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NONE-LINEAR CAUSALITY RELATIONSHIPS AMONG CRYPTO ASSETS

Yıl 2025, Cilt: 39 Sayı: 1, 152 - 179, 25.03.2025
https://doi.org/10.48070/erciyesakademi.1586676

Öz

This study aims to comprehensively understand the interactions among cryptocurrency assets by examining their causality relationships using nonlinear methods. The study utilizes weekly USD exchange rate data for eight major cryptocurrencies (Bitcoin, Ethereum, Tether, USD Coin, Binance Coin, Ripple, and Cardano) from the first week of 2020 to the thirty-first week of 2022. The dataset contains 135 observations. The study employs econometric time series methods and artificial neural network (ANN) analysis, focusing particularly on stationarity analysis and nonlinear causality analysis. The stationarity of the variables is determined based on three unit root tests: ADF Test, PP Test, and KPSS Test. The relationship among variables is explored using Nonlinear Granger Causality Analysis. All analyses are conducted using R-Studio. The stationarity analysis indicates that USDT and USDC are stationary at level (I (0)), while other variables are stationary at first difference (I (1)). The study finds no evidence of nonlinear causality relationships among the variables.

Proje Numarası

yok

Kaynakça

  • Agyei, S. K., Adam, A. M., Bossman, A., Asiamah, O., Owusu Junior, P., Asafo-Adjei, R., & Asafo-Adjei, E. (2022). Does volatility in cryptocurrencies drive the interconnectedness between the cryptocurrencies market? Insights from wavelets. Cogent Economics & Finance, 10(1), 2061682. https://doi.org/10.1080/23322039.2022.2061682
  • Akçalı, Y. B., & Şişmanoğlu, E. (2019). Analyzing the relationship between altcoins within top 15 market capitalizations and accessible data periods: A Toda-Yamamoto causality approach. Cogent Economics & Finance, 7(1), 1662635. https://doi.org/10.1080/23322039.2019.1662635
  • Aksoy, E., Teker, T., Mazak, M., & Kocabıyık, T. (2020). Discovering the price relationship among cryptocurrencies: A Toda-Yamamoto causality analysis. Economies, 8(3), 70. https://doi.org/10.3390/economies8030070
  • Arslan, E., & Güzel, G. (2021). The future perspectives of Bitcoin and other cryptocurrencies in the global financial system: A qualitative research. In Handbook of Research on Digital Finance and Cryptocurrency (pp. 250–266). IGI Global. https://doi.org/10.4018/978-1-7998-2788-6.ch014
  • Baek, E., & Brock, W. A. (1992). A general test for nonlinear Granger causality: Bivariate model. Journal of Econometrics, 54(1-3), 239-262. https://doi.org/10.1016/0304-4076(92)90015-D
  • Băroiu, A. C., & Bâra, A. (2024). Sosyal medya-kripto para birimleri ilişkisi için betimleyici-tahmin edici-önerici bir çerçeve. Elektronik, 13(7), 1277. https://doi.org/10.3390/electronics13071277
  • Bishop, C. M., & Nasrabadi, N. M. (2006). Pattern recognition and machine learning (4th ed.). Springer.
  • Bouoiyour, J., & Selmi, R. (2015). What does Bitcoin look like? Annals of Economics and Finance, 16(2), 449–492. https://doi.org/10.1142/S2010139215500155
  • Böhme, R., Christin, N., Edelman, B., & Moore, T. (2015). Bitcoin: Economics, technology, and governance. Journal of Economic Perspectives, 29(2), 213–238. https://doi.org/10.1257/jep.29.2.213
  • Buchholz, M., Delaney, J., Warren, J., & Parker, J. (2012). Bits and bets, information, price volatility, and demand for Bitcoin. Economics 312. Retrieved from www.bitcointrading.com/pdf/bitsandbets.pdf
  • Charles, A., & Darné, O. (2018). Volatility return intervals and the long memory of order flow in the cryptocurrency market. Research in International Business and Finance, 45, 339–349.
  • Ciaian, P., Rajcaniova, M., & Kancs, D. (2016a). The economics of Bitcoin price formation. Applied Economics, 48(19), 1799–1815. https://doi.org/10.1080/00036846.2015.1110170
  • Ciaian, P., Rajcaniova, M., & Kancs, D. (2016b). The digital agenda of virtual currencies: Can Bitcoin become a global currency? Information Systems and e-Business Management, 14(4), 883–919. https://doi.org/10.1007/s10203-015-0182-9
  • Ciaian, P., Rajcaniova, M., & Kancs, D. (2018). Virtual relationships: Short- and long-run evidence from Bitcoin and Altcoin markets. Journal of International Financial Markets, Institutions & Money, 52, 173–195. https://doi.org/10.1016/j.intfin.2017.11.001
  • Conti, M., Kumar, E. S., & Lal, C. (2017). A survey on security and privacy issues of Bitcoin. Retrieved from https://arxiv.org/pdf/1706.00916.pdf
  • Çakracıoğlu, A. (2016). Cryptocurrency Bitcoin. 2016 Capital Markets Board Research Report.
  • Dastgir, S., Demir, E., Downing, G., Gozgor, G., & Lau, C. K. M. (2019). The causal relationship between Bitcoin attention and Bitcoin returns: Evidence from the Copula-Based Granger Causality Test. Finance Research Letters, 28, 160-164. https://doi.org/10.1016/j.frl.2018.09.012
  • Demir, E., Simonyan, S., García-Gómez, C. D., & Lau, C. K. M. (2020). The asymmetric effect of Bitcoin on Altcoins: Evidence from the Nonlinear Autoregressive Distributed Lag (NARDL) model. Finance Research Letters. https://doi.org/10.1016/j.frl.2020.101754
  • Detthamrong, U., Prabpala, S., Takhom, A., Kaewboonma, N., Tuamsuk, K., & Chansanam, W. (2024). Kripto Para Birimleri ile Diğer Önemli Dünya Ekonomik Varlıkları Arasındaki Nedensel İlişki: Bir Granger Nedensellik Testi. ABAC Dergisi, 44(1), 124-144. https://doi.org/10.59865/abacj.2024.1
  • Dickey, D. A., & Fuller, W. A. (1981). Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica, 49(4), 1057-1072. https://doi.org/10.2307/1912517
  • Dirican, C., & Canöz, G. (2017a). Usage of cryptocurrencies on a global scale. In Handbook of Digital Currency (pp. 225–242). Academic Press.
  • Dirican, C., & Canöz, İ. (2017b). The cointegration relationship between Bitcoin prices and major world stock indices: An analysis with ARDL model approach. Journal of Economics, Finance and Accounting, 4(4), 377-392.
  • Dyhrberg, A. H. (2016). Bitcoin, Gold and The Dollar-a GARCH Volatility Analysis. Finance Research Letters, 16, 85– 92. https://doi.org/10.1016/j.frl.2015.10.008
  • Gandal, N., & Halaburda, H. (2016). Can We Predict The Winner in a Market with Network Effects? Competition in Cryptocurrency Market. Games, 7(16).
  • González, M. D. L. O., Jareño, F., & Skinner, F. S. (2020). Nonlinear autoregressive distributed lag approach: An application on the connectedness between Bitcoin returns and the other ten most relevant cryptocurrency returns. Mathematics, 8(5), 810.
  • Göttfert, J. (2019). Are daily cryptocurrency price changes associated with google search volume and trading volume? International Review of Financial Analysis, 61, 67–76.
  • Granger, C. W. J. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 37(3), 424-438. https://doi.org/10.2307/1912791
  • Granger, C. W. J. (1980). Testing for causality. Journal of Economic Dynamics and Control, 2, 329-352. https://doi.org/10.1016/0165-1889(80)90069-X
  • Hiemstra, C., & Jones, J. D. (1994). Testing for linear and nonlinear Granger causality in the stock price-volume relation. Journal of Finance, 49(5), 1639-1664. https://doi.org/10.1111/j.1540-6261.1994.tb04768.x
  • Karaağaç, G. A., & Altınırmak, S. (2018). Investigating the relationship between selected cryptocurrencies: A Johansen cointegration analysis. Journal of Academic Research in Economics, 10(3), 325–343.
  • Kim, M. J., Canh, N. P., & Park, S. Y. (2020). Causal relationship among cryptocurrencies: A conditional quantile approach. Finance Research Letters. https://doi.org/10.1016/j.frl.2020.101879
  • Konuşkan, A., Teker, T., Ömürbek, V., & Bekci, İ. (2019). Examining short and long-term relationships between selected cryptocurrencies: A Johansen cointegration analysis and a vector error correction model. International Journal of Financial Studies, 7(2), 30.
  • Köse, N., & Ünal, E. (2023). Causal relationships between cryptocurrencies: The effects of sampling interval and sample size. Studies in Nonlinear Dynamics & Econometrics. https://doi.org/10.1515/snde-2022-0054
  • Kwiatkowski, D., Phillips, P. C. B., Schmidt, P., & Shin, Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics, 54(1–3), 159–178. https://doi.org/10.1016/0304- 4076(92)90104-Y
  • Mensi, W., Rehman, M. U., Vo, X. V., & Kang, S. H. (2024). Spillovers and multiscale relationships among cryptocurrencies: A portfolio implication using high frequency data. Economic Analysis and Policy, 82, 449-479. https://doi.org/10.1016/j.eap.2024.03.021
  • Nakamoto, S. (2008). Bitcoin: A peer-to-peer electronic cash system. Retrieved from https://bitcoin.org/bitcoin.pdf
  • Phillips, P. C. B., & Perron, P. (1988). Testing for a unit root in time series regression. Biometrika, 75(2), 335-346. https://doi.org/10.1093/biomet/75.2.335
  • Polat, M., & Gemici, E. (2018). Determining the relationship between Bitcoin and Altcoins: A Johansen cointegration analysis. Journal of Economics, Finance, and Administrative Science, 23(45), 109–121.
  • Sahoo, P. K., Sethi, D., & Acharya, D. (2019). Is Bitcoin a near stock? Linear and non-linear causal evidence from a price–volume relationship. International Journal of Managerial Finance. https://doi.org/10.1108/IJMF-06-2017- 0107
  • Salihoğlu, E., & Han, A. (2019). Investigating the relationship between selected cryptocurrencies: Hacker Hatemi symmetric and Hatemi J asymmetric causality analyses. In Handbook of Research on Accounting and Financial Studies (pp. 309–325). IGI Global.
  • Sifat, I. M., Mohamad, A. & Shariff, M. S. B. M. (2019). Investigating the delayed relationship between Bitcoin and Ethereum: A VECM, Granger causality, ARMA, ARDL, and wavelet coherence analysis. PloS One, 14(9), e0222155.
  • Sockin, M. & Xiong, W. (2023). Kripto para birimlerinin bir modeli. Yönetim Bilimi, 69(11), 6684-6707.
  • Sünbül, E. (2023). Effect of linear data processing processes on the prediction performance of the neural network: An application with exchange rate data. Nişantaşı Üniversitesi Sosyal Bilimler Dergisi, 11(Özel Sayı), 33- 49. https://doi.org/10.52122/nisantasisbd.1346658
  • Şak, B. (2021). The effects of relationships among cryptocurrencies on investment decisions: A quantile regression approach. Journal of Behavioral Finance, 1–13.
  • Wei, W. C. (2018). The impact of Tether grants on Bitcoin. Economics Letters, 171, 9-22.
  • Wright, A. & De Filippi, P. (2015). Decentralized blockchain technology and the rise of Lex Cryptographia. https://doi.org/10.2139/ssrn.2580664.

KRİPTO VARLIKLAR ARASINDAKİ DOĞRUSAL OLMAYAN NEDENSELLİK İLİŞKİSİ

Yıl 2025, Cilt: 39 Sayı: 1, 152 - 179, 25.03.2025
https://doi.org/10.48070/erciyesakademi.1586676

Öz

Bu çalışma, kripto para birimlerinin nedensellik ilişkilerini doğrusal olmayan yöntemlerle inceleyerek, bu varlıkların birbirleriyle olan etkileşimlerini daha kapsamlı bir şekilde anlamayı amaçlamaktadır. Çalışmada, 2020'nin ilk haftasından 2022'nin otuz birinci haftasına kadar olan sekiz önemli kripto varlığının (Bitcoin, Ethereum, Tether, USD Coin, Binance Coin, Ripple ve Cardano) haftalık dolar cinsinden döviz kuru verileri kullanılmıştır. Veri seti 135 gözlemi içermektedir. Çalışma, özellikle durağanlık analizi ve doğrusal olmayan nedensellik analizi olmak üzere ekonometrik zaman serisi ve yapay sinir ağı (YSA) analiz yöntemlerini kullanmaktadır. Değişkenlerin durağanlık kararları, üç birim kök testine dayanmaktadır. Bunlar; ADF Testi, PP Testi ve KPSS Testleridir. Değişkenler arasındaki ilişki, Doğrusal olmayan Granger Nedensellik Analizi kullanılarak keşfedilmiştir. Tüm analizler R-Studio programında gerçekleştirilmiştir. Durağanlık analizinde, USDT ve USDC'nin düzeyde (I (0)) durağan olduğu, diğer değişkenlerin ise birinci farkta (I (1)) durağan olduğu belirlenmiştir. Çalışma sonucunda, hiçbir değişken arasında doğrusal olmayan nedensellik ilişkisine rastlanmamıştır.

Etik Beyan

Bu çalışma için etik kurul izni gerektirecek bir içerik bulunmamaktadır.

Destekleyen Kurum

yok

Proje Numarası

yok

Kaynakça

  • Agyei, S. K., Adam, A. M., Bossman, A., Asiamah, O., Owusu Junior, P., Asafo-Adjei, R., & Asafo-Adjei, E. (2022). Does volatility in cryptocurrencies drive the interconnectedness between the cryptocurrencies market? Insights from wavelets. Cogent Economics & Finance, 10(1), 2061682. https://doi.org/10.1080/23322039.2022.2061682
  • Akçalı, Y. B., & Şişmanoğlu, E. (2019). Analyzing the relationship between altcoins within top 15 market capitalizations and accessible data periods: A Toda-Yamamoto causality approach. Cogent Economics & Finance, 7(1), 1662635. https://doi.org/10.1080/23322039.2019.1662635
  • Aksoy, E., Teker, T., Mazak, M., & Kocabıyık, T. (2020). Discovering the price relationship among cryptocurrencies: A Toda-Yamamoto causality analysis. Economies, 8(3), 70. https://doi.org/10.3390/economies8030070
  • Arslan, E., & Güzel, G. (2021). The future perspectives of Bitcoin and other cryptocurrencies in the global financial system: A qualitative research. In Handbook of Research on Digital Finance and Cryptocurrency (pp. 250–266). IGI Global. https://doi.org/10.4018/978-1-7998-2788-6.ch014
  • Baek, E., & Brock, W. A. (1992). A general test for nonlinear Granger causality: Bivariate model. Journal of Econometrics, 54(1-3), 239-262. https://doi.org/10.1016/0304-4076(92)90015-D
  • Băroiu, A. C., & Bâra, A. (2024). Sosyal medya-kripto para birimleri ilişkisi için betimleyici-tahmin edici-önerici bir çerçeve. Elektronik, 13(7), 1277. https://doi.org/10.3390/electronics13071277
  • Bishop, C. M., & Nasrabadi, N. M. (2006). Pattern recognition and machine learning (4th ed.). Springer.
  • Bouoiyour, J., & Selmi, R. (2015). What does Bitcoin look like? Annals of Economics and Finance, 16(2), 449–492. https://doi.org/10.1142/S2010139215500155
  • Böhme, R., Christin, N., Edelman, B., & Moore, T. (2015). Bitcoin: Economics, technology, and governance. Journal of Economic Perspectives, 29(2), 213–238. https://doi.org/10.1257/jep.29.2.213
  • Buchholz, M., Delaney, J., Warren, J., & Parker, J. (2012). Bits and bets, information, price volatility, and demand for Bitcoin. Economics 312. Retrieved from www.bitcointrading.com/pdf/bitsandbets.pdf
  • Charles, A., & Darné, O. (2018). Volatility return intervals and the long memory of order flow in the cryptocurrency market. Research in International Business and Finance, 45, 339–349.
  • Ciaian, P., Rajcaniova, M., & Kancs, D. (2016a). The economics of Bitcoin price formation. Applied Economics, 48(19), 1799–1815. https://doi.org/10.1080/00036846.2015.1110170
  • Ciaian, P., Rajcaniova, M., & Kancs, D. (2016b). The digital agenda of virtual currencies: Can Bitcoin become a global currency? Information Systems and e-Business Management, 14(4), 883–919. https://doi.org/10.1007/s10203-015-0182-9
  • Ciaian, P., Rajcaniova, M., & Kancs, D. (2018). Virtual relationships: Short- and long-run evidence from Bitcoin and Altcoin markets. Journal of International Financial Markets, Institutions & Money, 52, 173–195. https://doi.org/10.1016/j.intfin.2017.11.001
  • Conti, M., Kumar, E. S., & Lal, C. (2017). A survey on security and privacy issues of Bitcoin. Retrieved from https://arxiv.org/pdf/1706.00916.pdf
  • Çakracıoğlu, A. (2016). Cryptocurrency Bitcoin. 2016 Capital Markets Board Research Report.
  • Dastgir, S., Demir, E., Downing, G., Gozgor, G., & Lau, C. K. M. (2019). The causal relationship between Bitcoin attention and Bitcoin returns: Evidence from the Copula-Based Granger Causality Test. Finance Research Letters, 28, 160-164. https://doi.org/10.1016/j.frl.2018.09.012
  • Demir, E., Simonyan, S., García-Gómez, C. D., & Lau, C. K. M. (2020). The asymmetric effect of Bitcoin on Altcoins: Evidence from the Nonlinear Autoregressive Distributed Lag (NARDL) model. Finance Research Letters. https://doi.org/10.1016/j.frl.2020.101754
  • Detthamrong, U., Prabpala, S., Takhom, A., Kaewboonma, N., Tuamsuk, K., & Chansanam, W. (2024). Kripto Para Birimleri ile Diğer Önemli Dünya Ekonomik Varlıkları Arasındaki Nedensel İlişki: Bir Granger Nedensellik Testi. ABAC Dergisi, 44(1), 124-144. https://doi.org/10.59865/abacj.2024.1
  • Dickey, D. A., & Fuller, W. A. (1981). Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica, 49(4), 1057-1072. https://doi.org/10.2307/1912517
  • Dirican, C., & Canöz, G. (2017a). Usage of cryptocurrencies on a global scale. In Handbook of Digital Currency (pp. 225–242). Academic Press.
  • Dirican, C., & Canöz, İ. (2017b). The cointegration relationship between Bitcoin prices and major world stock indices: An analysis with ARDL model approach. Journal of Economics, Finance and Accounting, 4(4), 377-392.
  • Dyhrberg, A. H. (2016). Bitcoin, Gold and The Dollar-a GARCH Volatility Analysis. Finance Research Letters, 16, 85– 92. https://doi.org/10.1016/j.frl.2015.10.008
  • Gandal, N., & Halaburda, H. (2016). Can We Predict The Winner in a Market with Network Effects? Competition in Cryptocurrency Market. Games, 7(16).
  • González, M. D. L. O., Jareño, F., & Skinner, F. S. (2020). Nonlinear autoregressive distributed lag approach: An application on the connectedness between Bitcoin returns and the other ten most relevant cryptocurrency returns. Mathematics, 8(5), 810.
  • Göttfert, J. (2019). Are daily cryptocurrency price changes associated with google search volume and trading volume? International Review of Financial Analysis, 61, 67–76.
  • Granger, C. W. J. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 37(3), 424-438. https://doi.org/10.2307/1912791
  • Granger, C. W. J. (1980). Testing for causality. Journal of Economic Dynamics and Control, 2, 329-352. https://doi.org/10.1016/0165-1889(80)90069-X
  • Hiemstra, C., & Jones, J. D. (1994). Testing for linear and nonlinear Granger causality in the stock price-volume relation. Journal of Finance, 49(5), 1639-1664. https://doi.org/10.1111/j.1540-6261.1994.tb04768.x
  • Karaağaç, G. A., & Altınırmak, S. (2018). Investigating the relationship between selected cryptocurrencies: A Johansen cointegration analysis. Journal of Academic Research in Economics, 10(3), 325–343.
  • Kim, M. J., Canh, N. P., & Park, S. Y. (2020). Causal relationship among cryptocurrencies: A conditional quantile approach. Finance Research Letters. https://doi.org/10.1016/j.frl.2020.101879
  • Konuşkan, A., Teker, T., Ömürbek, V., & Bekci, İ. (2019). Examining short and long-term relationships between selected cryptocurrencies: A Johansen cointegration analysis and a vector error correction model. International Journal of Financial Studies, 7(2), 30.
  • Köse, N., & Ünal, E. (2023). Causal relationships between cryptocurrencies: The effects of sampling interval and sample size. Studies in Nonlinear Dynamics & Econometrics. https://doi.org/10.1515/snde-2022-0054
  • Kwiatkowski, D., Phillips, P. C. B., Schmidt, P., & Shin, Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics, 54(1–3), 159–178. https://doi.org/10.1016/0304- 4076(92)90104-Y
  • Mensi, W., Rehman, M. U., Vo, X. V., & Kang, S. H. (2024). Spillovers and multiscale relationships among cryptocurrencies: A portfolio implication using high frequency data. Economic Analysis and Policy, 82, 449-479. https://doi.org/10.1016/j.eap.2024.03.021
  • Nakamoto, S. (2008). Bitcoin: A peer-to-peer electronic cash system. Retrieved from https://bitcoin.org/bitcoin.pdf
  • Phillips, P. C. B., & Perron, P. (1988). Testing for a unit root in time series regression. Biometrika, 75(2), 335-346. https://doi.org/10.1093/biomet/75.2.335
  • Polat, M., & Gemici, E. (2018). Determining the relationship between Bitcoin and Altcoins: A Johansen cointegration analysis. Journal of Economics, Finance, and Administrative Science, 23(45), 109–121.
  • Sahoo, P. K., Sethi, D., & Acharya, D. (2019). Is Bitcoin a near stock? Linear and non-linear causal evidence from a price–volume relationship. International Journal of Managerial Finance. https://doi.org/10.1108/IJMF-06-2017- 0107
  • Salihoğlu, E., & Han, A. (2019). Investigating the relationship between selected cryptocurrencies: Hacker Hatemi symmetric and Hatemi J asymmetric causality analyses. In Handbook of Research on Accounting and Financial Studies (pp. 309–325). IGI Global.
  • Sifat, I. M., Mohamad, A. & Shariff, M. S. B. M. (2019). Investigating the delayed relationship between Bitcoin and Ethereum: A VECM, Granger causality, ARMA, ARDL, and wavelet coherence analysis. PloS One, 14(9), e0222155.
  • Sockin, M. & Xiong, W. (2023). Kripto para birimlerinin bir modeli. Yönetim Bilimi, 69(11), 6684-6707.
  • Sünbül, E. (2023). Effect of linear data processing processes on the prediction performance of the neural network: An application with exchange rate data. Nişantaşı Üniversitesi Sosyal Bilimler Dergisi, 11(Özel Sayı), 33- 49. https://doi.org/10.52122/nisantasisbd.1346658
  • Şak, B. (2021). The effects of relationships among cryptocurrencies on investment decisions: A quantile regression approach. Journal of Behavioral Finance, 1–13.
  • Wei, W. C. (2018). The impact of Tether grants on Bitcoin. Economics Letters, 171, 9-22.
  • Wright, A. & De Filippi, P. (2015). Decentralized blockchain technology and the rise of Lex Cryptographia. https://doi.org/10.2139/ssrn.2580664.
Toplam 46 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular Uygulamalı Ekonomi (Diğer), Uluslararası Ticaret Finansmanı
Bölüm Makaleler
Yazarlar

Ersin Sünbül 0000-0001-6187-2038

Proje Numarası yok
Yayımlanma Tarihi 25 Mart 2025
Gönderilme Tarihi 16 Kasım 2024
Kabul Tarihi 21 Ocak 2025
Yayımlandığı Sayı Yıl 2025 Cilt: 39 Sayı: 1

Kaynak Göster

APA Sünbül, E. (2025). KRİPTO VARLIKLAR ARASINDAKİ DOĞRUSAL OLMAYAN NEDENSELLİK İLİŞKİSİ. Erciyes Akademi, 39(1), 152-179. https://doi.org/10.48070/erciyesakademi.1586676

ERCİYES AKADEMİ | 2021 | erciyesakademi@erciyes.edu.tr Bu eser Creative Commons Atıf-Gayri Ticari-Türetilemez 4.0 Uluslararası Lisansı ile lisanslanmıştır.