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KIYMETLİ METALLER PİYASASININ FRAKTAL ANALİZİ

Yıl 2018, Cilt: 11 Sayı: 3, 2203 - 2218, 31.12.2018
https://doi.org/10.17218/hititsosbil.441151

Öz

Kıymetli madenler antik dönemlerden bu yana insan hayatında hem ödeme aracı hem de tasarruf aracı olarak kullanılmaktadır. Modern piyasaların gelişmesi ile beraber, yatırımcılar tarafından portföye dahil edilmesi mümkün bir finansal varlık özelliği kazanmıştır. Tüm finansal varlık piyasalarında olduğu gibi kıymetli madenler piyasası da etkin piyasa hipotezi varsayımlarının muhatabıdır. Finansal piyasaların rassal yürüyüş özelliği sergilediği varsayımını ortaya atan etkin piyasa hipotezine karşılık, uzun zamandır birçok aksi görüş iddia edilmiştir. Bu görüşlerden birisi de fraktal piyasa hipotezidir ve gelecek dönem getirilerinin geçmiş dönem getirilerinden bağımsız olamayacağını ifade etmektedir. Çalışmanın temel amacı, kıymetli madenler piyasasında fraktal yapının varlığını araştırmaktır. Bu amaçla altın, gümüş, platin ve paladyum madenlerinin günlük, haftalık, aylık ve çeyreklik (dönemlik) frekanslarda getirileri kullanılmıştır. Elde edilen bulgular, söz konusu piyasaların fraktal yapıya sahip olabileceğini ve yatırımcının elde tutma süresi uzadıkça, varlığın getirilerinin geçmiş hareketlere (pozitif/negatif yönlü) daha bağımlı hale geldiğini ortaya koymaktadır.

Kaynakça

  • Aksoy, M., ve Topcu, N. (2013), Altın ile Hisse Senedi ve Enflasyon Arasındaki İlişki. Atatürk Üniversitesi İktisadi ve İdari Bilimler Dergisi, 27(1).
  • Apak, S. ve Çıtak, A. O. S. (2016), Finansal Varlık Olarak Altının Arz-Talep Dengesinin Kısa ve Uzun Dönem Kantitatif Analizi ve Altın Fiyat Fonksiyonunun Ampirik Olarak Test Edilmesi. International Conference on Eurasian Economies-2016.
  • Arouri, M. E. H., Hammoudeh, S., Lahiani, A., & Nguyen, D. K. (2012), Long memory and structural breaks in modeling the return and volatility dynamics of precious metals. The Quarterly Review of Economics and Finance, 52(2), 207-218.
  • Aygören, H. (2008), İstanbul Menkul Kıymetler Borsasının Fractal Analizi. Dokuz Eylül Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 23(1), 125-134.
  • Bachelier, L. (1964), The Theory of Speculation. P. Cootner (der), Random Character of Stock Market Prices içinde, Cambridge, MA: M.I.T Press, 17-78.
  • Barna, F., Ştefana Maria, D. I. M. A., Bogdan, D. I. M. A., & Paşca, L. (2016), Fractal Market Hypothesis: The Emergent Financial Markets Case. Economic Computation and Economic Cybernetics Studies and Research, 50(2), 137-150.
  • Batten, J., Lucey, B., McGroarty, F., Peat, M., & Urquhart, A. (2017), Stylized facts of intraday precious metals. PloS one, 12(4), e0174232.
  • Bhatia, V., Das, D., Tiwari, A. K., Shahbaz, M., & Hasim, H. M. (2017), Do Precious Metal Spot Prices Influence Each Other? Evidence from a Nonparametric Causality-in-Quantiles Approach. Resources Policy, 55, 244-252.
  • Brooks, C. (1995), A Measure of Persistence in Daily Pound Exchange Rates. Applied Economics Letters, 2 (11), 428-431
  • Brown, C. T. & Liebovitch, L. S. (2010), Fractal Analysis: Quantitative applications in The Social Sciences. Monograph No. 165. Thousand Oaks, Calif.: Sage Publications.
  • Chen, Q., & Giles, D. E. (2015), Risk Analysis for Three Precious Metals: An Application of Extreme Value Theory. In Econometrics Working Paper EWP1402.
  • Dar, A. B., Bhanja, N., & Tiwari, A. K. (2017), Do global financial crises validate assertions of fractal market hypothesis? International Economics and Economic Policy, 14(1), 153-165.
  • Du, Y. (2012), Modelling and Forecasting Volatility of Gold Price with Other Precious Metals Prices by Univariate GARCH Models. Master Dissertation, Upsala University.
  • Erdoğan, N. K. (2017), Finansal Zaman Serilerinin Fraktal Analizi. Aksaray Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 9(4), 49-54.
  • Eryiğit, M. (2017), Short-term and long-term relationships between gold prices and precious metal (palladium, silver and platinum) and energy (crude oil and gasoline) prices. Economic research-Ekonomska istraživanja, 30(1), 499-510.
  • Evci, S. ve Kandır, S. Y. (2015), Altın Piyasasında Piyasa Riskinin Ölçülmesi: Riske Maruz Değer (VAR) Yöntemi İle Bir Uygulama. Bankacılar Dergisi, 92, 53-70.
  • Eyüboğlu, K., ve Eyüboğlu, S. (2016), Metal Fiyatları İle BİST-Madencilik Endeksinde İşlem Gören Hisse Senetleri Arasındaki İlişkinin Test Edilmesi. Selçuk Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, (36), 130-141.
  • Fama, E. F. (2017), The Fama Portfolio: Selected Papers of Eugene F. Fama. University of Chicago Press.
  • Fama, E.F. (1965), The Behavior of Stock Market Prices. Journal of Business, 38(1), 34-105.
  • Fama, E.F. (1970), Efficient Capital Markets: A Review Theory and Empirical Work. Journal of Finance, 25(2), 338-417.
  • Gangopadhyay, K., Jangir, A., & Sensarma, R. (2016), Forecasting the price of gold: An error correction approach. IIMB Management Review, 28(1), 6-12.
  • Grasman, J., & van Straten, G. (2012), Predictability and Nonlinear Modelling in Natural Sciences and Economics. Springer Science & Business Media.
  • Günay, S. (2015), BİST100 Endeksi Fiyat ve İşlem Hacminin Fraktallık Analizi. Doğuş Üniversitesi Dergisi, 16(1), 35-50.
  • He, K., Chen, Y., & Tso, G. K. (2017), Price forecasting in the precious metal market: A multivariate EMD denoising approach. Resources Policy, 54, 9-24.
  • Horasanli, M. (2007), Rescaled range analysis and predictability of stock market indices. Yönetim, 58, 36-40.
  • Hurst, H. (1951), Long Term Storage Capacity of Reservoirs. Transactions of the American Society of Civil Engineers, 116(776), 770-799.
  • Kamışlı, M., Kamışlı, S., & Temizel, F. (2017), Emtia Fiyatları Birbirlerini Etkiler Mi? Asimetrik Frekans Nedensellik Analizi. International Journal of Management Economics & Business, 13, 1079-1093.
  • Kirkulak-Uludag, B., & Lkhamazhapov, Z. (2017), Volatility Dynamics of Precious Metals: Evidence from Russia. Finance a Uver, 67(4), 300-317.
  • Koveos, P. E., DeFusco, R. A., Booth, G. G., & Brannigan, E. (1982), Stochastic Time-Series Forecasts of Gold and Silver Prices. In Precious Metals, 95-100.
  • Koy, A., ve Çetin, G. (2016), Metal Vadeli İşlem Piyasaları ve Doğrusal Olmayan Dinamikleri. İşletme ve İktisat Çalışmaları Dergisi, 4(4), 165-176.
  • Krężołek, D. (2017), The Use of Value-At-Risk Methodology in The Assessment of Investor's Risk Attitudes on The Precious Metals Market. Econometrics/Ekonometria, 3(57), 101-112.
  • Kristoufek, L. (2013), Fractal markets hypothesis and the global financial crisis: wavelet power evidence. Scientific Reports, 3(2857), 1-7.
  • Kumar, A. S., & Bandi, K. (2015), Explaining Financial Crisis by Fractal Market Hypothesis: Evidences from Indian Equity Markets. Hyperion International Journal of Econophysics & New Economy, 8(1), 83-96.
  • Küçükaksoy, İ., ve Yalçın, D. (2017), Altın Fiyatlarını Etkileyebilecek Faktörlerin İncelenmesi. AİBÜ-İİBF Ekonomik ve Sosyal Araştırmalar Dergisi, 13(2), 1-19.
  • Li, D. Y., Nishimura, Y., & Men, M. (2014), Fractal markets: Liquidity and investors on different time horizons. Physica A: Statistical Mechanics and its Applications, 407, 144-151.
  • Liberda, M. (2017), Mixed-Frequency Drivers of Precious Metal Prices. Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, 65(6), 2007-2015.
  • Macneill, I.B., & Umphrey, G. J. (1987), Time Series and Econometric Modelling. Reidel Publishing Company, Dordrecht
  • Mandelbrot, B. B. (1963a), New Methods in Statistical Economics. Journal of Political Economy, 71(5), 421–440.
  • Mandelbrot, B. B. (1963b), The Variation of Certain Speculative Prices. Journal of Business, 36(3), 394–419.
  • Mandolbrot, B. B., Fisher, A., & Calvet, L. (1997), A multifractal model of asset returns (Cowles Foundation Discussion Paper No. 1164). Yale University.
  • Mochnacz, F. (2013), Do Precious Metals Have a Capacity to Hedge against Inflation? Yayımlanmamış Doktora Tezi, Tilburg Üniversitesi.
  • Mulligan, R. F. (2004), Fractal analysis of highly volatile markets: an application to technology equities. The Quarterly Review of Economics and Finance, 44(1), 155-179.
  • Panas, E., & Ninni, V. (2010), The Distribution of London Metal Exchange Prices: A Test of The Fractal Market Hypothesis. European Research Studies, 13(2), 193-210.
  • Peters, E.E. (1991), Chaos and Order in The Capital Markets: A New View of Cycles, Prices, and Market Volatility, John Wiley and Sons, Inc., New York.
  • Peters, E.E. (1994), Fractal Market Analysis, Applying Chaos Theory to investment and Economics. John Wiley&Sons Inc. Newyork
  • Rachev, S. T., Weron, A., & Weron, R. (1999), CED Model for Asset Returns and Fractal Market Hypothesis. Mathematical and Computer Modelling, 29(10-12), 23-36.
  • Riste, T., & Sherrington, D. (2012), Spontaneous Formation of Space-Time Structures and Critically. Springer Science & Business Media.
  • Ural, M., ve Demireli, E. (2009), Hurst Üstel Katsayısı Aracılığıyla Fraktal Yapı Analizi ve İMKB’DE Bir Uygulama. Atatürk Üniversitesi İktisadi ve İdari Bilimler Dergisi, 23(2), 243-255.
  • Urquhart, A. (2017). How Predictable are Precious Metal Returns? The European Journal of Finance, 23(14), 1390-1413.
  • Wang, X., Lei, T., Liu, Z., & Wang, Z. (2017), Long-memory behavior analysis of China stock market based on Hurst exponent. 29th Chinese Control and Decision Conference (CCDC), 1710-1712.

THE FRACTAL ANALYSIS OF PRECIOUS METALS MARKET

Yıl 2018, Cilt: 11 Sayı: 3, 2203 - 2218, 31.12.2018
https://doi.org/10.17218/hititsosbil.441151

Öz

Precious metals have been using not only a payment instrument but also a saving instrument since the antique era by human. Associated with modern markets, they are seen as an investment instrument which could be a part of portfolio by investors. As with all financial markets, the precious metals market is also a subject of efficient market hypothesis assumptions. Although the assumption of the random walk of efficient market hypothesis, there are some counter ideas which claim random walk has not existed in literature. One of these counter ideas is the fractal market hypothesis. The hypothesis claims that the current or future returns cannot be independent of past returns or price fluctuations, so, the financial markets have a long-memory. The main purpose of the study, to investigate the existence of the fractal market hypothesis in the gold, silver, platinum and palladium markets. With that purpose, different return frequencies which daily, weekly, monthly and quarterly used for the various precious metal assets. The results show that the fractal market hypothesis could be valid for the precious metal markets. Moreover, the findings indicate that while the holding period of assets is increasing, the existence of long-memory (positive/negative direction) is more possible.

Kaynakça

  • Aksoy, M., ve Topcu, N. (2013), Altın ile Hisse Senedi ve Enflasyon Arasındaki İlişki. Atatürk Üniversitesi İktisadi ve İdari Bilimler Dergisi, 27(1).
  • Apak, S. ve Çıtak, A. O. S. (2016), Finansal Varlık Olarak Altının Arz-Talep Dengesinin Kısa ve Uzun Dönem Kantitatif Analizi ve Altın Fiyat Fonksiyonunun Ampirik Olarak Test Edilmesi. International Conference on Eurasian Economies-2016.
  • Arouri, M. E. H., Hammoudeh, S., Lahiani, A., & Nguyen, D. K. (2012), Long memory and structural breaks in modeling the return and volatility dynamics of precious metals. The Quarterly Review of Economics and Finance, 52(2), 207-218.
  • Aygören, H. (2008), İstanbul Menkul Kıymetler Borsasının Fractal Analizi. Dokuz Eylül Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 23(1), 125-134.
  • Bachelier, L. (1964), The Theory of Speculation. P. Cootner (der), Random Character of Stock Market Prices içinde, Cambridge, MA: M.I.T Press, 17-78.
  • Barna, F., Ştefana Maria, D. I. M. A., Bogdan, D. I. M. A., & Paşca, L. (2016), Fractal Market Hypothesis: The Emergent Financial Markets Case. Economic Computation and Economic Cybernetics Studies and Research, 50(2), 137-150.
  • Batten, J., Lucey, B., McGroarty, F., Peat, M., & Urquhart, A. (2017), Stylized facts of intraday precious metals. PloS one, 12(4), e0174232.
  • Bhatia, V., Das, D., Tiwari, A. K., Shahbaz, M., & Hasim, H. M. (2017), Do Precious Metal Spot Prices Influence Each Other? Evidence from a Nonparametric Causality-in-Quantiles Approach. Resources Policy, 55, 244-252.
  • Brooks, C. (1995), A Measure of Persistence in Daily Pound Exchange Rates. Applied Economics Letters, 2 (11), 428-431
  • Brown, C. T. & Liebovitch, L. S. (2010), Fractal Analysis: Quantitative applications in The Social Sciences. Monograph No. 165. Thousand Oaks, Calif.: Sage Publications.
  • Chen, Q., & Giles, D. E. (2015), Risk Analysis for Three Precious Metals: An Application of Extreme Value Theory. In Econometrics Working Paper EWP1402.
  • Dar, A. B., Bhanja, N., & Tiwari, A. K. (2017), Do global financial crises validate assertions of fractal market hypothesis? International Economics and Economic Policy, 14(1), 153-165.
  • Du, Y. (2012), Modelling and Forecasting Volatility of Gold Price with Other Precious Metals Prices by Univariate GARCH Models. Master Dissertation, Upsala University.
  • Erdoğan, N. K. (2017), Finansal Zaman Serilerinin Fraktal Analizi. Aksaray Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi, 9(4), 49-54.
  • Eryiğit, M. (2017), Short-term and long-term relationships between gold prices and precious metal (palladium, silver and platinum) and energy (crude oil and gasoline) prices. Economic research-Ekonomska istraživanja, 30(1), 499-510.
  • Evci, S. ve Kandır, S. Y. (2015), Altın Piyasasında Piyasa Riskinin Ölçülmesi: Riske Maruz Değer (VAR) Yöntemi İle Bir Uygulama. Bankacılar Dergisi, 92, 53-70.
  • Eyüboğlu, K., ve Eyüboğlu, S. (2016), Metal Fiyatları İle BİST-Madencilik Endeksinde İşlem Gören Hisse Senetleri Arasındaki İlişkinin Test Edilmesi. Selçuk Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, (36), 130-141.
  • Fama, E. F. (2017), The Fama Portfolio: Selected Papers of Eugene F. Fama. University of Chicago Press.
  • Fama, E.F. (1965), The Behavior of Stock Market Prices. Journal of Business, 38(1), 34-105.
  • Fama, E.F. (1970), Efficient Capital Markets: A Review Theory and Empirical Work. Journal of Finance, 25(2), 338-417.
  • Gangopadhyay, K., Jangir, A., & Sensarma, R. (2016), Forecasting the price of gold: An error correction approach. IIMB Management Review, 28(1), 6-12.
  • Grasman, J., & van Straten, G. (2012), Predictability and Nonlinear Modelling in Natural Sciences and Economics. Springer Science & Business Media.
  • Günay, S. (2015), BİST100 Endeksi Fiyat ve İşlem Hacminin Fraktallık Analizi. Doğuş Üniversitesi Dergisi, 16(1), 35-50.
  • He, K., Chen, Y., & Tso, G. K. (2017), Price forecasting in the precious metal market: A multivariate EMD denoising approach. Resources Policy, 54, 9-24.
  • Horasanli, M. (2007), Rescaled range analysis and predictability of stock market indices. Yönetim, 58, 36-40.
  • Hurst, H. (1951), Long Term Storage Capacity of Reservoirs. Transactions of the American Society of Civil Engineers, 116(776), 770-799.
  • Kamışlı, M., Kamışlı, S., & Temizel, F. (2017), Emtia Fiyatları Birbirlerini Etkiler Mi? Asimetrik Frekans Nedensellik Analizi. International Journal of Management Economics & Business, 13, 1079-1093.
  • Kirkulak-Uludag, B., & Lkhamazhapov, Z. (2017), Volatility Dynamics of Precious Metals: Evidence from Russia. Finance a Uver, 67(4), 300-317.
  • Koveos, P. E., DeFusco, R. A., Booth, G. G., & Brannigan, E. (1982), Stochastic Time-Series Forecasts of Gold and Silver Prices. In Precious Metals, 95-100.
  • Koy, A., ve Çetin, G. (2016), Metal Vadeli İşlem Piyasaları ve Doğrusal Olmayan Dinamikleri. İşletme ve İktisat Çalışmaları Dergisi, 4(4), 165-176.
  • Krężołek, D. (2017), The Use of Value-At-Risk Methodology in The Assessment of Investor's Risk Attitudes on The Precious Metals Market. Econometrics/Ekonometria, 3(57), 101-112.
  • Kristoufek, L. (2013), Fractal markets hypothesis and the global financial crisis: wavelet power evidence. Scientific Reports, 3(2857), 1-7.
  • Kumar, A. S., & Bandi, K. (2015), Explaining Financial Crisis by Fractal Market Hypothesis: Evidences from Indian Equity Markets. Hyperion International Journal of Econophysics & New Economy, 8(1), 83-96.
  • Küçükaksoy, İ., ve Yalçın, D. (2017), Altın Fiyatlarını Etkileyebilecek Faktörlerin İncelenmesi. AİBÜ-İİBF Ekonomik ve Sosyal Araştırmalar Dergisi, 13(2), 1-19.
  • Li, D. Y., Nishimura, Y., & Men, M. (2014), Fractal markets: Liquidity and investors on different time horizons. Physica A: Statistical Mechanics and its Applications, 407, 144-151.
  • Liberda, M. (2017), Mixed-Frequency Drivers of Precious Metal Prices. Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, 65(6), 2007-2015.
  • Macneill, I.B., & Umphrey, G. J. (1987), Time Series and Econometric Modelling. Reidel Publishing Company, Dordrecht
  • Mandelbrot, B. B. (1963a), New Methods in Statistical Economics. Journal of Political Economy, 71(5), 421–440.
  • Mandelbrot, B. B. (1963b), The Variation of Certain Speculative Prices. Journal of Business, 36(3), 394–419.
  • Mandolbrot, B. B., Fisher, A., & Calvet, L. (1997), A multifractal model of asset returns (Cowles Foundation Discussion Paper No. 1164). Yale University.
  • Mochnacz, F. (2013), Do Precious Metals Have a Capacity to Hedge against Inflation? Yayımlanmamış Doktora Tezi, Tilburg Üniversitesi.
  • Mulligan, R. F. (2004), Fractal analysis of highly volatile markets: an application to technology equities. The Quarterly Review of Economics and Finance, 44(1), 155-179.
  • Panas, E., & Ninni, V. (2010), The Distribution of London Metal Exchange Prices: A Test of The Fractal Market Hypothesis. European Research Studies, 13(2), 193-210.
  • Peters, E.E. (1991), Chaos and Order in The Capital Markets: A New View of Cycles, Prices, and Market Volatility, John Wiley and Sons, Inc., New York.
  • Peters, E.E. (1994), Fractal Market Analysis, Applying Chaos Theory to investment and Economics. John Wiley&Sons Inc. Newyork
  • Rachev, S. T., Weron, A., & Weron, R. (1999), CED Model for Asset Returns and Fractal Market Hypothesis. Mathematical and Computer Modelling, 29(10-12), 23-36.
  • Riste, T., & Sherrington, D. (2012), Spontaneous Formation of Space-Time Structures and Critically. Springer Science & Business Media.
  • Ural, M., ve Demireli, E. (2009), Hurst Üstel Katsayısı Aracılığıyla Fraktal Yapı Analizi ve İMKB’DE Bir Uygulama. Atatürk Üniversitesi İktisadi ve İdari Bilimler Dergisi, 23(2), 243-255.
  • Urquhart, A. (2017). How Predictable are Precious Metal Returns? The European Journal of Finance, 23(14), 1390-1413.
  • Wang, X., Lei, T., Liu, Z., & Wang, Z. (2017), Long-memory behavior analysis of China stock market based on Hurst exponent. 29th Chinese Control and Decision Conference (CCDC), 1710-1712.
Toplam 50 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Makaleler
Yazarlar

Tuncay Moralı Bu kişi benim

Umut Uyar 0000-0001-6217-8283

Yayımlanma Tarihi 31 Aralık 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 11 Sayı: 3

Kaynak Göster

APA Moralı, T., & Uyar, U. (2018). KIYMETLİ METALLER PİYASASININ FRAKTAL ANALİZİ. Hitit Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, 11(3), 2203-2218. https://doi.org/10.17218/hititsosbil.441151
AMA Moralı T, Uyar U. KIYMETLİ METALLER PİYASASININ FRAKTAL ANALİZİ. hititsosbil. Aralık 2018;11(3):2203-2218. doi:10.17218/hititsosbil.441151
Chicago Moralı, Tuncay, ve Umut Uyar. “KIYMETLİ METALLER PİYASASININ FRAKTAL ANALİZİ”. Hitit Üniversitesi Sosyal Bilimler Enstitüsü Dergisi 11, sy. 3 (Aralık 2018): 2203-18. https://doi.org/10.17218/hititsosbil.441151.
EndNote Moralı T, Uyar U (01 Aralık 2018) KIYMETLİ METALLER PİYASASININ FRAKTAL ANALİZİ. Hitit Üniversitesi Sosyal Bilimler Enstitüsü Dergisi 11 3 2203–2218.
IEEE T. Moralı ve U. Uyar, “KIYMETLİ METALLER PİYASASININ FRAKTAL ANALİZİ”, hititsosbil, c. 11, sy. 3, ss. 2203–2218, 2018, doi: 10.17218/hititsosbil.441151.
ISNAD Moralı, Tuncay - Uyar, Umut. “KIYMETLİ METALLER PİYASASININ FRAKTAL ANALİZİ”. Hitit Üniversitesi Sosyal Bilimler Enstitüsü Dergisi 11/3 (Aralık 2018), 2203-2218. https://doi.org/10.17218/hititsosbil.441151.
JAMA Moralı T, Uyar U. KIYMETLİ METALLER PİYASASININ FRAKTAL ANALİZİ. hititsosbil. 2018;11:2203–2218.
MLA Moralı, Tuncay ve Umut Uyar. “KIYMETLİ METALLER PİYASASININ FRAKTAL ANALİZİ”. Hitit Üniversitesi Sosyal Bilimler Enstitüsü Dergisi, c. 11, sy. 3, 2018, ss. 2203-18, doi:10.17218/hititsosbil.441151.
Vancouver Moralı T, Uyar U. KIYMETLİ METALLER PİYASASININ FRAKTAL ANALİZİ. hititsosbil. 2018;11(3):2203-18.