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Published in: Journal of Economics and Finance 3/2022

24-04-2022

Evaluating measures of dependence for linearly generated nonlinear time series along with spurious correlation

Authors: Christos Agiakloglou, Anil Bera, Emmanouil Deligiannakis

Published in: Journal of Economics and Finance | Issue 3/2022

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Abstract

The issue of determining dependence between two series is typically one of the most important aspects in any quantitative analysis. This study, using a Monte Carlo analysis, investigates the performance of several dependence measures for linearly generated nonlinear time series based on the family of AR(1) – ARCH(1) in variable models presented by Bera et al. (1992 and 1996) and it finds that copulas capture the concept of dependence better than the correlation coefficient. In addition, this study examines the performance of the test for zero association and it discovers that the spurious behavior can be eliminated asymptotically for this type on nonlinear processes, although the power of the test remains relatively low.

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Footnotes
1
The Monte Carlo analysis is conducted in Python.
 
2
The results for values of ρ = 0.5 and 0.9 are not included, simply because they are not adding value to the general picture obtained from this analysis, but they are available upon request.
 
Literature
go back to reference Agiakloglou C, Agiropoulos C (2016) The Balance between Size and Power in testing for linear association for two stationary AR(1) processes. Appl Econ Lett 23:230–234CrossRef Agiakloglou C, Agiropoulos C (2016) The Balance between Size and Power in testing for linear association for two stationary AR(1) processes. Appl Econ Lett 23:230–234CrossRef
go back to reference Agiakloglou C, Tsimpanos A (2012) An alternative approach for testing for linear association for two independent stationary AR(1) processes. Appl Econ 44:4799–4803CrossRef Agiakloglou C, Tsimpanos A (2012) An alternative approach for testing for linear association for two independent stationary AR(1) processes. Appl Econ 44:4799–4803CrossRef
go back to reference Banerjee A, Dolado J, Galbraith JW, Hendry DF (1993) Co-integration, error correction and the econometric analysis of non-stationary data. Oxford University Press, OxfordCrossRef Banerjee A, Dolado J, Galbraith JW, Hendry DF (1993) Co-integration, error correction and the econometric analysis of non-stationary data. Oxford University Press, OxfordCrossRef
go back to reference Bera A, Higgins ML, Lee S (1992) Interaction between autocorrelation and conditional heteroscedasticity: A random-coefficient approach. J Bus Economic Stat 10:133–142 Bera A, Higgins ML, Lee S (1992) Interaction between autocorrelation and conditional heteroscedasticity: A random-coefficient approach. J Bus Economic Stat 10:133–142
go back to reference Bera A, Higgins ML, Lee S (1996) Random coefficient Formulation of conditional heteroscedasticity and augmented ARCH models. Indian J Stat 58:199–220 Bera A, Higgins ML, Lee S (1996) Random coefficient Formulation of conditional heteroscedasticity and augmented ARCH models. Indian J Stat 58:199–220
go back to reference Box GEP, Jenkins GM (1976) Time Series Analysis, Forecasting and Control. Holden Day, San Francisco Box GEP, Jenkins GM (1976) Time Series Analysis, Forecasting and Control. Holden Day, San Francisco
go back to reference Embrechts P, McNeil AJ, Straumann D (1999) Correlation: Pitfalls and Alternatives, Risk, 12, 69 71 Embrechts P, McNeil AJ, Straumann D (1999) Correlation: Pitfalls and Alternatives, Risk, 12, 69 71
go back to reference Embrechts P, McNeil A, Straumann D (2002) Correlation and Dependence in Risk Management: Properties and Pitfalls, Risk Management: Value at Risk and Beyond, edited by Dempster, M., 176–223, Cambridge University Press, Cambridge Embrechts P, McNeil A, Straumann D (2002) Correlation and Dependence in Risk Management: Properties and Pitfalls, Risk Management: Value at Risk and Beyond, edited by Dempster, M., 176–223, Cambridge University Press, Cambridge
go back to reference Embrechts P, Hoing A, Juri A (2003) Using copulae to bound the value-at-risk for functions of dependent risks. Finance Stochast 7:145–167CrossRef Embrechts P, Hoing A, Juri A (2003) Using copulae to bound the value-at-risk for functions of dependent risks. Finance Stochast 7:145–167CrossRef
go back to reference Engle RF (1982) Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica 50:987–1007CrossRef Engle RF (1982) Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica 50:987–1007CrossRef
go back to reference Fisher RA (1915) Frequency distribution of the values of the correlation coefficient in samples from infinitely large population. Biometrika 10:507–521 Fisher RA (1915) Frequency distribution of the values of the correlation coefficient in samples from infinitely large population. Biometrika 10:507–521
go back to reference Genest C, MacKay RJ (1986) The joy of copulas: Bivariate distributions with uniform marginal. Am Stat 40:280–283 Genest C, MacKay RJ (1986) The joy of copulas: Bivariate distributions with uniform marginal. Am Stat 40:280–283
go back to reference Granger CWJ, Newbold P (1974) Spurious regressions in econometrics. J Econ 2:111–120CrossRef Granger CWJ, Newbold P (1974) Spurious regressions in econometrics. J Econ 2:111–120CrossRef
go back to reference Granger CWJ, Hyung N, Jeon Y (2001) Spurious regressions with stationary series. Appl Econ 33:899–904CrossRef Granger CWJ, Hyung N, Jeon Y (2001) Spurious regressions with stationary series. Appl Econ 33:899–904CrossRef
go back to reference Granger CWJ (2008) Non-linear Models: Where do we go next – time varying parameter models? Stud Nonlinear Dynamics Econometrics 12:1–9CrossRef Granger CWJ (2008) Non-linear Models: Where do we go next – time varying parameter models? Stud Nonlinear Dynamics Econometrics 12:1–9CrossRef
go back to reference Janus P, Koopman SJ, Lucas A (2014) Long memory dynamics for multivariate dependence under heavy tails. J Empir Finance 29:187–206CrossRef Janus P, Koopman SJ, Lucas A (2014) Long memory dynamics for multivariate dependence under heavy tails. J Empir Finance 29:187–206CrossRef
go back to reference Joe H (1997) Multivariate Models and Dependence Concepts. Chapman & Hall, LondonCrossRef Joe H (1997) Multivariate Models and Dependence Concepts. Chapman & Hall, LondonCrossRef
go back to reference Jondeau E, Rockinger M (2006) The Copula-GARCH model of conditional dependencies: an international stock market application. J Int Money Finance 25:827–853CrossRef Jondeau E, Rockinger M (2006) The Copula-GARCH model of conditional dependencies: an international stock market application. J Int Money Finance 25:827–853CrossRef
go back to reference Kendall MG (1954) Exercises in theoretical statistics, Griffin, London Kendall MG (1954) Exercises in theoretical statistics, Griffin, London
go back to reference Kenny JF, Keeping ES (1951) Mathematics of Statistics, part two, 2nd edition, New York, Van Nostrand Kenny JF, Keeping ES (1951) Mathematics of Statistics, part two, 2nd edition, New York, Van Nostrand
go back to reference Ning C (2010) Dependence structure between the equity market and the foreign exchange market – A copula approach. J Int Money Finance 29:743–759CrossRef Ning C (2010) Dependence structure between the equity market and the foreign exchange market – A copula approach. J Int Money Finance 29:743–759CrossRef
go back to reference Sklar A (1959) Fonctions de répartition à n dimensions et leurs marges. Publications de l’Institut de Statistique de L’Université de Paris 8:229–231 Sklar A (1959) Fonctions de répartition à n dimensions et leurs marges. Publications de l’Institut de Statistique de L’Université de Paris 8:229–231
go back to reference Yule GU (1926) Why do we sometimes get nonsense-correlations between time-series? A study in sampling and the nature of time-series. J Roy Stat Soc 89:1–64CrossRef Yule GU (1926) Why do we sometimes get nonsense-correlations between time-series? A study in sampling and the nature of time-series. J Roy Stat Soc 89:1–64CrossRef
go back to reference Zimmerman W, Zumbo D, Williams H, R (2003) Bias in Estimation and Hypothesis Testing of Correlation. Psicológica 24:133–158 Zimmerman W, Zumbo D, Williams H, R (2003) Bias in Estimation and Hypothesis Testing of Correlation. Psicológica 24:133–158
Metadata
Title
Evaluating measures of dependence for linearly generated nonlinear time series along with spurious correlation
Authors
Christos Agiakloglou
Anil Bera
Emmanouil Deligiannakis
Publication date
24-04-2022
Publisher
Springer US
Published in
Journal of Economics and Finance / Issue 3/2022
Print ISSN: 1055-0925
Electronic ISSN: 1938-9744
DOI
https://doi.org/10.1007/s12197-022-09579-7

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