Semiparametric Bootstrap Methods for Time Series

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ABSTRACTPROPOSAL NUMBER: 0241152INSTITUTION: University of Wisconsin, MadisonNSF PROGRAM: ECONOMICSPRINCIPAL INVESTIGATOR: Hansen, BrucePROPOSAL TITLE: Semiparametric Bootstrap Methods for Time SeriesThe bootstrap is a method of statistical inference is growing in popularity in applied econometrics due to its broad applicability and success in improving the accuracy of statistical inferences. Bootstrap methods for time-series data are fundamentally different from those for random samples, as the bootstrap needs to replicate the dependence structure in the data. The theory for flexible and practical bootstrap methods for time-series is sorely lacking. A promising new bootstrap method for time-series is the Markov bootstrap (MB), which is based on nonparametric estimation of the one-step-ahead conditional distribution function, and uses this estimator to construct the bootstrap distribution. This research extends the MB method to time-series. It investigates theoretical structure of the bootstrap, leading to concrete methods of implementation. The research discusses how to construct the ergodic density of the MB and how to calculate bootstrap parameters and moments from the ergodic density. This is essential for practical implementation of the MB, as these calculations are a necessary input in its application. It also investigates the imposition of constrained on the ergodic density. This is necessary for efficient inference, as a full nonparametric estimator does not make use of the available information about the model. Furthermore, constraints must be imposed when the bootstrap is used to construct efficient confidence intervals.The accuracy of the MB will depend on the accuracy of the nonparametric estimator of the conditional distribution; accordingly the research develops methods to improve estimation efficiency. In this connection, new high order and low-bias kernel estimators explored. The improvements in density estimation lead to improved rates of asymptotic refinements for bootstrap inference. This improvement in density estimation requires theoretical investigation of the methods developed, which this research investigates. The theory and methods developed by this research will have broad impacts on bootstrap applications and will be useful to applied economists in both academic and public sectors.