Standard Errors in Semiparametric Copula-based Univariate Time Series Models

This paper investigates the estimation of standard errors in semipametric univariate copulabased time series models. In such models, the marginal distributions are estimated with the Empirical Distribution Function (EDF), which needs to be taken into account in the computation of (correct) MSML standard errors of copula parameter estimates. Patton (2012) compares MSML standard errors to `naive' standard errors, which ignore this estimation of the marginal distribution, and attributes the difference between the naive and MSML standard errors to this naivety. We show that `naive' standard errors are not only naive in this aspect, but also ignore autocorrelation in observations and possible misspecification. We define the alternative Truly Naive standard error, which only ignores the use of the EDF, and the Doubly Naive standard error, which only ignores the use of the EDF and the autocorrelation. For three data sets and a simulation study, we find that the Truly Naive standard errors are (almost) equal to the correct MSML standard errors. We conclude that any difference between the naive and MSML standard errors cannot be attributed to estimation of the marginal distribution.