gsis.2011.6044084
Erdoğan, M. A. (2021). Türkiye'de şeftali fiyatlarının analizi ve fiyatların Box-Jenkins yöntemiyle tahmini [Bursa Uludağ University]. http://hdl.handle.net/11452/21704
Es, H. A. (2020). Gri Tahmin Modelleri ile Toplam Enerji Talep Tahmini: Türkiye Örneği. Gümüşhane Üniversitesi Fen Bilimleri Enstitüsü Dergisi. https://doi.org/10.17714/gumusfenbil.676909
Fan, G.-F., Wang, A., & Hong, W.-C. (2018). Combining Grey Model and Self-Adapting Intelligent Grey Model with Genetic Algorithm and Annual Share Changes in Natural Gas Demand Forecasting. Energies, 11(7), 1625. https://doi.org/10.3390/en11071625
Groebner, D. F., Shannon, P. W., & Fry, P. C. (2018). Business statistics: a decision-making approach (Tenth edition). Pearson.
Gülerce, M., & Ünal, G. (2017). Forecasting of Oil and Agricultural Commodity Prices: VARMA Versus ARMA. Annals of Financial Economics, 12(3), 1750012. https://doi.org/10.1142/s2010495217500129
Hanke, J., & Wichern, D. (2014). Business Forecasting. Pearson Education.
Hasan, M. B., & Dhali, M. N. (2017). Determination of Optimal Smoothing Constants for Exponential Smoothing Method & Holt's Method. Dhaka University Journal of Science, 65(1), 55–59. https://doi.org/10.3329/dujs.v65i1.54509
Hu, Y.-C., & Jiang, P. (2017). Forecasting energy demand using neural-network-based grey residual modification models. Journal of the Operational Research Society, 68(5), 556–565. https://doi.org/10.1057/s41274-016-0130-2
Huang, K. Y., & Jane, C.-J. (2009). A hybrid model for stock market forecasting and portfolio selection based on ARX, grey system and RS theories. Expert Systems with Applications, 36(3), 5387–5392. https://doi.org/10.1016/j.eswa.2008.06.103
Iqelan, B. M. (2017). Forecasts of female breast cancer referrals using grey prediction model GM(1,1). Applied Mathematical Sciences, 11, 2647–2662. https://doi.org/10.12988/ams.2017.79273
Javed, S. A., Ikram, M., Tao, L., & Liu, S. (2020). Forecasting key indicators of China's inbound and outbound tourism: optimistic–pessimistic method. Grey Systems: Theory and Application, 11(2), 265–287. https://doi.org/10.1108/gs-12-2019-0064
Jha, S. N., Jaiswal, P., Narsaiah, K., Kumar, R., Sharma, R., Gupta, M., Bhardwaj, R., & Singh, A. K. (2013). Authentication of Mango Varieties Using Near-Infrared Spectroscopy. Agricultural Research, 2(3), 229–235. https://doi.org/10.1007/s40003-013-0068-4
Jia, W. (2024). Research on pricing and replenishment strategy of superstore goods based on linear regression and gray prediction models. Highlights in Business, Economics and Management, 24, 18–24. https://doi.org/10.54097/6eztb071
Kayacan, E., Ulutas, B., & Kaynak, O. (2010). Grey system theory-based models in time series prediction. Expert Systems with Applications, 37(2), 1784–1789. https://doi.org/10.1016/j.eswa.2009.07.064
Khairina, D. M., Muaddam, A., Maharani, S., & Rahmania, H. (2019). Forecasting of Groundwater Tax Revenue Using Single Exponential Smoothing Method. E3s Web of Conferences, 125, 23006. https://doi.org/10.1051/e3sconf/201912523006
Kling, J. L., & Bessler, D. A. (1985). A comparison of multivariate forecasting procedures for economic time series. International Journal of Forecasting, 1(1), 5–24. https://doi.org/10.1016/s0169-2070(85)80067-4
Kohzadi, N., Boyd, M. S., Kermanshahi, B., & Kaastra, I. (1996). A comparison of artificial neural network and time series models for forecasting commodity prices. Neurocomputing, 10(2), 169–181. https://doi.org/10.1016/0925-2312(95)00020-8
Kutlar, A. (1998). Introduction to Computer Applied Econometrics. Beta Press.
Kuzu Yıldırım, S. (2021). Analysis of Mobile Banking Data with R (1st ed.). Dora Publishing.
Küçükoflaz, M., Akçay, A., Çelik, E., & Sarıozkan, S. (2019). Türkiye'de kırmızı et ve süt fiyatlarının Box-Jenkins modeller ile geleceğe yönelik kestirimleri. Veteriner Hekimler Derneği Dergisi, 90(2), 122–131. https://doi.org/10.33188/vetheder.534469
Li, B., Yang, W., & Li, X. (2018). Application of combined model with DGM(1,1) and linear regression in grain yield prediction. Grey Systems: Theory and Application, 8(1), 25–34. https://doi.org/10.1108/gs-07-2017-0020
Li, J., Wang, Y., Li, J., & Jiang, R. (2023). Forecasting the Impact of the COVID-19 Outbreak on China's Cotton Exports by Modified Discrete Grey Model with Limited Data. AATCC Journal of Research, 247234442211479. https://doi.org/10.1177/24723444221147966
Lin, Y., & Liu, S. A historical introduction to grey systems theory. 2004 IEEE International Conference on Systems, Man and Cybernetics (IEEE Cat. No.04ch37583), 3, 2403–2408. https://doi.org/10.1109/icsmc.2004.1400689
Liu, S., & Forrest, J. Y.-L. (2010). Grey Systems: Theory and Applications. Springer Verlag.
Liu, S., & Yang, Y. (2017). Explanation of terms of grey forecasting models. Grey Systems: Theory and Application, 7(1), 123–128. https://doi.org/10.1108/gs-11-2016-0047
Liu, Y., & Li, K. (2019). Research on House Price Forecast Based on Grey System GM (1, 1). 5th International Conference on Finance, Investment, And Law (ICFIL 2019), 200–206.
Manalu, A., Roito, D., Rizkiadina, E., & Laia, Y. (2022). Analysis Forecasting Sales With Single Exponential Smoothing Method. Paradigma - Jurnal Komputer Dan Informatika, 24(2), 135–138. https://doi.org/10.31294/paradigma.v24i2.1255
Manickam, A., Indrakala, S., & Kumar, P. (2023). A Novel Mathematical Study on the Predictions of Volatile Price of Gold Using Grey Models. Contemporary Mathematics, 270–285. https://doi.org/10.37256/cm.4220232389
Norouzi, N., & Fani, M. (2020). Black gold falls, black plague arise - An Opec crude oil price forecast using a gray prediction model. Upstream Oil and Gas Technology, 5, 100015. https://doi.org/10.1016/j.upstre.2020.100015
Oladipo, S., Sun, Y., & Adeleke, O. (2023). An Improved Particle Swarm Optimization and Adaptive Neuro-Fuzzy Inference System for Predicting the Energy Consumption of University Residence. International Transactions on Electrical Energy Systems, 2023, 1–16. https://doi.org/10.1155/2023/8508800
P. Vatcheva, K., & Lee, M. (2016). Multicollinearity in Regression Analyses Conducted in Epidemiologic Studies. Epidemiology: Open Access, 6(2). https://doi.org/10.4172/2161-1165.1000227
Petmezas, G., Cheimariotis, G.-A., Stefanopoulos, L., Rocha, B., Paiva, R. P., Katsaggelos, A. K., & Maglaveras, N. (2022). Automated Lung Sound Classification Using a Hybrid CNN-LSTM Network and Focal Loss Function. Sensors, 22(3), 1232. https://doi.org/10.3390/s22031232
Ramadhan, A. S., Prabowo, A., Kankarofi, R. H., & Sulaiman, I. M. (2023). Forecasting Human Development Index With Double Exponential Smoothing Method And Acorrect Determination. International Journal of Business, Economics, And Social Development, 4(1), 25–31. https://doi.org/10.46336/ijbesd.v4i1.375
Rathnayaka, R. K. T., & Seneviratna, D. (2019). Taylor series approximation and unbiased GM(1,1) based hybrid statistical approach for forecasting daily gold price demands. Grey Systems: Theory and Application, 9(1), 5–18. https://doi.org/10.1108/gs-08-2018-0032
Shahwan, T., & Odening, M. (2017). Forecasting Agricultural Commodity Prices using Hybrid Neural Networks. In Computational Intelligence in Economics and Finance (pp. 63–74). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-72821-4\_3
Shrestha, N. (2020). Detecting Multicollinearity in Regression Analysis. American Journal of Applied Mathematics and Statistics, 8(2), 39–42. https://doi.org/10.12691/ajams-8-2-1
Singh, P. K., Pandey, A. K., & Bose, S. C. (2022). A new grey system approach to forecast closing price of Bitcoin, Bionic, Cardano, Dogecoin, Ethereum, XRP Cryptocurrencies. Quality & Quantity, 57(3), 2429–2446. https://doi.org/10.1007/s11135-022-01463-0
Soysal, M., & Ömürgönülşen, M. (2010). Türk turizm sektöründe talep tahmini üzerine bir uygulama. Anatolia: Turizm Araştırmaları Dergisi, 21(1), 128–136.
Sukardi, S., Anisa, A. Y., & Herha, S. K. N. (2023). Application of the Single Exponential Smoothing Method For Flood Disaster Prediction. Journal of Computer Networks, Architecture and High Performance Computing, 5(2), 515–525. https://doi.org/10.47709/cnahpc.v5i2.2455
Temuçin, T., & Temiz, İ. (2016). Türkiye Dış Ticaret İhracat Hacminin Projeksiyonu: Holt-Winters ve Box-Jenkins Modellerinin Kıyaslanması. Süleyman Demirel Üniversitesi İktisadi Ve İdari Bilimler Fakültesi Dergisi, 21(3), 937–960.
Tulkinov, S. (2023). Grey forecast of electricity production from coal and renewable sources in the USA, Japan and China. Grey Systems: Theory and Application, 13(3), 517–543. https://doi.org/10.1108/gs-10-2022-0107
Wang, C.-N., & Le, A. P. (2019). Application of Multi-Criteria Decision-Making Model and GM (1,1) Theory for Evaluating Efficiency of FDI on Economic Growth: A Case Study in Developing Countries. Sustainability, 11(8), 2389. https://doi.org/10.3390/su11082389
Weng, Y., Wang, X., Hua, J., Wang, H., Kang, M., & Wang, F.-Y. (2019). Forecasting Horticultural Products Price Using ARIMA Model and Neural Network Based on a Large-Scale Data Set Collected by Web Crawler. IEEE Transactions on Computational Social Systems, 6(3), 547–553. https://doi.org/10.1109/tcss.2019.2914499
Wu, L., & Wang, Y. (2009). Modelling DGM(1,1) under the Criterion of the Minimization of Mean Absolute Percentage Error. 2009 Second International Symposium on Knowledge Acquisition and Modeling, 123–126. https://doi.org/10.1109/kam.2009.175
Wu, W.-Z., Jiang, J., & Li, Q. (2019). A Novel Discrete Grey Model and Its Application. Mathematical Problems in Engineering, 2019(1). https://doi.org/10.1155/2019/9623878
Xu, X., & Zhang, Y. (2021). Corn cash price forecasting with neural networks. Computers and Electronics in Agriculture, 184, 106120. https://doi.org/10.1016/j.compag.2021.106120
Xu, Z., Lin, C., Zhuang, Z., & Wang, L. (2023). Research on Multistage Dynamic Trading Model Based on Gray Model and Auto-Regressive Integrated Moving Average Model. Discrete Dynamics in Nature and Society, 2023, 1–15. https://doi.org/10.1155/2023/1552074
Yamak, R., & Erkan, E. (2021). Kripto Para Getirilerinde Haftanın Gün Etkisi. Atatürk Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 25(3), 1356–1372. https://doi.org/10.53487/ataunisosbil.883979
Yang, X., Zou, J., Kong, D., & Jiang, G. (2018). The analysis of GM (1, 1) grey model to predict the incidence trend of typhoid and paratyphoid fevers in Wuhan City, China. Medicine, 97(34), e11787. https://doi.org/10.1097/md.0000000000011787
Yapar, G., Taylan Selamlar, H., Capar, S., & Yavuz, İ. (2019). ATA Method. Hacettepe Journal of Mathematics and Statistics, 48(6), 1838–1844. https://doi.org/10.15672/hujms.461032
Yu, L. (2019). Adaptive Variable Weight Accumulation AVWA-DGM(1,1) Model Based on Particle Swarm Optimization. Journal of Advances in Mathematics and Computer Science, 1–17. https://doi.org/10.9734/jamcs/2019/v32i430150
Yıldırım, B. F., & Kesintürk, T. (2015). Kredi Kartı Kullanım İstatistiklerinin Gri Tahmin ve Genetik Algoritma Tabanlı Gri Tahmin Metodu İle Tahmini: Karşılaştırmalı Analiz. Bankacılar, 26(94), 65–80.
Yıldız, M., & Atış, E. (2019). Estimation of Turkey's organic fig export price using the ARMA method. Journal of Agricultural Economics, 25(2), 141–147.
Zhang, D., & Luo, D. (2022). Evaluation of regional agricultural drought vulnerability based on unbiased generalized grey relational closeness degree. Grey Systems: Theory and Application, 12(4), 839–856. https://doi.org/10.1108/GS-12-2021-0187
Zhao, Y., Xie, Q., & Zhang, Y. (2021). Assessment and Prediction for China's Regional Agricultural Sustainability. E3s Web of Conferences, 228, 2007. https://doi.org/10.1051/e3sconf/202122802007
Zhou, W., & Ding, S. (2021). A novel discrete grey seasonal model and its applications. Communications in Nonlinear Science and Numerical Simulation, 93, 105493. https://doi.org/10.1016/j.cnsns.2020.105493
Zong, J., & Zhu, Q. (2012). Price forecasting for agricultural products based on BP and RBF Neural Network. 2012 IEEE International Conference on Computer Science and Automation Engineering, 607–610. https://doi.org/10.1109/icsess.2012.6269540
Zou, H., Xia, G., Yang, F., & Wang, H. (2007). An investigation and comparison of artificial neural network and time series models for Chinese food grain price forecasting. Neurocomputing, 70(16–18), 2913–2923. https://doi.org/10.1016/j.neucom.2007.01.009
Çuhadar, M. (2006). Turizm sektöründe talep tahmini için yapay sinir ağları kullanımı ve diğer yöntemlerle karşılaştırmalı analizi (Antalya ilinin dış turizm talebinde uygulama). Süleyman Demirel University.
Ömürbek, V., Aksoy, E., & Akçakanat, Ö. (2018). Bankaların Grup Bazlı Karlılıklarının Gri Tahmin Yontemi Ile Deg\uerlendirilmesi. Mehmet Akif Ersoy Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 10(23), 75–89. https://doi.org/10.20875/makusobed.375038
Özdemir, M., & Çılgın, C. (2022). Buğday Fiyatının Öngörümlenmesinde Makine Öğrenmesi ve Zaman Serisi Tahmin Modellerinin Performanslarının Karşılaştırılması. In M. Özcan (Ed.), 21. Yüzyılda İktisadı Anlamak : Güncel Ekonometrik Zaman Serileri Çalışmaları. Gazi Kitabevi.
Özden, C. (2023). İstatistiksel ve Derin Öğrenme Yöntemlerini Kullanarak Tarımsal Girdi Fiyat Endeksi'nin Tahmin Edilmesi. Turkish Journal of Agriculture - Food Science and Technology, 11(9), 1751–1755. https://doi.org/10.24925/turjaf.v11i9.1751-1755.6359
Özen, N. S., Saraç, S., & Koyuncu, M. (2021). COVID-19 Vakalarının Makine Öğrenmesi Algoritmaları ile Tahmini: Amerika Birleşik Devletleri Örneği. European Journal of Science and Technology. https://doi.org/10.31590/ejosat.855113
Şahin, E. E., & Bağcı, B. (2020). Kripto Para Fiyatlarının Tahmininde Gri Sistem Teorisi: Yöntemsel Karşılaştırma. Anadolu Üniversitesi Sosyal Bilimler Dergisi, 20(1), 219–232. https://doi.org/10.18037/ausbd.700349
Şahin, U. (2018). Forecasting of Turkey's electricity generation and consumption with grey prediction method. Mugla Journal of Science and Technology, 4(2), 205–209. https://doi.org/10.22531/muglajsci.450307
Şahin, Y., & Aydemir, E. (2019). Akıllı Telefon Teknik Özellik Önem Derecelerinin AHP Ağırlıklı Gri İlişkisel Analizi Yöntemi İle Belirlenmesi. Eskişehir Osmangazi Üniversitesi İktisadi Ve İdari Bilimler Dergisi, 14(1), 225–238. https://doi.org/10.17153/oguiibf.486920
Şahin, Y., & Kılınç, M. (2022). Analysis of Economic and Epidemic Performances of Countries During the Covid-19 Pandemic Period. Düzce Üniversitesi Bilim Ve Teknoloji Dergisi, 10(2), 729–747. https://doi.org/10.29130/dubited.934715
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