Dependences between long-run covariability and data frequencies

In order to deal with paucity of sample inference and the problem that inference critically depends on the long-run persistence of the data, Müller and Watson (2018) propose models that use low-frequency weighted averages to construct asymptotically efficient confidence intervals for long-run covariability parameters. The (A, B, c, d) model constructs these confidence intervals for a wide range of persistence patterns. The accurateness of the constructed confidence intervals using the (A, B, c, d) model is demonstrated by the simulaton section. Furthermore, this paper elaborates on Müller and Watson (2018) by measuring the performance of their models on data sets with higher frequencies on the basis of the relationship between the S&P 500 Index and the S&P 500 Futures. Further knowledge on the performance of the methods proposed by Müller and Watson (2018) can be of value to econometric and economic researchers and knowledge on the relationship between the S&P 500 Index and the S&P 500 Futures is interesting to worldwide investing market participants. It is observed that the impact of different data frequencies on the long-run covariability between the S&P 500 Index and the S&P 500 Futures does not follow a clear pattern. Furthermore, differences between sub-sample are captured by the (A;B; c; d) model considering, for example, the sharp decrease of long-run covariability between both variables after the U.S. stock market crisis in December 2018.