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Econometrics 2017, 5(1), 15;

A Simple Test for Causality in Volatility

Department of Applied Economics, Department of Finance, National Chung Hsing University, 40227 Taichung City, Taiwan
Department of Quantitative Finance, National Tsing Hua University, 30013 Hsinchu City, Taiwan
Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam, 3062 PA Rotterdam, The Netherlands
Department of Quantitative Economics, Complutense University of Madrid, 28040 Madrid, Spain
Institute of Advanced Sciences, Yokohama National University, 240-8501 Yokohama, Japan
Author to whom correspondence should be addressed.
Academic Editor: Marc S. Paolella
Received: 3 January 2017 / Revised: 7 March 2017 / Accepted: 16 March 2017 / Published: 20 March 2017
Full-Text   |   PDF [192 KB, uploaded 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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Chang, C.-L.; McAleer, M. A Simple Test for Causality in Volatility. Econometrics 2017, 5, 15.

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