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MULTIVARIATE MARKOV CHAIN MODEL: AN APPLICATION TO S&P500 AND FTSE-100 STOCK EXCHANGES

Yıl 2018, Cilt: 2 Sayı: 1, 75 - 88, 01.03.2018

Öz

Markov chains are the stochastic processes that have many application areas. The data that belong to the system being analyzed in the Markov chains stem from a single source. The multivariate Markov chain model is a model that is used for the purpose of showing the behavior of multivariate categorical data sequences produced from the same source or a similar source. In this study we explain the multivariate Markov chain model that is based on the Markov chains from a theoretical standpoint in detail. As for an application, we take on the daily changes that occur in the S&P-500 Index in which the shares of the 500 greatest companies of the United States of America are traded and the daily changes that occur in the UK FTSE 100 Index as two categorical sequences. And we display the proportions that show how much they influence each other via a multivariate Markov chain model. 

Kaynakça

  • Can, T. (2006). Sektörler arası ilişkilerin Markov Zinciri ile Analizi ve Tahmini: Türkiye Örneği, İstanbul: Der Yayınları.
  • Cheng, C. J., Chiu S.W., Cheng C. B. and Wu J. Y. (2012). Customer Lifetime Value Prediction by a Markov Chain Based Data Mining Model: Application to an Auto Repair and Maintenance Company in Taiwan. Scientia Iranica, 19(3): 849–855.
  • Ching, W., Fung, E. S. and NG M. (2002). A Multivariate Markov Chain Model for Categorical Data Sequences and Its Applications in Demand Predictions. IMA Journal of Management Mathematics, 13: 187-199.
  • Ching, W., Fung E., Ng M. and Akutsu T. (2005). On Construction of Stochastic Genetic Networks Based on Gene Expression Sequences. International Journal of Neural Systems, 15: 297–310.
  • Ching, W. and Ng, M. (2006). Markov Chains: Models, Algorithms and Applications. Springer Science and Business Media, Inc.
  • Ching, W., Li, L., Li, T. and Zhang, S. (2007). A New Multivariate Markov Chain Model with Applications to Sales Demand Forecasting. International Conference on Industrial Engineering and Systems Management IESM 2007, Beijing – China.
  • Chinnaratha, M.A., Kaambwa B., Woodman R.J., Fraser R. and Wigg A. (2017). Assessing the Clinical and Economic Impact of Increasing Treatment Uptake in Chronic Hepatitis B Infection Using a Markov Model. Journal of Gastroenterology and Hepatology, 32(7): 1370-1377.
  • Constant, A. F. and Zimmermann, K. F. (2012). The Dynamics of Repeat Migration: A Markov Chain Analysis. International Migration Review, 46(2): 362-388.
  • Dongmei, Z., and Ching W. (2010). A New Estimation Method for Multivariate Markov Chain Model with Application in Demand Predictions. The 3rd International Conference on Business Intelligence and Financial Engineering (BIFE 2010), Hong Kong.
  • Feng, R. H. (2002). On Markov Chains Induced from Stock Processes Having Barriers in Finance Market. Osaka Journal of Mathematics, 39(2): 487-509.
  • Gill, K. K., Aggarwal R. and Goyal P. (2015). Rainfall Probabilities for Crop Planning in Ludhiana by Markov Chain Analysis. Indian Journal of Ecology, 42(1): 16-20.
  • Gillespie, J. M. and Fulton, J. R. (2001). A Markov Chain Analysis of the Size of Hog Production Firms in the United States. Agribusiness, 17(4): 557-570. Investing Web Page, http://tr.investing.com, retrieved from: 19.12.2015.
  • Levin, R. I., Rubin, D. S. and Stinson, J. P. (1982). Quantitave Approaches to Management, Tokyo, Mc-Graw- Hill (5th ed.).
  • Maskawa, J. (2003). Multivariate Markov Chain Modeling for Stock Markets. Physica A, 324: 317-322. Pettiway, L.E., Dolinsky, S. and Grigoryan, A. (1994). The Drug and Criminal Activity Patterns of Urban Offenders: A Markov chain analysis. Journal of Quantitative Criminology, 10(1): 79–107.
  • Rey, S. (2014). Rank-based Markov Chains for Regional Income Distribution Dynamics. Journal of Geographical Systems, 16(2): 115-137.
  • Sheldon, M. R. (1996). Stochastic Processes. New York: Jhon Wiley & Sons Inc. (2nd ed.).
  • Sheldon, M. R. (2009). Introduction to Probability Models. United States of America, Academic Press, (10th ed.). Singh, L., Rajput, H., Vinod, G. and Tripathi, A. K. (2016). Computing Transition Probability in Markov Chain for Early Prediction of Software Reliability. Quality and Reliability Engineering International, 32(3): 1253-1263.
  • Siu, T., Ching, W, Ng, M. and Fung, E. (2005). On Multivariate Credibility Approach for Portfolio Credit Risk Measurement. Quantitative Finance, 5: 543–556.
  • Yang, C., Kim, Y. P., Ponsford, B. J. and Garland, B.C. (2010). Impact of Wal-Mart on Market Share in a Rural Grocery Market: An Application of the Markov Chain Model”, Journal of Food Products Marketing, 16(2): 232-245.
  • Zhang, S., Ching, W., Jiao, Y., Wu, L. and Chan, R. H. (2008). Construction and Control of Genetic Regulatory Networks: A Multivariate Markov Chain Approach. Journal of Biomedical Science and Engineering, 1: 15-21.
Yıl 2018, Cilt: 2 Sayı: 1, 75 - 88, 01.03.2018

Öz

Kaynakça

  • Can, T. (2006). Sektörler arası ilişkilerin Markov Zinciri ile Analizi ve Tahmini: Türkiye Örneği, İstanbul: Der Yayınları.
  • Cheng, C. J., Chiu S.W., Cheng C. B. and Wu J. Y. (2012). Customer Lifetime Value Prediction by a Markov Chain Based Data Mining Model: Application to an Auto Repair and Maintenance Company in Taiwan. Scientia Iranica, 19(3): 849–855.
  • Ching, W., Fung, E. S. and NG M. (2002). A Multivariate Markov Chain Model for Categorical Data Sequences and Its Applications in Demand Predictions. IMA Journal of Management Mathematics, 13: 187-199.
  • Ching, W., Fung E., Ng M. and Akutsu T. (2005). On Construction of Stochastic Genetic Networks Based on Gene Expression Sequences. International Journal of Neural Systems, 15: 297–310.
  • Ching, W. and Ng, M. (2006). Markov Chains: Models, Algorithms and Applications. Springer Science and Business Media, Inc.
  • Ching, W., Li, L., Li, T. and Zhang, S. (2007). A New Multivariate Markov Chain Model with Applications to Sales Demand Forecasting. International Conference on Industrial Engineering and Systems Management IESM 2007, Beijing – China.
  • Chinnaratha, M.A., Kaambwa B., Woodman R.J., Fraser R. and Wigg A. (2017). Assessing the Clinical and Economic Impact of Increasing Treatment Uptake in Chronic Hepatitis B Infection Using a Markov Model. Journal of Gastroenterology and Hepatology, 32(7): 1370-1377.
  • Constant, A. F. and Zimmermann, K. F. (2012). The Dynamics of Repeat Migration: A Markov Chain Analysis. International Migration Review, 46(2): 362-388.
  • Dongmei, Z., and Ching W. (2010). A New Estimation Method for Multivariate Markov Chain Model with Application in Demand Predictions. The 3rd International Conference on Business Intelligence and Financial Engineering (BIFE 2010), Hong Kong.
  • Feng, R. H. (2002). On Markov Chains Induced from Stock Processes Having Barriers in Finance Market. Osaka Journal of Mathematics, 39(2): 487-509.
  • Gill, K. K., Aggarwal R. and Goyal P. (2015). Rainfall Probabilities for Crop Planning in Ludhiana by Markov Chain Analysis. Indian Journal of Ecology, 42(1): 16-20.
  • Gillespie, J. M. and Fulton, J. R. (2001). A Markov Chain Analysis of the Size of Hog Production Firms in the United States. Agribusiness, 17(4): 557-570. Investing Web Page, http://tr.investing.com, retrieved from: 19.12.2015.
  • Levin, R. I., Rubin, D. S. and Stinson, J. P. (1982). Quantitave Approaches to Management, Tokyo, Mc-Graw- Hill (5th ed.).
  • Maskawa, J. (2003). Multivariate Markov Chain Modeling for Stock Markets. Physica A, 324: 317-322. Pettiway, L.E., Dolinsky, S. and Grigoryan, A. (1994). The Drug and Criminal Activity Patterns of Urban Offenders: A Markov chain analysis. Journal of Quantitative Criminology, 10(1): 79–107.
  • Rey, S. (2014). Rank-based Markov Chains for Regional Income Distribution Dynamics. Journal of Geographical Systems, 16(2): 115-137.
  • Sheldon, M. R. (1996). Stochastic Processes. New York: Jhon Wiley & Sons Inc. (2nd ed.).
  • Sheldon, M. R. (2009). Introduction to Probability Models. United States of America, Academic Press, (10th ed.). Singh, L., Rajput, H., Vinod, G. and Tripathi, A. K. (2016). Computing Transition Probability in Markov Chain for Early Prediction of Software Reliability. Quality and Reliability Engineering International, 32(3): 1253-1263.
  • Siu, T., Ching, W, Ng, M. and Fung, E. (2005). On Multivariate Credibility Approach for Portfolio Credit Risk Measurement. Quantitative Finance, 5: 543–556.
  • Yang, C., Kim, Y. P., Ponsford, B. J. and Garland, B.C. (2010). Impact of Wal-Mart on Market Share in a Rural Grocery Market: An Application of the Markov Chain Model”, Journal of Food Products Marketing, 16(2): 232-245.
  • Zhang, S., Ching, W., Jiao, Y., Wu, L. and Chan, R. H. (2008). Construction and Control of Genetic Regulatory Networks: A Multivariate Markov Chain Approach. Journal of Biomedical Science and Engineering, 1: 15-21.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular İşletme
Bölüm Makaleler
Yazarlar

Murat Gül Bu kişi benim

Ersoy Öz

Yayımlanma Tarihi 1 Mart 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 2 Sayı: 1

Kaynak Göster

APA Gül, M., & Öz, E. (2018). MULTIVARIATE MARKOV CHAIN MODEL: AN APPLICATION TO S&P500 AND FTSE-100 STOCK EXCHANGES. Marmara İktisat Dergisi, 2(1), 75-88.
AMA Gül M, Öz E. MULTIVARIATE MARKOV CHAIN MODEL: AN APPLICATION TO S&P500 AND FTSE-100 STOCK EXCHANGES. mje. Mart 2018;2(1):75-88.
Chicago Gül, Murat, ve Ersoy Öz. “MULTIVARIATE MARKOV CHAIN MODEL: AN APPLICATION TO S&P500 AND FTSE-100 STOCK EXCHANGES”. Marmara İktisat Dergisi 2, sy. 1 (Mart 2018): 75-88.
EndNote Gül M, Öz E (01 Mart 2018) MULTIVARIATE MARKOV CHAIN MODEL: AN APPLICATION TO S&P500 AND FTSE-100 STOCK EXCHANGES. Marmara İktisat Dergisi 2 1 75–88.
IEEE M. Gül ve E. Öz, “MULTIVARIATE MARKOV CHAIN MODEL: AN APPLICATION TO S&P500 AND FTSE-100 STOCK EXCHANGES”, mje, c. 2, sy. 1, ss. 75–88, 2018.
ISNAD Gül, Murat - Öz, Ersoy. “MULTIVARIATE MARKOV CHAIN MODEL: AN APPLICATION TO S&P500 AND FTSE-100 STOCK EXCHANGES”. Marmara İktisat Dergisi 2/1 (Mart 2018), 75-88.
JAMA Gül M, Öz E. MULTIVARIATE MARKOV CHAIN MODEL: AN APPLICATION TO S&P500 AND FTSE-100 STOCK EXCHANGES. mje. 2018;2:75–88.
MLA Gül, Murat ve Ersoy Öz. “MULTIVARIATE MARKOV CHAIN MODEL: AN APPLICATION TO S&P500 AND FTSE-100 STOCK EXCHANGES”. Marmara İktisat Dergisi, c. 2, sy. 1, 2018, ss. 75-88.
Vancouver Gül M, Öz E. MULTIVARIATE MARKOV CHAIN MODEL: AN APPLICATION TO S&P500 AND FTSE-100 STOCK EXCHANGES. mje. 2018;2(1):75-88.