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Bootstrapping two-stage quasi-maximum likelihood estimators of time series models*

This paper’s main contribution is to theoretically justify the application of bootstrap methods in multistage quasi-maximum likelihood estimation involving time series data. Two consistency results are provided: consistency of the bootstrap distribution and consistency of bootstrap variance estimators. These results justify constructing bootstrap percentile intervals and computing bootstrap standard errors using multi-step quasi-maximum likelihood estimation, avoiding the need to analytically quantify the estimation uncertainty caused by the multistage estimation process. Our results should be useful for inference in many models in finance and economics such as multivariate copula models or large multivariate GARCH models, which are often estimated in stages.