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Juan Carlos Escanciano, Indiana U. Print
Thursday, 28 May 2009, 12:15 - 13:15

Simple Bootstrap Tests for Conditional Moment Restrictions

Juan Carlos Escanciano, Indiana University

This paper proposes consistent tests for conditional moment restrictions of stationary time series. The proposed tests are based on continuous functionals of a projected integrated conditional moment process which acknowledges that deviations in the direction of the score function cannot be differentiated from deviations within the parametric model. As a result, the new tests are expected to have better power properties than existing tests and allow for a simple multiplier-type-bootstrap approximation. Thereby extending the scope of the wild-bootstrap and related methods to general conditional moment restrictions, including quantile regressions for which wild-bootstrap methods were not available. The new tests have the following remarkable properties: (i) they do not need to choose a tuning parameter, other than the number of bootstrap replications; (ii) there is no need for re-estimating the unknown parameters in each bootstrap replication; (iii) the new tests are valid under higher order conditional moments of unknown form; and (iv) they allow for non-separable and non-smooth moment functions and any root-n consistent estimator. A Monte Carlo experiment shows that the new method presents more accurate size and higher power than subsampling procedures. In an empirical application we study the dynamics in mean and variance of the Hong Kong stock market index and we evaluate models for the Value-at-Risk of the S&P 500. These applications highlight the merits of our approach and show that the new methods have higher power than popular backtesting methods.

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