Are American and European equity markets in phase? --- Frequency aspects of return and volatility spillovers

We consider three equity markets, represented by stock indices DJIA (USA), FTSE 100 (UK), and EURO STOXX 50 (euro area). Connecting these three markets together via vector autoregressive processes in index returns (or volatilities), we construct "propagation values" to measure, on a daily basis, the relative importance of a market as a volatility creator within the network, where volatility is due to either a return shock (case ret2vol) or a volatility shock (case vol2vol) in a market. A cross-wavelet analysis can reveal the joint frequency structure of pairs of the propagation value series, in particular whether or not two series tend to move in the same direction at a given frequency. This approach can replicate certain findings of traditional business cycle research, and it has the advantage of using readily available stock market data. Our findings are: (i) Frequency properties of ret2vol and vol2vol propagation values are by and large similar, namely such that the European markets are in phase, while the US market is not in phase with either European market; (ii) the band of relevant frequencies has become narrower in ret2vol propagation values from year 2000 onwards, but not in vol2vol propagation values; (iii) the financial crisis of 2007/08 and the European debt crisis since the end of 2009 have left traces in vol2vol, but not ret2vol, propagation values. This provides new insight into the time-dependent interplay of equity markets.