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Dynamic relationship analysis between NAFTA stock markets using nonlinear, nonparametric, non-stationary methods. (English) Zbl 1431.62660

Summary: This paper seeks to investigate the dynamic relationship between daily stock market indices in NAFTA countries from 8 November 1991 to 16 March 2018, using for the first time nonlinear, nonparametric, non-stationary methods. We apply two novel nonlinear, nonparametric, non-stationary dynamic correlation techniques – rolling window Spearman correlation and wavelet coherence – to study the relationships between the three pairwise comparisons. We apply a nonlinear, nonparametric causality test to four specific sub-periods and to the full period of these indices to check the direction of causality. Our results show the following: (1) the correlation between the indices increases from 2000 to 2011, but that correlation increase is interrupted around 2011/2012 and then falls noticeably, picking up again from 2015 onwards. (2) The pairs that show the lowest correlation are those involving the IPC. (3) The causality test reveals nonlinear bidirectional causality for all three indices and all the intervals analysed, indicating that there is a strong interrelationship between NAFTA members. These results are relevant to obtain a better understanding of the complex dynamical system formed by NAFTA stock markets and have direct implications for hedging and portfolio diversification policies.

MSC:

62P20 Applications of statistics to economics
37N40 Dynamical systems in optimization and economics
91B80 Applications of statistical and quantum mechanics to economics (econophysics)
91B84 Economic time series analysis
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[1] Aggarwal, R., Kyaw, N.A.: Equity market integration in the NAFTA region: evidence from unit root and cointegration tests. Int. Rev. Financ. Anal. 14(4), 393-406 (2005)
[2] Aguiar-Conraria, L., Azevedo, N., Soares, M.J.: Using wavelets to decompose the time-frequency effects of monetary policy. Phys. A: Stat. Mech. Appl. 387(12), 2864-2878 (2008)
[3] Auer, B.R., Schuhmacher, F.: Robust evidence on the similarity of sharpe ratio and drawdown-based hedge fund performance rankings. J. Int. Financ. Mark. Inst. Money 24, 153-165 (2013)
[4] Baek, E., Brock, W.: A general test for nonlinear Granger causality: bivariate model. In: Iowa State University and University of Wisconsin at Madison Working Paper (1992)
[5] Bekiros, S.D., Diks, C.: The relationship between crude oil spot and futures prices: cointegration, linear and nonlinear causality. Energy Econ. 30(5), 2673-2685 (2008)
[6] Bell, D., Kay, J., Malley, J.: A non-parametric approach to non-linear causality testing. Econ. Lett. 51(1), 7-18 (1996) · Zbl 0875.90178
[7] Benhmad, F.: Bull or bear markets: a wavelet dynamic correlation perspective. Econ. Model. 32, 576-591 (2013)
[8] Benjamini, Y., Hochberg, Y.: Controlling the false discovery rate: a practical and powerful approach to multiple testing. J. R. Stat. Soc. Ser. B 57(1), 289-300 (1995) · Zbl 0809.62014
[9] Cabrera, G., Coronado, S., Rojas, O., Romero-Meza, R.: A bayesian approach to model changes in volatility in the Mexican stock exchange index. Appl. Econ. 50(15), 1716-1724 (2018)
[10] Cazelles, B., Chavez, M., Berteaux, D., Ménard, F., Vik, J.O., Jenouvrier, S., Stenseth, N.: Wavelet analysis of ecological time series. Oecologia 156(2), 287-304 (2008)
[11] Chen, Y., Mantegna, R.N., Pantelous, A.A., Zuev, K.M.: A dynamic analysis of S&P 500, FTSE 100 and EURO STOXX 50 indices under different exchange rates. PloS one 13(3), e0194067 (2018)
[12] Cont, R.: Empirical properties of asset returns: stylized facts and statistical issues. Quant. Finance 1(2), 223-236 (2001) · Zbl 1408.62174
[13] Coronel-Brizio, H., Hernández-Montoya, A., Huerta-Quintanilla, R., Rodriguez-Achach, M.: Evidence of increment of efficiency of the Mexican Stock Market through the analysis of its variations. Phys. A: Stat. Mech. Appl. 380, 391-398 (2007)
[14] Crowley, P.M., Mayes, D.G.: How fused is the euro area core? OECD J.: J. Bus. Cycle Meas. Anal. 4(1), 63-95 (2009)
[15] Dajcman, S., Festic, M., Kavkler, A.: European stock market comovement dynamics during some major financial market turmoils in the period 1997 to 2010: a comparative DCC-GARCH and wavelet correlation analysis. Appl. Econ. Lett. 19(13), 1249-256 (2012)
[16] Daelemans, B., Daniels, J.P., Nourzad, F.: Free trade agreements and volatility of stock returns and exchange rates: evidence from NAFTA. Open Econ. Rev. 29(1), 141-163 (2018) · Zbl 1412.91092
[17] Darrat, A.F., Zhong, M.: Equity market linkage and multinational trade accords: the case of NAFTA. J. Int. Money Finance 24(5), 793-817 (2005)
[18] Diks, C., Panchenko, V.: A new statistic and practical guidelines for nonparametric Granger causality testing. J. Econ. Dyn. Control 30(9), 1647-1669 (2006) · Zbl 1162.91477
[19] Dionisio, A., Menezes, R., Mendes, D.A.: Mutual information: a measure of dependency for nonlinear time series. Phys. A: Stat. Mech. Appl. 344(1), 326-329 (2004)
[20] Dooley, M., Hutchison, M.: Transmission of the us subprime crisis to emerging markets: evidence on the decoupling-recoupling hypothesis. J. Int. Money Finance 28(8), 1331-1349 (2009)
[21] Duarte, F.B., Machado, J.T., Duarte, G.M.: Dynamics of the Dow Jones and the NASDAQ stock indexes. Nonlinear Dyn. 61(4), 691-705 (2010) · Zbl 1204.91110
[22] Durante, F., Foscolo, E., Weissensteiner, A.: Dependence between stock returns of Italian banks and the sovereign risk. Econometrics 5(2), 23 (2017)
[23] World’s Top Exports: Canadas top trading partners (2018). http://www.worldstopexports.com/canadas-top-import-partners/
[24] Farge, M.: Wavelet transforms and their applications to turbulence. Annu. Rev. Fluid Mech. 24(1), 395-458 (1992) · Zbl 0743.76042
[25] Fleischer, P., Maller, R., Müller, G.: A bayesian analysis of market information linkages among NAFTA countries using a multivariate stochastic volatility model. J. Econ. Fnance 35(2), 123-148 (2011)
[26] Filipovic, V., Nedic, N., Stojanovic, V.: Robust identification of pneumatic servo actuators in the real situations. Forschung im Ingenieurwesen 75(4), 183-196 (2011)
[27] Forbes, K.J., Rigobon, R.: No contagion, only interdependence: measuring stock market comovements. J. Finance 57(5), 2223-2261 (2002)
[28] Funashima, Y.: Time-varying leads and lags across frequencies using a continuous wavelet transform approach. Econ. Model. 60, 24-28 (2017)
[29] Gallegati, M.: Wavelet analysis of stock returns and aggregate economic activity. Comput. Stat. Data Anal. 52(6), 3061-3074 (2008) · Zbl 1452.62910
[30] Gallegati, M.: A wavelet-based approach to test for financial market contagion. Comput. Stat. Data Anal. 56(11), 3491-3497 (2012) · Zbl 1254.91657
[31] Gentile, M., Giordano, L.: Financial contagion during the Lehman Brothers default and sovereign debt crisis. J. Financ. Manag. Mark. Inst. 1(2), 197-224 (2013)
[32] Gençay, R., Selçuk, F., Whitcher, B.: An Introduction to Wavelets and Other Filtering Methods in Finance and Economics. Academic Press, London (2002) · Zbl 1068.42029
[33] Granger, Clive, W.J.: Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37, 424-438 (1969) · Zbl 1366.91115
[34] Grinsted, A., Moore, J.C., Jevrejeva, S.: Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlinear Process. Geophys. 11, 561-566 (2004)
[35] Hiemstra, C., Jones, J.D.: Testing for linear and nonlinear Granger causality in the stock price-volume relation. J. Finance 49(5), 1639-1664 (1994)
[36] Kalbaska, A., Gatkowski, M.: Eurozone sovereign contagion: evidence from the CDS market (2005-2010). J. Econ. Behav. Organ. 83(3), 657-673 (2012)
[37] Kirby, J.F.: Which wavelet best reproduces the Fourier power spectrum? Comput. Geosci. 31(7), 846-864 (2005)
[38] Kirilina, E., Yu, N., Jelzow, A., Wabnitz, H., Jacobs, A.M., Tachtsidis, I.: Identifying and quantifying main components of physiological noise in functional near infrared spectroscopy on the prefrontal cortex. Front. Hum. Neurosci. 7, 827 (2013)
[39] Kiviaho, J., Nikkinen, J., Piljak, V., Rothovius, T.: The co-movement dynamics of European frontier stock markets. Eur. Financ. Manag. 20(3), 574-595 (2014)
[40] Lahrech, A., Sylwester, K.: The impact of NAFTA on North American stock market linkages. N. Am. J. Econ Finance 25, 94-108 (2013)
[41] Lee, H.S.: International transmission of stock market movements: a wavelet analysis. Appl. Econ. Lett. 11(3), 197-201 (2004)
[42] Li, J., Shang, P.: Financial time series analysis using total-CApEn and Avg-CApEn with cumulative histogram matrix. Commun. Nonlinear Sci. Numer. Simul. 63, 239-252 (2018) · Zbl 07265243
[43] López-Herrera, F., Santillán-Salgado, R.J., Ortiz, E.: Interdependence of NAFTA capital markets: a minimum variance portfolio approach. Panoeconomicus 61(6), 691-707 (2014)
[44] Machado, J.T., Duarte, F.B., Duarte, G.M.: Analysis of stock market indices through multidimensional scaling. Commun. Nonlinear Sci. Numer. Simul. 16(12), 4610-4618 (2011)
[45] Madaleno, M., Pinho, C.: International stock market indices comovements: a new look. Int. J. Finance Econ. 17(1), 89-102 (2011)
[46] Mantegna, R.N., Stanley, H.E.: Introduction to Econophysics: Correlations and Complexity in Finance. Cambridge University Press, Cambridge (1999) · Zbl 1138.91300
[47] Maraun, D.: Sowas: software for wavelet analysis and synthesis (2017). https://rdrr.io/github/Dasonk/SOWAS/
[48] Maraun, D., Kurths, J.: Cross wavelet analysis: significance testing and pitfalls. Nonlinear Process. Geophys. 11(4), 505-514 (2004)
[49] Maraun, D., Kurths, J., Holschneider, M.: Nonstationary Gaussian processes in wavelet domain: synthesis, estimation, and significance testing. Phys. Rev. E 75(1), 16707 (2007)
[50] Meyers, S.D., Kelly, B.G., O’Brien, J.J.: Introduction to wavelet analysis in oceanography and meteorology: with application to the dispersion of Yanai waves. Monthly Weather Rev. 121(10), 2858-2866 (1993)
[51] Mi, X., Ren, H., Ouyang, Z., Wei, W., Ma, K.: The use of the Mexican Hat and the Morlet wavelets for detection of ecological patterns. Plant Ecol. 179(1), 1-19 (2005)
[52] Mudelsee, M.: Climate Time Series Analysis: Classical Statistical and Bootstrap Methods. Springer, Berlin (2014) · Zbl 1300.86001
[53] Nedic, N., Prsic, D., Dubonjic, L., Stojanovic, V., Djordjevic, V.: Optimal cascade hydraulic control for a parallel robot platform by PSO. Int. J. Adv. Manuf. Technol. 72(5-8), 1085-1098 (2014)
[54] Nedic, N., Stojanovic, V., Djordjevic, V.: Optimal control of hydraulically driven parallel robot platform based on firefly algorithm. Nonlinear Dyn. 82(3), 457-1473 (2015) · Zbl 1441.70003
[55] Nedic, N., Pršić, D., Fragassa, C., Stojanović, V., Pavlovic, A.: Simulation of hydraulic check valve for forestry equipment. Int. J. Heavy Veh. Syst. 24(3), 260-276 (2017)
[56] Nikkinen, J., Pynnönen, S., Ranta, M., Vähämaa, S.: Cross-dynamics of exchange rate expectations: a wavelet analysis. Int. J. Finance Econ. 16(3), 205-217 (2011)
[57] Olayeni, O.R.: Causality in continuous wavelet transform without spectral matrix factorization: theory and application. Comput. Econ. 47(3), 321-340 (2016)
[58] Papastamatiou, Y.P., Meyer, C.G., Kosaki, R.K., Wallsgrove, N.J., Popp, B.N.: Movements and foraging of predators associated with mesophotic coral reefs and their potential for linking ecological habitats. Mar. Ecol. Prog. Ser. 521, 155-170 (2015)
[59] Percival, D.B., Walden, A.T.: Wavelet Methods for Time Series Analysis. Cambridge University Press, Cambridge (2006) · Zbl 1129.62080
[60] Phengpis, C., Swanson, P.E.: Portfolio diversification effects of trading blocs: the case of NAFTA. J. Multinatl. Financ. Manag. 16(3), 315-331 (2006)
[61] Polanco, J., Ganzedo, U., Sáenz, J., Caballero-Alfonso, A., Castro-Hernández, J.: Wavelet analysis of correlation among Canary Islands octopus captures per unit effort, sea-surface temperatures and the North Atlantic Oscillation. Fish. Res. 107(1-3), 177-183 (2011)
[62] Polanco-Martínez, J., Fernández-Macho, J., Neumann, M., Faria, S.: A pre-crisis vs. crisis analysis of peripheral EU stock markets by means of wavelet transform and a nonlinear causality test. Phys. A: Stat. Mech. Appl. 490, 1211-1227 (2018)
[63] Polanco-Martínez, J.M., Abadie, L.: Analyzing crude oil spot price dynamics versus long term future prices: a wavelet analysis approach. Energies 9(12), 1089 (2016)
[64] Polanco-Martínez, J.M., Fernández-Macho, F.J.: Package W2CWM2C: description, features, and applications. Comput. Sci. Eng. 16(6), 68-78 (2014)
[65] Polanco-Martínez, J.M., Abadie, L.M., Fernández-Macho, J.: A multi-resolution and multivariate analysis of the dynamic relationships between crude oil and petroleum-product prices. Appl. Energy 228, 1550-1560 (2018)
[66] Ranta, M.: Contagion among major world markets: a wavelet approach. Int. J. Manag. Finance 9(2), 133-149 (2013)
[67] Razdan, A.: Wavelet correlation coefficient of ‘strongly correlated’ time series. Phys. A: Stat. Mech. Appl. 333, 335-342 (2004)
[68] Sander, H., Kleimeier, S.: Contagion and causality: an empirical investigation of four Asian crisis episodes. J. Int. Financ. Mark. Inst. Money 13(2), 171-186 (2003)
[69] Savit, R.: When random is not random: an introduction to chaos in market prices. J. Futures Mark. 8(3), 271-290 (1988)
[70] Schulte, J.A.: Wavelet analysis for non-stationary, nonlinear time series. Nonlinear Process. Geophys. 23(4), 257-267 (2016)
[71] Shen, M., Ye, D., Wang, Q.G.: Mode-dependent filter design for Markov jump systems with sensor nonlinearities in finite frequency domain. Signal Process. 134, 1-8 (2017)
[72] Shen, M., Zhang, H., Park, J.H.: Observer-based quantized sliding mode \[{{{\cal{H}}}}_{{\infty }} H\]∞ control of Markov jump systems. Nonlinear Dyn. 92(2), 415-427 (2018) · Zbl 1398.93358
[73] Schaefli, B., Maraun, D., Holschneider, M.: What drives high flow events in the Swiss Alps? Recent developments in wavelet spectral analysis and their application to hydrology. Adv. Water Resour. 30(12), 2511-2525 (2007)
[74] Su, L., White, H.: A nonparametric Hellinger metric test for conditional independence. Econom. Theory 24(4), 829-864 (2008) · Zbl 1284.62285
[75] Stojanovic, V., Nedic, N.: Joint state and parameter robust estimation of stochastic nonlinear systems. Int. J. Robust Nonlinear Control 26(14), 3058-3074 (2016) · Zbl 1346.93367
[76] Telford, R.: Running correlations – running into problems (2013). https://quantpalaeo.wordpress.com/2013/01/04/running-correlations-running-into-problems/
[77] Tiwari, A.K., Mutascu, M.I., Albulescu, C.T.: Continuous wavelet transform and rolling correlation of European stock markets. Int. Rev. Econ. Finance 42, 237-256 (2016)
[78] Torrence, C., Compo, G.P.: A practical guide to wavelet analysis. Bull. Am. Meteorol. Soc. 79(1), 61-78 (1998)
[79] Veleda, D., Montagne, R., Araujo, M.: Cross-wavelet bias corrected by normalizing scales. J. Atmos. Ocean. Technol. 29(9), 1401-1408 (2012)
[80] Wang, G.J., Xie, C.: Cross-correlations between the CSI 300 spot and futures markets. Nonlinear Dyn. 73(3), 1687-1696 (2013)
[81] Torrence, C., Webster, P.J.: Interdecadal changes in the ENSO-monsoon system. J. Clim. 12(8), 2679-2690 (1999)
[82] Zadourian, R., Grassberger, P.: Asymmetry of cross-correlations between intra-day and overnight volatilities. Europhys. Lett. 118(1), 18004 (2017)
[83] Zebende, G., Da Silva, M., Machado Filho, A.: DCCA cross-correlation coefficient differentiation: theoretical and practical approaches. Phys. A: Stat. Mech. Appl. 392(8), 1756-1761 (2013)
[84] Zhang, T., Ma, G., Liu, G.: Nonlinear joint dynamics between prices of crude oil and refined products. Phys. A: Stat. Mech. Appl. 419, 444-456 (2015) · Zbl 1402.91972
[85] Zhang, X., Podobnik, B., Kenett, D., Stanley, H.E.: Systemic risk and causality dynamics of the world international shipping market. Phys. A: Stat. Mech. Appl. 415, 43-53 (2017) · Zbl 1395.90032
[86] Zivot, E., Wang, J.: Modeling Financial Time Series with S-Plus \[^{\copyright }\]©. Springer, Berlin (2007) · Zbl 1092.91067
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