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 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 simulations results to show that their LM test was more powerful than the portmanteau statistic. 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 that 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 for which the (quasi-) maximum likelihood estimates have valid asymptotic properties. 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.

Additional Metadata
Keywords Random coefficient stochastic process, Simple test, Granger non-causality, Regularity conditions, Asymptotic properties, Conditional volatility
JEL Time-Series Models; Dynamic Quantile Regressions (jel C22), Time-Series Models; Dynamic Quantile Regressions (jel C32), Model Evaluation and Testing (jel C52), Financial Econometrics (jel C58)
Persistent URL
Series Econometric Institute Research Papers
Note For financial support, the first author wishes to thank the National Science Council, Ministry of Science and Technology, Taiwan, and the second author acknowledges the Australian Research Council and the National Science Council, Ministry of Science and Technology, Taiwan.
Chang, C-L, & McAleer, M.J. (2016). A Simple Test for Causality in Volatility (No. EI2016-40). Econometric Institute Research Papers. Retrieved from