A Model for Daily Global Stock Market Returns

Most stock markets are open for 6-8 hours per trading day. The Asian, European and American stock markets are separated in time by time-zone differences. We propose a statistical dynamic factor model for a large number of daily returns across multiple time zones. Our model has a common global factor as well as continent factors. Under a mild fixed-signs assumption, our model is identified and has a structural interpretation. We derive the asymptotic theories of the quasi-maximum likelihood estimator (QMLE) of our model. As QMLE is inefficient by definition in this article, we outline three related estimators for practical use; Monte Carlo simulations reveal that two of them work well. We then apply our model to two real data sets - the equity portfolio returns of Japan, Europe and US and MSCI equity indices of 41 developed and emerging markets. Some new insights about linkages between different markets are drawn. Last, a Bayesian estimator (i.e., the Gibbs sampling) is also explained and suitable for estimation when the number of stocks is not too big.