Abstract
The Granger causality test is essential for detecting lead–lag relationships between time series. Traditionally, one uses a linear version of the test, essentially based on a linear time series regression, itself being based on autocorrelations and cross-correlations of the series. In the present paper, we employ a local Gaussian approach in an empirical investigation of lead–lag and causality relations. The study is carried out for monthly recorded financial indices for ten countries in Europe, North America, Asia and Australia. The local Gaussian approach makes it possible to examine lead–lag relations locally and separately in the tails and in the center of the return distributions of the series. It is shown that this results in a new and much more detailed picture of these relationships. Typically, the dependence is much stronger in the tails than in the center of the return distributions. It is shown that the ensuing nonlinear Granger causality tests may detect causality where traditional linear tests fail.
Highlights
We can move on to examine the lead–lag relationships between a larger selection of monthly stock return time series using the methods from earlier sections
We have carried out an empirical investigation of monthly financial indices in 10 countries from Europe, North America, Asia, and Australia
This has been done using the approach of a local Gaussian approximation that has been explored in the book by [6] and in several recent papers
Summary
The autocorrelation, partial autocorrelation, and cross-correlation functions of a pair of time series play fundamental roles in classical Box–Jenkins analysis. [2] used the same quantities in a time series regression in his derivation of a linear causality test, which subsequently was named after him as a “Granger causality” test It is well known that the returns of financial time series possess properties that make them less suitable for linear correlation-based models; see, e.g., [4] These properties are especially pronounced for daily data, and present for monthly data, which is the type of data we will analyze in this paper. Gaussian approach in an empirical study of nonlinear lead–lag relationships and Granger causality for monthly stock return data from 10 countries and compare them to traditional linear analysis.
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