Granger causality in mixed frequency time series

It is a classic topic in time series econometrics to test Granger causality among multiple variables. While many Granger causality tests have been invented in the literature, they are often vulnerable to temporal aggregation which potentially generates or hides causality. Based on the growing literature of Mixed Data Sampling (MIDAS) analysis, this dissertation proposes a set of mixed frequency Granger causality tests which are robust against temporal aggregation. The mixed frequency causality tests take an explicit treatment of data sampled at different frequencies, and hence enable more accurate statistical inference than the conventional approach that aggregates all time series into the common lowest frequency.;Depending on the magnitude of the ratio of sampling frequencies, this dissertation proposes two types of mixed frequency causality tests. The first one handles a small ratio of sampling frequencies like month vs. quarter. Exploiting Ghysels' mixed frequency vector autoregressive (MF-VAR) models, we extend Dufour, Pelletier, and Renault's VAR-based causality test to the mixed frequency context. We prove that the mixed frequency approach better recovers the underlying causal patterns than the existing low frequency approach. Moreover, we demonstrate via local asymptotic power analysis and simulations that the mixed frequency test has higher power than the low frequency test in both large sample and small sample. In an empirical application on U.S. macroeconomy, we show that the mixed frequency approach and the low frequency approach produce very different causal implications, with the former yielding more intuitive results.;The second part of this dissertation deals with a relatively large ratio of sampling frequencies like month vs. year. Inspired by Sims' regression-based causality tests, we develop a new test that achieves higher power than the conventional test in both large sample and small sample. In this framework, a larger ratio of sampling frequencies is likely to improve power since our methodology circumvents parameter proliferation. We apply our test to weekly interest rate spread and quarterly GDP in the U.S. The empirical result shows that the interest rate spread used to be a valid predictor of GDP but its predictability has declined more recently.