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A Simple Test for Causality in Volatility

by 1 and 2,3,4,5,*
1
Department of Applied Economics, Department of Finance, National Chung Hsing University, 40227 Taichung City, Taiwan
2
Department of Quantitative Finance, National Tsing Hua University, 30013 Hsinchu City, Taiwan
3
Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam, 3062 PA Rotterdam, The Netherlands
4
Department of Quantitative Economics, Complutense University of Madrid, 28040 Madrid, Spain
5
Institute of Advanced Sciences, Yokohama National University, 240-8501 Yokohama, Japan
*
Author to whom correspondence should be addressed.
Academic Editor: Marc S. Paolella
Econometrics 2017, 5(1), 15; https://doi.org/10.3390/econometrics5010015
Received: 3 January 2017 / Revised: 7 March 2017 / Accepted: 16 March 2017 / Published: 20 March 2017
An early development in testing for causality (technically, Granger non-causality) in the conditional variance (or volatility) associated with financial returns was the portmanteau statistic for non-causality in the variance of Cheng and Ng (1996). A subsequent development was the Lagrange Multiplier (LM) test of non-causality in the conditional variance by Hafner and Herwartz (2006), who provided simulation results to show that their LM test was more powerful than the portmanteau statistic for sample sizes of 1000 and 4000 observations. While the LM test for causality proposed by Hafner and Herwartz (2006) is an interesting and useful development, it is nonetheless arbitrary. In particular, the specification on which the LM test is based does not rely on an underlying stochastic process, so the alternative hypothesis is also arbitrary, which can affect the power of the test. The purpose of the paper is to derive a simple test for causality in volatility that provides regularity conditions arising from the underlying stochastic process, namely a random coefficient autoregressive process, and a test for which the (quasi-) maximum likelihood estimates have valid asymptotic properties under the null hypothesis of non-causality. The simple test is intuitively appealing as it is based on an underlying stochastic process, is sympathetic to Granger’s (1969, 1988) notion of time series predictability, is easy to implement, and has a regularity condition that is not available in the LM test. View Full-Text
Keywords: random coefficient stochastic process; simple test; Granger non-causality; regularity conditions; asymptotic properties; conditional volatility random coefficient stochastic process; simple test; Granger non-causality; regularity conditions; asymptotic properties; conditional volatility
MDPI and ACS Style

Chang, C.-L.; McAleer, M. A Simple Test for Causality in Volatility. Econometrics 2017, 5, 15. https://doi.org/10.3390/econometrics5010015

AMA Style

Chang C-L, McAleer M. A Simple Test for Causality in Volatility. Econometrics. 2017; 5(1):15. https://doi.org/10.3390/econometrics5010015

Chicago/Turabian Style

Chang, Chia-Lin, and Michael McAleer. 2017. "A Simple Test for Causality in Volatility" Econometrics 5, no. 1: 15. https://doi.org/10.3390/econometrics5010015

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