Abstract: A new causality measure of nonstationary processes with stochastic trend is proposed in this paper, which is proved to be equivalent with Hosoya's one-sided causality measure. The new measure avoids complicated cointegration analysis in the literature and two tests are discussed in detail. One is the wavelet Wald test, the other is likelihood ratio test. They work well both in numerical simulation and empirical example.

Key words: Fractionally differenced stationary process, Wavelet transform,
Causality measure, Noncausality test.