The investigate Irregular Behavioral Stock, Stock Expects and Stock Returns Using the Liponov and Kolmogorov Method and BDS in the Tehran Stock Exchange with an Emphasis on Copula Garch and Copula TGarch
Subject Areas : Financial engineering
mohammadreza Navaeian
1
,
Mohammadreza Vatanparast
2
,
Hadi Saeidi
3
,
Shaban Mohammadi
4
1 - Department of financial engineering, Rasht Branch, Islamic Azad University, Rasht, Iran.
2 - Department of Accounting, Rasht Branch, Islamic Azad University, Rasht, Iran
3 - Department of Accounting, Shirvan Branch, Islamic Azad University, Shirvan, Iran
4 - Department of Accounting, Shahid Rajaee Faculty, Vocational University of Khorasan, Iran.
Keywords: Stock Return, stock price, investor expectation, Copula Garch,
Abstract :
The purpose of this study was to investigate irregular behavior in stock prices, investors' expectations and stock returns using the Liponov index and the Kolmogorov index. It also analyzes the related behavior of stock prices, investors' expectations and stock returns during the period of 2012-2018 in Tehran Stock Exchange. The BDS method was used to detect and measure irregular behavior. Copula Garch and Copula T-Gearch were used to study the joint motion among selected variables. The results showed that stock prices and stock returns are irregular according to the Liponov index and the Kolmogorov index. There is a significant evidence of a nonlinear sequence dependent between stock price fluctuations, investor expectations and stock returns. In addition, the high and low dependence sequence and the mobility between the analyzed series were confirmed. Also, fluctuations in stock prices have a huge impact on stock returns and long-term investor expectations of Capoula Garch and Kapila T-GARCH.
References:
Adrangi B, Chatrath A, Dhanda KK, Raffiee K. (2001).Chaos in oil prices? Evidence from futures markets. Energy Econ, 23(4): 405–25.
Alvarez-Ramirez J, Rodriguez E. (2008).Short-term predictability of crude oil markets: a detrended fluctuation analysis approach. Energy Econ, 30:2645–56.
Awartani B, Maghyereh AI. (2013). Dynamic spillovers between oil and stock markets in the Gulf Cooperation Council Countries. Energy Econ, 36:28–42.
Arouri M, Fouquau J. (2009). On the short-term influence of oil price changes on stock markets in GCC countries: linear and nonlinear analyses. Econ Bull, 29(2):795–804.
Bachelier L. (1964).Theory of speculation (Ph.D. Thesis, Faculty of the Academy of Paris, 1900and Theory of Speculation, the random character of stock market prices. M.I.T Press.
Barnett WA, Hinich MJ. (1992)Empirical chaotic dynamics in economics. Ann Oper Res, 37:1–15.
Barnett WA, Gallant AR, Hinich MJ. (1995).Robustness of nonlinearity and chaos tests to measurement error, inference method, and sample size. J Econ Behav Org, 27(2):301–20.
Barnett WA, Gallant AR, Hinich MJ. (1997) A single-blind controlled competition among tests for nonlinearity and chaos. J Econom, 82(1):157–92.
Barone-Adesi G, Bourgoin F, Giannopoulos K. Don’t look back. Risk. 1998; 11:100–3.
Bjørnland HC. (2009).Oil price shocks and stock market booms in an oil exporting country. Scott J Polit Econ, 56(2):232–54.
Bildik R, Yılmaz M. (2008).The market performance of initial public offerings in the I˙stanbul stock exchange, BDDK Banka. Financ Piyas, 2(2):49–75.
Bildirici M, Sonustun FO. (2018).Chaotic structure of oil prices. In: AIP conference proceedings 1926, p. 020009.
Bildirici M, Ersın O, Onat I. (2017). The Baltic dry index as a leading economic indicator: an investigation with volatility models. In: Bildirci M, Zehir C, Kayıkc¸ı F, Karago¨z M, Bakırtas¸ T, editors. Istanbul as a Global Financial Center. Cambridge: Cambridge Scholar Publishing.
Boubaker H, Sghaier N. (2016).Contagion effect and change in the dependence between oil and ten MENA stock markets. RRJSMS, 2(1):1–17.
Boubaker H, Sghaier N. (2016).Markov-switching time-varying copula modeling of dependence structure between oil and GCC stock markets. Open J Stat, 6:565–89.
Bouri E. (2015).Oil volatility shocks and the stock markets of oil-importing MENA economies: a tale from the financial crisis. Energy Econ, 51:590–8.
Bouri E. (2015).Return and volatility linkages between oil prices and the Lebanese stock market in crisis periods. Energy, 89:365– 71.
Brenner MF, Galai D. (1989).New financial instruments for hedge changes in volatility. Financ Anal J, 45(4):61–5
Brock WA, Dechert W, Scheinkman J. (1987). A test for independence based on the correlation dimension. Working paper, University of Winconsin at Madison, University of Houston, and University of Chicago, 1987.
Brock WA, Hsieh DA, LeBaron BD. (1991). Nonlinear dynamics, chaos, and instability: statistical theory and economic evidence. Cambridge: MIT press.
Ciner, C. (2001).Energy shocks and financial markets: nonlinear linkages. Stud Nonlinear Dyn Econom, 5(3):203–12.
Ciner, C. (2013).Oil and stock returns: frequency domain evidence. J Int Financ Mark Inst Money. 23:1–11.
Cologni, A. (2009). Manera M. The asymmetric effects of oil shocks on output growth: a Markov-switching analysis for the G-7 countries. Econ Modell, 26:1–29.
DeLisle RJ, Doran JS, and Peterson DR. (2011).Asymmetric pricing of implied systematic volatility in the cross-section of expected returns. J Future Mark. 2011; 31(1):34–54.
Dowling S, Muthuswamy J. The implied volatility of Australian index options. R Future Mark, 14(1):117–55.
Dutta, A. (2017) Nikkinen J, Rothovius T. Impact of oil price uncertainty on Middle East and African stock markets. Energy, 123:189–97.
Ederington, LH, Guan W. (2010).How asymmetric is U.S. stock market volatility? J Financ Mark, 13(2):225–48.
Fama, EF. (1970).Efficient capital markets: a review of theory and empirical work. J Financ, 25(4):383–417.
Filho, OC. (2012). Ziegelmann FA, Dueker MJ. (2012).Modelling dependence dynamics through copulas with regime switching. Insur Math Econ, 50(3):346–56.
Giot, P. (2005) Relationships between implied volatility indexes and stock index returns. J PortManag, 31(3):92–100.
Hamilton, JD. (1996).This is what happened to the oil price-macroeconomy relationship. J Monet Econ, 38:215–20.
Hamilton, JD. (2003).What is an oil shock? J Econ, 113:363–98.
Hammoudeh S, Aleisa E. (2004).Dynamic relationship among GCC stock markets and NYMEX oil futures. Contemp Econ Policy, 22:250–69.
Hammoudeh, S, Choi K. (2006).Behavior of GCC stock markets and impacts of US oil and financial markets. Res Int Bus Financ, 20(1):22–44.
Hansen B. (2000) Sample splitting and threshold estimation. Economet, 68(3):575–603.
Hansen, B. (1996) Inference when a nuisance parameter is not identified under the null hypothesis. Economet, 64:413–30
Hansen, B. (2000). Testing for structural change in conditional models. J Econom, 97(1):93–115
He, L-Y. (2011).Chaotic structures in Brent & WTI crude oil markets: empirical evidence. Int J Econ Financ, 3(5):242–9.
He L-Y. (2010).Chen S-P. Are crude oil markets multifractal? Evidence from MF-DFA and MF-SSA perspectives. Phys A, 389(16)3218–29.
He L-Y, Fan Y, Wei Y-M.(2007).The empirical analysis for fractal features and long-run memory mechanism in petroleum pricing systems. Int J Glob Energy Issue, 27(4):492–502
He L-Y, Fan Y, Wei Y-M. (2009). Impact of speculator’s expectations of returns and time scales of investment on crude oil price behaviors. Energy Econ, 31(1):77–84.
He L-Y, Zheng F. (2008).Empirical evidence of some stylized facts in international crude oil markets. Complex Syst, 17(4): 413–25.
ISE, ISE 2010 Annual Report, Istanbul, 2010.
Jones CM, Kaul G. (1996).Oil and the stock markets. J Financ, 51(2):463–91.
Kantz, H. (1944).A robust method to estimate the maximal Lyapunov exponent for a time series. Phys Lett A, 185(1):77–87.
Keynes, JM. (1936). the general theory of employment, interest and money. London: Palgrave MacMillan.
Kolmogorov, AN. (1960). Foundations of the theory of probability. 2nd Ed. (Trans. 1960). New York: Chelsea Publishing Co.
Kolmogorov, AN. (1959). Entropy per unit time as a metric invariant of automorphism. Docl. Russ. Acad. Sci, 124, 754–5.
Komijani A, Naderi E, Alikhani NG. (2014).A hybrid approach for forecasting of oil prices volatility. OPEC Energy Rev, 38(3):323–40.
Lahmiri, S. (2017). A study on chaos in crude oil markets before and after 2008 international financial crisis. Phys A, 38(3):389–95.
Lardic S, Mignon V. (2006). The impact of oil prices on GDP in European countries: an empirical investigation based on asymmetric cointegration. Energy Policy, 34(18):3910–5
Lee, TH, Chang, Y. (2011). Dynamic relationships between the price of oil, gold and financial variables in Japan: a bounds testing approach. MPRA paper, No.33030.
Lintner, J. (1965).The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Rev Econ Stat, 47:13–37.
Liu ML, Ji Q, Fan Y. (2013). How does oil market uncertainty interact with other markets: an empirical analysis of implied volatility index? Energy, 55:860–8
Maghyereh A, Al-Kandari A. (2007). Oil prices and stock markets in GCC countries: new evidence from nonlinear cointegration analysis. Manag Financ. 33(7):449–60.
Mohanty SK, Nandha M, Turkistani AQ, Alaitani MY.(2011). Oil price movements and stock market returns: evidence from Gulf Cooperation Council (GCC) countries. Glob Financ J, 22(1):42–55.
Odabas¸ı A, Aksu C, Akgiray V. (2004). The statistical evolution of prices on the Istanbul Stock Exchange. Eur J Financ, 10:510–25.
Panas E, Ninni V. (2000).Are oil markets chaotic? A non-linear dynamic analysis. Energy Econ, 22(5):549–68.
Papapetrou E. (2001). Oil price shocks, stock market, economic activity and employment in Greece. Energy Econ, 23:511–32
Park J, Ratti RA.(2008). Oil price shocks and stock markets in the US and 13 European countries. Energy Econ, 30(5):2587–608.
Pindyck R. (1991). Irreversibility, uncertainty, and investment. J Econ Lit, 29:110–48.
Plerou V, Gopikrishnan P, Gabaix X. (2001).Price fluctuations, market activity and trading volume. Quant Financ, 1(2):262-9.
Rosenstein M, Collins J, De Luca C. (1993). A practical method for calculating largest Lyapunov exponents from small data sets. Phys D Nonlinear Phenom, 65:117–34.
Sadorsky P. (1999).Oil price shocks and stock market activity. Energy Econ, 21(5):449–69.
Shaikh, I, Padhi, P. (2015). The implied volatility index: is ‘investor fear gauge’ or ‘forward-looking’? Borsa Istanb Rev, 15(1):44–52
Smales L. (2017). Effect of investor fear on Australian financial markets. Appl Econ Lett, 24(16):1148–53
Sharpe WF. (1964).Capital asset prices: a theory of market equilibrium under conditions of risk. J Financ, 19:425–42.
Tabak BM, Cajueiro DO. (2007). Are the crude oil markets becoming weakly efficient over time? A test for time-varying long-range dependence in prices and volatility. Energy Econ, 29(1):28–36.
Viana R, Barbosa J. (2003) Simulating a chaotic process. Braz J Phys, 5(1):139–47
Wang Y, Wu C, (2013).Oil price shocks and stock market activities: evidence from oil-importing and oil-exporting countries. J Comp Econ, 41:1220–39.
Wernecke, H, Sa´ndor B, Gros C. (2017).How to test for partially predictable chaos. Sci Rep, 7:1087.
*Whaley RE. (2000). the investor fear gauge. J Port Manag, 26(3):12–7.
Whaley, RE. (1993). Derivatives on market volatility: hedging tools long overdue. J Deriv, 1:71–84.
Whaley, RE. (2009). Understanding the VIX. J Port Manag, 35(3):98–105.
Zakoian, JM. (1994). Threshold heteroskedastic models. J Econ Dyn Control, 18(5): 931–55.
Zhang, D. (2008). Oil shock and economic growth in Japan: a nonlinear approach. Energy Econ, 30(5):2374–90.
Zhao L, Wang Z, Chen C. (2009). Is international oil price chaotic?—Empirical evidence from spot market. In: 2009 International conference on business intelligence and financial engineering.
Zheng, Y. (2014). The linkage between aggregate stock market investor sentiment and commodity futures returns. Appl Financ Econ, 24(23):1491–513.
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Adrangi B, Chatrath A, Dhanda KK, Raffiee K. (2001).Chaos in oil prices? Evidence from futures markets. Energy Econ, 23(4): 405–25.
Alvarez-Ramirez J, Rodriguez E. (2008).Short-term predictability of crude oil markets: a detrended fluctuation analysis approach. Energy Econ, 30:2645–56.
Awartani B, Maghyereh AI. (2013). Dynamic spillovers between oil and stock markets in the Gulf Cooperation Council Countries. Energy Econ, 36:28–42.
Arouri M, Fouquau J. (2009). On the short-term influence of oil price changes on stock markets in GCC countries: linear and nonlinear analyses. Econ Bull, 29(2):795–804.
Bachelier L. (1964).Theory of speculation (Ph.D. Thesis, Faculty of the Academy of Paris, 1900and Theory of Speculation, the random character of stock market prices. M.I.T Press.
Barnett WA, Hinich MJ. (1992)Empirical chaotic dynamics in economics. Ann Oper Res, 37:1–15.
Barnett WA, Gallant AR, Hinich MJ. (1995).Robustness of nonlinearity and chaos tests to measurement error, inference method, and sample size. J Econ Behav Org, 27(2):301–20.
Barnett WA, Gallant AR, Hinich MJ. (1997) A single-blind controlled competition among tests for nonlinearity and chaos. J Econom, 82(1):157–92.
Barone-Adesi G, Bourgoin F, Giannopoulos K. Don’t look back. Risk. 1998; 11:100–3.
Bjørnland HC. (2009).Oil price shocks and stock market booms in an oil exporting country. Scott J Polit Econ, 56(2):232–54.
Bildik R, Yılmaz M. (2008).The market performance of initial public offerings in the I˙stanbul stock exchange, BDDK Banka. Financ Piyas, 2(2):49–75.
Bildirici M, Sonustun FO. (2018).Chaotic structure of oil prices. In: AIP conference proceedings 1926, p. 020009.
Bildirici M, Ersın O, Onat I. (2017). The Baltic dry index as a leading economic indicator: an investigation with volatility models. In: Bildirci M, Zehir C, Kayıkc¸ı F, Karago¨z M, Bakırtas¸ T, editors. Istanbul as a Global Financial Center. Cambridge: Cambridge Scholar Publishing.
Boubaker H, Sghaier N. (2016).Contagion effect and change in the dependence between oil and ten MENA stock markets. RRJSMS, 2(1):1–17.
Boubaker H, Sghaier N. (2016).Markov-switching time-varying copula modeling of dependence structure between oil and GCC stock markets. Open J Stat, 6:565–89.
Bouri E. (2015).Oil volatility shocks and the stock markets of oil-importing MENA economies: a tale from the financial crisis. Energy Econ, 51:590–8.
Bouri E. (2015).Return and volatility linkages between oil prices and the Lebanese stock market in crisis periods. Energy, 89:365– 71.
Brenner MF, Galai D. (1989).New financial instruments for hedge changes in volatility. Financ Anal J, 45(4):61–5
Brock WA, Dechert W, Scheinkman J. (1987). A test for independence based on the correlation dimension. Working paper, University of Winconsin at Madison, University of Houston, and University of Chicago, 1987.
Brock WA, Hsieh DA, LeBaron BD. (1991). Nonlinear dynamics, chaos, and instability: statistical theory and economic evidence. Cambridge: MIT press.
Ciner, C. (2001).Energy shocks and financial markets: nonlinear linkages. Stud Nonlinear Dyn Econom, 5(3):203–12.
Ciner, C. (2013).Oil and stock returns: frequency domain evidence. J Int Financ Mark Inst Money. 23:1–11.
Cologni, A. (2009). Manera M. The asymmetric effects of oil shocks on output growth: a Markov-switching analysis for the G-7 countries. Econ Modell, 26:1–29.
DeLisle RJ, Doran JS, and Peterson DR. (2011).Asymmetric pricing of implied systematic volatility in the cross-section of expected returns. J Future Mark. 2011; 31(1):34–54.
Dowling S, Muthuswamy J. The implied volatility of Australian index options. R Future Mark, 14(1):117–55.
Dutta, A. (2017) Nikkinen J, Rothovius T. Impact of oil price uncertainty on Middle East and African stock markets. Energy, 123:189–97.
Ederington, LH, Guan W. (2010).How asymmetric is U.S. stock market volatility? J Financ Mark, 13(2):225–48.
Fama, EF. (1970).Efficient capital markets: a review of theory and empirical work. J Financ, 25(4):383–417.
Filho, OC. (2012). Ziegelmann FA, Dueker MJ. (2012).Modelling dependence dynamics through copulas with regime switching. Insur Math Econ, 50(3):346–56.
Giot, P. (2005) Relationships between implied volatility indexes and stock index returns. J PortManag, 31(3):92–100.
Hamilton, JD. (1996).This is what happened to the oil price-macroeconomy relationship. J Monet Econ, 38:215–20.
Hamilton, JD. (2003).What is an oil shock? J Econ, 113:363–98.
Hammoudeh S, Aleisa E. (2004).Dynamic relationship among GCC stock markets and NYMEX oil futures. Contemp Econ Policy, 22:250–69.
Hammoudeh, S, Choi K. (2006).Behavior of GCC stock markets and impacts of US oil and financial markets. Res Int Bus Financ, 20(1):22–44.
Hansen B. (2000) Sample splitting and threshold estimation. Economet, 68(3):575–603.
Hansen, B. (1996) Inference when a nuisance parameter is not identified under the null hypothesis. Economet, 64:413–30
Hansen, B. (2000). Testing for structural change in conditional models. J Econom, 97(1):93–115
He, L-Y. (2011).Chaotic structures in Brent & WTI crude oil markets: empirical evidence. Int J Econ Financ, 3(5):242–9.
He L-Y. (2010).Chen S-P. Are crude oil markets multifractal? Evidence from MF-DFA and MF-SSA perspectives. Phys A, 389(16)3218–29.
He L-Y, Fan Y, Wei Y-M.(2007).The empirical analysis for fractal features and long-run memory mechanism in petroleum pricing systems. Int J Glob Energy Issue, 27(4):492–502
He L-Y, Fan Y, Wei Y-M. (2009). Impact of speculator’s expectations of returns and time scales of investment on crude oil price behaviors. Energy Econ, 31(1):77–84.
He L-Y, Zheng F. (2008).Empirical evidence of some stylized facts in international crude oil markets. Complex Syst, 17(4): 413–25.
ISE, ISE 2010 Annual Report, Istanbul, 2010.
Jones CM, Kaul G. (1996).Oil and the stock markets. J Financ, 51(2):463–91.
Kantz, H. (1944).A robust method to estimate the maximal Lyapunov exponent for a time series. Phys Lett A, 185(1):77–87.
Keynes, JM. (1936). the general theory of employment, interest and money. London: Palgrave MacMillan.
Kolmogorov, AN. (1960). Foundations of the theory of probability. 2nd Ed. (Trans. 1960). New York: Chelsea Publishing Co.
Kolmogorov, AN. (1959). Entropy per unit time as a metric invariant of automorphism. Docl. Russ. Acad. Sci, 124, 754–5.
Komijani A, Naderi E, Alikhani NG. (2014).A hybrid approach for forecasting of oil prices volatility. OPEC Energy Rev, 38(3):323–40.
Lahmiri, S. (2017). A study on chaos in crude oil markets before and after 2008 international financial crisis. Phys A, 38(3):389–95.
Lardic S, Mignon V. (2006). The impact of oil prices on GDP in European countries: an empirical investigation based on asymmetric cointegration. Energy Policy, 34(18):3910–5
Lee, TH, Chang, Y. (2011). Dynamic relationships between the price of oil, gold and financial variables in Japan: a bounds testing approach. MPRA paper, No.33030.
Lintner, J. (1965).The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Rev Econ Stat, 47:13–37.
Liu ML, Ji Q, Fan Y. (2013). How does oil market uncertainty interact with other markets: an empirical analysis of implied volatility index? Energy, 55:860–8
Maghyereh A, Al-Kandari A. (2007). Oil prices and stock markets in GCC countries: new evidence from nonlinear cointegration analysis. Manag Financ. 33(7):449–60.
Mohanty SK, Nandha M, Turkistani AQ, Alaitani MY.(2011). Oil price movements and stock market returns: evidence from Gulf Cooperation Council (GCC) countries. Glob Financ J, 22(1):42–55.
Odabas¸ı A, Aksu C, Akgiray V. (2004). The statistical evolution of prices on the Istanbul Stock Exchange. Eur J Financ, 10:510–25.
Panas E, Ninni V. (2000).Are oil markets chaotic? A non-linear dynamic analysis. Energy Econ, 22(5):549–68.
Papapetrou E. (2001). Oil price shocks, stock market, economic activity and employment in Greece. Energy Econ, 23:511–32
Park J, Ratti RA.(2008). Oil price shocks and stock markets in the US and 13 European countries. Energy Econ, 30(5):2587–608.
Pindyck R. (1991). Irreversibility, uncertainty, and investment. J Econ Lit, 29:110–48.
Plerou V, Gopikrishnan P, Gabaix X. (2001).Price fluctuations, market activity and trading volume. Quant Financ, 1(2):262-9.
Rosenstein M, Collins J, De Luca C. (1993). A practical method for calculating largest Lyapunov exponents from small data sets. Phys D Nonlinear Phenom, 65:117–34.
Sadorsky P. (1999).Oil price shocks and stock market activity. Energy Econ, 21(5):449–69.
Shaikh, I, Padhi, P. (2015). The implied volatility index: is ‘investor fear gauge’ or ‘forward-looking’? Borsa Istanb Rev, 15(1):44–52
Smales L. (2017). Effect of investor fear on Australian financial markets. Appl Econ Lett, 24(16):1148–53
Sharpe WF. (1964).Capital asset prices: a theory of market equilibrium under conditions of risk. J Financ, 19:425–42.
Tabak BM, Cajueiro DO. (2007). Are the crude oil markets becoming weakly efficient over time? A test for time-varying long-range dependence in prices and volatility. Energy Econ, 29(1):28–36.
Viana R, Barbosa J. (2003) Simulating a chaotic process. Braz J Phys, 5(1):139–47
Wang Y, Wu C, (2013).Oil price shocks and stock market activities: evidence from oil-importing and oil-exporting countries. J Comp Econ, 41:1220–39.
Wernecke, H, Sa´ndor B, Gros C. (2017).How to test for partially predictable chaos. Sci Rep, 7:1087.
*Whaley RE. (2000). the investor fear gauge. J Port Manag, 26(3):12–7.
Whaley, RE. (1993). Derivatives on market volatility: hedging tools long overdue. J Deriv, 1:71–84.
Whaley, RE. (2009). Understanding the VIX. J Port Manag, 35(3):98–105.
Zakoian, JM. (1994). Threshold heteroskedastic models. J Econ Dyn Control, 18(5): 931–55.
Zhang, D. (2008). Oil shock and economic growth in Japan: a nonlinear approach. Energy Econ, 30(5):2374–90.
Zhao L, Wang Z, Chen C. (2009). Is international oil price chaotic?—Empirical evidence from spot market. In: 2009 International conference on business intelligence and financial engineering.
Zheng, Y. (2014). The linkage between aggregate stock market investor sentiment and commodity futures returns. Appl Financ Econ, 24(23):1491–513.
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